TI-89 Titanium Graphing Calculator
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Getting Started Initial start-up Installing the AAA Batteries The TI-89 Titanium uses four AAA alkaline batteries and a backup silver oxide battery (SR44SW or 303). The backup battery is already installed, and the AAA batteries are provided with the product. 1. Remove the battery cover from the back of the calculator. 2. Unwrap the four AAA batteries provided with your product and insert them in the battery compartment.
Turning on your TI-89 Titanium for the first time After installing the batteries included with the calculator, press ´. The Apps desktop appears. Note: If your calculator initializes the preinstalled Apps, a progress bar will appear with the message “Installation in progress . . . Do not interrupt!” instead of the Apps desktop. To avoid losing Apps, do not remove the batteries during initialization. (You can re-install Apps from either the Product CD-ROM or education.ti.com.
• Select and edit categories of Apps. • View all of the Apps installed on your calculator. • View the full name of the highlighted App. • View and edit the time and date. • Check status line information. • View split-screen mode information. Ê Ë Ï Ì Î Í TI-89 Titanium Apps desktop Ê View full name of highlighted App. Ë View time and date. Ì Press ¸ to open highlighted App. Í Scroll down to view additional Apps. Î Check status line information.
Ï Edit categories. To return to the Apps desktop at any time, press O. The last category selected appears with the last open App highlighted. Turning off the calculator Press 2 ®. The next time you turn on the calculator, the Apps desktop appears with the same settings and memory contents retained. (If you turned off the Apps desktop, the calculator Home screen appears.) You can use either of the following keys to turn off the TI-89 Titanium.
Note: ® is the second function of the ´ key. The calculator’s Automatic Power Down™ (APD™) feature prolongs battery life by turning the calculator off automatically following several minutes of inactivity. When you turn on the calculator after APD: • The display, cursor, and any error conditions are exactly the same as before APD. • All settings and memory contents are retained. Note: APD does not occur if a calculation or program is in progress, unless the program is paused.
TI-89 Titanium keys Ê Í Ë Ì Getting Started 9
TI-89 Titanium keys Ê Function keys (ƒ– Š) open toolbar menus, access Apps, and edit categories of Apps. Ë Cursor keys (A, B, C, D) move the cursor. Ì Numeric keypad performs math and scientific functions. Í Modifier keys (2, 8, 7) add features by increasing the number of key commands. Entering special characters Use the CHAR (Character) menu and key commands to enter special characters. The CHAR menu lets you access Greek, math, international, and other special characters.
Example: Enter the right arrow symbol (→) in the Text Editor. Press Result 2G 4 Scroll down for more characters. 9 – or – Press D repeatedly to select 9:→ and press ¸ Symbol displayed at cursor location. To open the keyboard map, press 8 ”. The keyboard map appears.
To type most characters, press 8 and the corresponding key. Press N to close the map. Example: Use the keyboard map to find the “not equal to” symbol (ƒ) shortcut and enter the symbol in the Program Editor. Press Result 8” ¥Á Symbol displayed at cursor location.
Modifier keys Modifier keys add features by increasing the number of keyboard operations at your fingertips. To access a modifier function, press a modifier key and then press the key for the corresponding operation. Keys Description 2 Accesses Apps, menu options, and other operations. Second functions are printed above their corresponding keys in the same color as the 2 key. (Second) 8 (Diamond) ¤ (Shift) j (Alpha) Getting Started Accesses Apps, menu options, and other operations.
Example: Access the VAR-LINK [All] screen, where you can manage variables and Apps. Press Result 2° Function keys Use the function keys to perform the following operations: • On the Apps desktop, open Apps and select or edit Apps categories. • On the calculator Home screen, open toolbar menus to select math-related operations. • Within Apps, open toolbar menus to select App options. Numeric keypad The numeric keypad lets you enter positive and negative numbers.
To enter a number in scientific notation: 1. Type the numbers that precede the exponent. (This value can be an expression.) 2. Press ^. The exponent symbol (í) follows the numbers you entered. 3. Type the exponent as an integer with up to three digits. (As the following example shows, you can use a negative exponent.) Example: On the calculator Home screen, enter 0.00685 using scientific notation. Press Result 6¶85 ^ ?3 ¸ Other important keys Key Command Description 8# Displays the Y= Editor.
Key Command Description 8$ Displays the Window Editor. 8% Displays the Graph screen. 8& Sets parameters for the Table screen. 8' Displays the Table screen. ¥5 ¥6 ¥7 These keys let you edit entered information by performing a cut, copy, or paste operation. O Displays the Apps desktop. 8O With the Apps desktop off, displays the FLASH APPLICATIONS menu. 2a Switches between the last two chosen Apps. 2¾ Turns the custom menu on and off. 24 Converts measurement units.
Key Command Description 2¯ Displays the MEMORY screen. ½ Displays a list of commands. 2£ Recalls the contents of a variable. § Stores a value to a variable. 2G Displays the CHAR menu, which lets you select Greek letters, international accented characters, and other special characters.. 2K • In full-screen mode, displays the Apps desktop. • In split-screen mode, displays the full-screen view of the active App. • With the Apps desktop off, displays the calculator Home screen.
1. Press 3. Page 1 of the MODE dialog box appears. 2. Press „ or … to display the modes listed on Page 2 or Page 3. Note: Modes that are grayed out are available only if other required mode settings are selected. For example, the Custom Units mode listed on Page 3 is available only if the Unit System mode is set to CUSTOM.
Press Result … Changing mode settings Example: Change the Language mode setting to Spanish (Español).
Press Result Scroll down to the Language field. D Press B and then press D until 3:Español is highlighted. Note: Your menu list might vary, depending on the languages installed.
Press Result ¸ Note: The previous open App appears (in this example, the calculator Home screen). To return the Language mode setting to English, repeat the steps, selecting 1:English in the Language field. Using the Catalog to access commands Use the Catalog to access a list of TI-89 Titanium commands, including functions, instructions, and user-defined programs. Commands are listed alphabetically. Commands not beginning with a letter are found at the end of the list (&, /, +, –, etc.).
Note: Typing a letter takes you to the first command in the list starting with the same letter. Press Result ½ (displays Built-in commands) … (displays Flash Apps commands, if any) † (displays User-Defined commands, if any) Select commands from the Catalog and insert them onto the calculator Home screen entry line or paste them to other Apps, such as the Y= Editor, Text Editor, or CellSheet Apps.
Example: Insert the comDenom( command on the calculator Home screen entry line. Note: Before selecting a command, position the cursor where you want the command to appear. Pressing 2 D advances the Catalog list one page at a time. Press Result ½C 2D Then press D until the pointer is at the comDenom( function. ¸ The status line displays any required and optional parameters for the selected command. Optional parameters appear in square brackets.
Selected command Command parameters Brackets [ ] indicate optional parameters To exit the Catalog without selecting a command, press N. Calculator Home screen The calculator Home screen is the starting point for math operations, including executing instructions, evaluating expressions, and viewing results. To display the calculator Home screen, press: " You can also display the calculator Home screen from the Apps desktop by highlighting the Home icon and pressing ¸.
Ë Ê Ï Ì Î Í Ê History area lists the entry/answer pairs entered. Ë Tabs display menus for selecting lists of operations. Press ƒ, „, and so on to display menus. Ì Result of last entry is displayed here. (Note that results are not displayed on the entry line.) Í Status line shows the current state of the calculator. Î Entry line displays your current entry. Ï Your previous entry is displayed here. To return to the Apps desktop from the calculator Home screen, press O.
About the history area The history area displays up to eight entry/answer pairs, depending on the complexity and height of the expressions. When the display is filled, information scrolls off the top of the screen. Use the history area to: • Review previous entries and answers. Use the cursor keys to view entries and answers that have scrolled off the screen. • Recall or auto-paste a previous entry or answer onto the entry line to reuse or edit.
Interpreting history information on the status line Use the history indicator on the status line for information about the entry/answer pairs.
• Enter ClrHome on the calculator Home screen entry line. To delete an entry/answer pair, move the cursor to either the entry or answer, and press 0 or M. Working with Apps The TI-89 Titanium organizes Apps by category on the Apps desktop. To select a category, press a function key („ through 2 Š ). The App icons for the selected category appear on the Apps desktop. Note: If the name under an Apps desktop icon is truncated, use the cursor keys to highlight the icon.
Option Description New Creates a new file with the name typed in the field. Select an option, enter any required information, and press ¸. The App appears. Example: Create a new program using the Program Editor.
Press Result ¸ DD program1 ¸¸ The newly created program variable, program1, is saved to the Main folder.
Returning to the Apps desktop from within an App Press O. The icons for the last Apps category selected appear on the Apps desktop with the icon for the last App opened highlighted. You can also return to the Apps desktop by pressing 2 K in full-screen mode. In split-screen mode, press 2 K twice. To return to the last open App from the Apps desktop, press 2 a. Selecting an Apps category On the TI-89 Titanium, the Apps category names appear only in the F1 Menu.
Key Description 2 ˆ Graphing Customizable category. Graphing is the default. 2 ‰ Science Customizable category. Science is the default. 2 Š Organizr Customizable category. Organizr (organizer) is the default. Example: Select the All category. Press Result „ If you select an Apps category containing no Apps, a message appears to confirm that the category is empty and point you to the ƒ 1:Edit Categories menu, where you can add App shortcuts to the category.
Customizing the Apps categories The TI-89 Titanium organizes your Apps into seven categories, six of which you can customize to fit your individual needs. (The All category contains every installed App and cannot be edited.) To customize the … through 2 Š Apps categories: 1. Select ƒ 1:Edit Categories. A submenu displays the six customizable Apps category names. (The All category is not listed.) 2. Highlight an Apps category and press ¸.
Example: Replace the Social Studies category with the Business category and add the CellSheet and Finance App shortcuts.
Press Result 2™ ¤Business D © B D © B Getting Started 35
Press Result ¸ † Open Apps and split-screen status Your TI-89 Titanium lets you split the screen to view two Apps simultaneously. For example, view the Y= Editor and Graph screens simultaneously to see the list of functions and how they are graphed. Select the Split Screen mode from Page 2 of the MODE screen. The TI-89 Titanium displays the selected Apps in the split-screen view as shown. Split the screen horizontally (top-bottom) or vertically (left-right).
Top-bottom split screen To return to the Apps desktop, press O. The split-screen status appears at the top of the Apps desktop with the names of the open Apps and the portions of the screen in which each is displayed. The highlighted numeral indicates the split-screen portion where the next App you open will appear. Note: The Apps desktop always appears in the full-screen view. Split-screen status (highlight indicates the portion where the next App selected will open.
More information is available about using split screens. (For more information, see the electronic Split Screens chapter.) Checking status information Look to the status line, located at the bottom of the screen, for information about the current state of your TI-89 Titanium. Ê Ë Ì Í Î Ï Ð Ñ Indicator Meaning Ê Current folder Name of the selected folder (MAIN is the default folder.) Ë Modifier key Selected modifier key (2, 8, 7), if any.
Indicator Meaning Ð Entry/Answer pairs 22/30–Number of entry/answer pairs (default is 30, maximum is 99) in the history area of the calculator Home screen. Ñ Replace batteries Displayed when batteries are low (BATT). If BATT is highlighted with a black background, change the batteries as soon as possible ( ).
Press Result … DDBC ¸¸ Note: The previous open App appears (in this example, the calculator Home screen). To turn on the Apps desktop, repeat the procedure, selecting ON in the Apps Desktop mode field. To return to the Apps desktop from the calculator Home screen, press O. Using the clock Use the CLOCK dialog box to set the time and date, select the clock display format, and turn the clock off and on.
The clock is turned on by default. If you turn off the clock, all Clock dialog box options except Clock ON/OFF are grayed out. 6 indicates you can scroll down for more options) Displaying the CLOCK dialog box 1. Use the cursor keys to highlight the Clock icon on the Apps desktop. 2. Press ¸. The CLOCK dialog box appears with the Time Format field highlighted.
6. If the time format is 24 hours, proceed to step 9. — or — If the time format is 12 hours, press D to highlight the AM/PM field. 7. Press B to open the list of AM/PM options. 8. Press C or D to highlight an AM/PM option, then press ¸. The selected AM/PM option appears. 9. Set the date (for procedures, see Setting the date). — or — To save your settings and exit, press ¸. The time is updated in the top right corner of the Apps desktop. Setting the date 1.
9. Type the day, then press ¸ ¸ to save your settings and exit. The date is updated in the top right corner of the Apps desktop. Example: Set the time and date to 19/10/02 (October 19, 2002) at 1:30 p.m.
Press Result 30D BD ¸D Getting Started 44
Press Result BD ¸D 2002 Getting Started 45
Press Result DB Scroll down to October and press ¸ D19 Getting Started 46
Press ¸¸ Result Revised time and date Turning off the clock From the Apps desktop, open the CLOCK dialog box and select OFF in the Clock field. Example: Turn off the clock.
Press Result ¸ Scroll down to the Clock field. BC¸ ¸ Clock off To turn on the clock, repeat the procedure, selecting ON in the Clock field. Remember to reset the time and date.
Using menus To select most TI-89 Titanium menus, press the function keys corresponding to the toolbars at the top of the calculator Home screen and most App screens. Select other menus using key commands. Toolbar menus The starting point for TI-89 Titanium math operations, the calculator Home screen displays toolbar menus that let you choose math-related options. Toolbar menus also appear at the top of most App screens. These menus list common functions of the active App.
Press To display O APPLICATIONS menu. Lists the installed Apps. (Menu is available only when the Apps desktop is turned off; Apps are normally accessed from the Apps desktop.) 8O FLASH APPLICATIONS menu. Lists the installed Flash Apps. (Menu is available only when Apps desktop is turned off; Flash Apps are normally accessed from the Apps desktop.) Selecting menu options • Press the number or letter to the left of the option you want to select.
Example: Select factor( from the Algebra menu on the calculator Home screen. Press Result Press: " – or – From the Apps desktop, use the cursor keys to highlight and press ¸ „ 6 indicates Algebra menu will open when you press „.
Selecting submenu options A small arrow symbol (ú) to the right of a menu option indicates that selecting the option will open a submenu. $ points to additional options. Example: Select ord( from the MATH menu on the calculator Home screen.
Press Result D – or – CCB B – or – C¸ Using dialog boxes An ellipsis (…) at the end of a menu option indicates that choosing the option will open a dialog box. Select the option and press ¸.
Example: Open the SAVE COPY AS dialog box from the Window Editor. Press Result O Use the cursor keys to highlight and press ¸ ƒ 2 – or – D¸ Press B to display a list of folders. Type the name of the variable.
Note: Pressing the 8 S key shortcut also opens the SAVE COPY AS dialog box in most Apps. Canceling a menu To cancel a menu without making a selection, press N. Moving among toolbar menus To move among the toolbar menus without selecting a menu option: • Press the function key (ƒ through Š) of a toolbar menu. • Press a function key, then press B or A to move from one toolbar menu to the next. Press B from the last menu to move to the first menu. Press A to move from the first menu to the last menu.
The custom menu replaces the standard toolbar menu on the calculator Home screen. (For details on creating a custom menu, see the electronic Programming chapter.) More information is available about custom menus. (See the electronic Operating the Calculator chapter.) Example: Turn on and turn off the custom menu from the calculator Home screen. Press Result 2F Default custom menu 2F Normal toolbar menu Example: Restore the default custom menu.
Note: Restoring the default custom menu erases the previous custom menu. If you created the previous custom menu with a program, you can run the program again to reuse the menu.
Press Result ¸ Opening Apps with the Apps desktop turned off If you turn off the Apps desktop, use the APPLICATIONS menu to open Apps. To open the APPLICATIONS menu with the Apps desktop off, press O. Note: If you press O with the Apps desktop turned on, the Apps desktop will appear instead of the APPLICATIONS menu. Example: With the Apps desktop turned off, open the Window Editor from the APPLICATIONS menu.
Press Result 3 – or – DD¸ To access Apps not listed on the APPLICATIONS menu, select 1:FlashApps. Using split screens The TI-89 Titanium lets you split the screen to show two Apps at the same time. For example, display both the Y= Editor and Graph screens to compare the list of functions and how they are graphed. Setting split-screen mode You can split the screen either top to bottom or left to right from the MODE dialog box. The split-screen setting stays in effect until you change it. 1.
Example: Set split-screen mode to TOP-BOTTOM.
Press Result ¸ ¸ Setting the initial Apps for split screen After you select either TOP-BOTTOM or LEFT-RIGHT split-screen mode, additional mode settings become available.
Mode Description Split 2 App Lets you specify the App displayed in the bottom or right portion of the split screen. Works together with Split 1 App, which lets you specify the App displayed in the top or left portion of the split screen. Number of Graphs Lets you set up and display two independent graphs. To set the initial App for each split-screen portion: 1. Select the Split 1 App mode setting and press B to display a menu of available Apps. (See “Setting split-screen mode” on page 59.) 2.
Press Result 2 DB 4 ¸ Getting Started 63
If you set Split 1 App and Split 2 App to the same nongraphing App or to the same graphing App with Number of Graphs set to 1, the TI-89 Titanium exits split-screen mode and displays the App in full-screen mode. Selecting the active App In split-screen mode, only one App can be active at a time. • To switch between active Apps, press 2 a. • To open a third App, press O and select the App. This App replaces the active split-screen App.
Managing Apps and operating system (OS) versions Using the TI-89 Titanium connectivity features, you can download Apps from: • The TI Educational & Productivity Solutions (E&PS) Web site at: education.ti.com/latest • The CD-ROM included with your TI-89 Titanium. • A compatible graphing calculator. Adding Apps to your TI-89 Titanium is like loading software on a computer. All you need is TI Connect software and the USB computer cable that came with your TI-89 Titanium.
To display the ABOUT screen, press ƒ 3:About from the Apps desktop. The ABOUT screen displays the following information about your TI-89 Titanium: Ê Ë Î Í Ì Ê OS version Ë Hardware version Ì Unit ID (required to obtain certificates for installing purchased Apps). Similar to a serial number. Write this number down and keep it in a safe place in case the calculator is ever lost or stolen. Í Apps certificate revision number (Cert. Rev.) Î Product identifier (Product ID). Similar to a model number.
Deleting an Application Deleting an application removes it from the TI-89 Titanium and increases space for other applications. Before deleting an application, consider storing it on a computer for reinstallation later. 1. Quit the application. 2. Press 2 ° to display the VAR-LINK (All) screen. 3. Press 2 ‰ to display the list of installed applications. 4. Select the application you want to delete by pressing †. (Press † again to deselect.) 5. Press ƒ 1:Delete.
To connect your calculator to another calculator – Use the USB unit-to-unit cable or an I/O unit-to-unit cable to connect the TI-89 Titanium to a compatible graphing calculator or peripheral device, such as a TI-89 or TI-92 Plus graphing calculator or the CBL 2™ and CBR™ systems. To show your calculator’s display to the classroom – Use the accessory port to connect the TI-Presenter™ video adapter to the teacher model of the TI-89 Titanium.
USB port I/O port Accessory port TI-89 Titanium ports (teacher model) Batteries The TI-89 Titanium uses four AAA alkaline batteries and a backup silver oxide battery (SR44SW or 303). The backup battery is already installed, and the AAA batteries are provided with your product. Important OS download information New batteries should be installed before beginning an OS download. When in OS download mode, the APD feature does not function.
You can also transfer the OS to another TI-89 Titanium using a USB unit-to-unit cable . If you accidentally interrupt the transfer before it is complete, you will need to reinstall the OS via a computer. Again, remember to install new batteries before downloading. Please contact Texas Instruments as described in Service & Support Information, if you experience a problem. Battery Precautions Take these precautions when replacing batteries: • Do not leave batteries within the reach of children.
3. Replace the battery cover on the calculator. The cover should snap into place. Replacing the AAA (alkaline) batteries As the batteries lose power, the display begins to dim, especially during calculations. If you find yourself increasing the contrast frequently, replace the AAA alkaline batteries. The status line also gives battery information. Indicator Meaning Batteries are low. Replace batteries as soon as possible.
Replacing the backup (silver oxide) battery 1. To replace the silver oxide backup battery, remove the battery cover and unscrew the tiny screw holding the BACK UP BATTERY cover in place. 2. Remove the old battery and install a new SR44SW or 303 battery, positive (+) side up. Replace the cover and the screw.
Previews Performing Computations This section provides several examples for you to perform from the Calculator Home screen that demonstrate some of the computational features of the TI-89 Titanium. The history area in each screen was cleared by pressing ƒ and selecting 8:Clear Home, before performing each example, to illustrate only the results of the example’s keystrokes. Showing Computations Steps and keystrokes Display Compute sin(p/4) and display the result in symbolic and numeric format.
Finding the Factorial of Numbers Steps and keystrokes Display Compute the factorial of several numbers to see how the TI-89 Titanium handles very large integers. To get the factorial operator (!), press 2 I, select 7:Probability, and then select 1:!. Press 5 2 I 7 1 ¸ 20 2 I 7 1 ¸ 30 2 I 7 1 ¸ Expanding Complex Numbers Steps and keystrokes Display Compute (3+5i) 3 to see how the TI-89 Titanium handles computations involving complex numbers.
Finding Prime Factors Steps and keystrokes Display Compute the factors of the rational number 2634492. You can enter “factor” on the entry line by typing FACTOR on the keyboard, or by pressing „ and selecting 2:factor(. Press „ 2 2634492 d ¸ (Optional) Enter other numbers on your own. Finding Roots Steps and keystrokes Display Find the root of the expression (x,y). You can enter “root” on the entry line by typing ROOT on the keyboard, or by pressing 8 9.
Expanding Expressions Steps and keystrokes Display Expand the expression (xN5) 3. You can enter “expand” on the entry line by typing EXPAND on the keyboard, or by pressing „ and selecting 3:expand(. Press „ 3 c X | 5 d Z 3 d ¸ (Optional) Enter other expressions on your own. Reducing Expressions Steps and keystrokes Display Reduce the expression (x 2N2xN5)/(xN1) to its simplest form.
Factoring Polynomials Steps and keystrokes Display Factor the polynomial (x 2N5) with respect to x. You can enter “factor” on the entry line by typing FACTOR on the keyboard or by pressing „ and selecting 2:factor(. Press „ 2 X Z 2 | 5 b X d ¸ Solving Equations Steps and keystrokes Display Solve the equation x 2N2xN6=2 with respect to x. You can enter “solve(” on the entry line by selecting “solve(” from the Catalog menu, by typing SOLVE( on the keyboard, or by pressing „ and selecting 1:solve(.
Solving Equations with a Domain Constraint Steps and keystrokes Display Solve the equation x 2N2xN6=2 with respect to x where x is greater than zero. The “with” (I) operator provides domain constraint. Press „ 1 X Z 2 | 2 X | 6 Á 2 b X d Í X2Ã0¸ Solving Inequalities Steps and keystrokes Display Solve the inequality (x2>1,x) with respect to x.
Finding the Derivative of Functions Steps and keystrokes Display Find the derivative of (xNy) 3/(x+y)2 with respect to x. This example illustrates using the calculus differentiation function and how the function is displayed in “pretty print” in the history area. Press 2 = c X | Y d Z 3 e c X « Y dZ2bXd¸ Finding Implicit Derivatives Steps and keystrokes Display Compute implicit derivatives for equations in two variables in which one variable is defined implicitly in terms of another.
Finding the Integral of Functions Steps and keystrokes Display Find the integral of x…sin(x) with respect to x. This example illustrates using the calculus integration function. Press 2 < X p 2 W X d b X d ¸ Solving Problems Involving Vectors Steps and keystrokes Display 1. Input a row or column of vectors. Press 2 g ? 6 b 0 b 0 2 h § jd ¸2 g 4 b 0 b 2 2 h §ja ¸2 g ? 1 b 2 b 1 2 h §jb ¸2 g 7 b 6 b 5 2 h §jc ¸ 2.
Log to Any Base Steps and keystrokes Display Find log (x,b). You can enter “log” on the entry line by typing LOG on the keyboard, or by pressing 8 7. Press 8 7 X , j b d ¸ Converting Angle Measures Steps and keystrokes Display 1. Display the MODE dialog box. For Angle mode select DEGREE. Convert 345 degrees to Gradian angle measure. You can enter “ úGrad ” on the entry line by selecting “ úGrad ” from the Catalog menu, or from the Math menu by pressing 2 I and selecting 2:angle, A:úGrad.
Steps and keystrokes Display 2. Convert 345 degrees to Radian angle measure. You can enter “ úRad ” on the entry line by selecting “ úRad ” from the Catalog menu, or from the Math menu by pressing 2 I and selecting 2:angle, B:úRad. Press 3 D D D B 2 ¸ 345 2 v2I2 jB ¸ Note: You can also use ó,ô, or G to override the angle mode setting temporarily. Symbolic Manipulation Solve the system of equations 2x N 3y = 4 and Lx + 7y = L12. Solve the first equation so that x is expressed in terms of y.
equation, and solve for the value of y. Then substitute the y value back into the first equation to solve for the value of x. Steps and keystrokes Display 1. Display the Home screen and clear the entry line. Solve the equation 2x N 3y = 4 for x. „ 1 selects solve( from the Algebra menu. You can also type solve( directly from the keyboard or select it from the Catalog. Press " M M „ 1 2 X | 3 Y Á4bXd¸ 2. Begin to solve the equation Lx + 7y = L12 for y, but do not press ¸ yet.
Steps and keystrokes Display 4. Highlight the equation for x in the history area. Press C C C 5. Auto-paste the highlighted expression to the entry line. Then substitute the value of y that was calculated from the second equation. Press ¸ Í C ¸ ¸ The solution is: x = L8/11 and y = L20/11 This example is a demonstration of symbolic manipulation. A one-step function is available for solving systems of equations.
acceleration due to gravity, which is a constant named _g). Convert the result from newtons to kilograms of force. Steps and keystrokes Display 1. Display the MODE dialog box, Page 3. For Unit System mode, select SI for the metric system of measurements. Results are displayed according to these default units. Press 3 … B 1 ¸ 2. Create an acceleration unit for meters/second 2 named _ms2. The UNITS dialog box lets you select units from an alphabetical list of categories.
Steps and keystrokes Display 3. Calculate the force when m = 5 kilograms (_kg) and a = 20 meters/second 2 (_ms2). If you know the abbreviation for a unit, you can type it from the keyboard. Press 5 8 5 2 ™ KG j p 20 8 5 2 ™ MS j 2 ¸ 4. Using the same m, calculate the force for an acceleration due to gravity (the constant _g). For _g, you can use the pre-defined constant available from the UNITS dialog box or you can type _g. Press 5 8 5 2 ™ KG j p 2 ÀBjG¸¸ 5. Convert to kilograms of force (_kgf).
learn how to enter a function, produce a graph of the function, trace a curve, find a minimum point, and transfer the minimum coordinates to the Home screen. Explore the graphing capabilities of the TI-89 Titanium by graphing the function y=(|x2N3|N10)/2. Steps and keystrokes Display 1. Display the Y= Editor. Press 8 # entry line 2. Enter the function (abs(x2N3)N10)/2. The screen shot shows the “pretty print” display at y1=. Press c ½ A ¸ X Z 2 | 3 d |10de2¸ 3. Display the graph of the function.
Steps and keystrokes Display 4. Turn on Trace. The tracing cursor, and the x and y coordinates are displayed. Press … tracing cursor 5. Open the MATH menu and select 3:Minimum. Press ‡ D D ¸ 6. Set the lower bound. Press B (right cursor) to move the tracing cursor until the lower bound for x is just to the left of the minimum node before pressing ¸ the second time. Press B ... B ¸ 7. Set the upper bound.
Steps and keystrokes Display 8. Find the minimum point on the graph between the lower and upper bounds. Press ¸ minimum point minimum coordinates 9. Transfer the result to the Home screen, and then display the Home screen. Press 8 ? " Basic Function Graphing II Graph a circle of radius 5, centered on the origin of the coordinate system. View the circle using the standard viewing window (ZoomStd). Then use ZoomSqr to adjust the viewing window. Steps and keystrokes Display 1.
Steps and keystrokes 2. Display the Home screen. Then store the radius, 5, in variable r. Display 5!r Press " 5 9 j R ¸ 3. Display and clear the Y= Editor. Then define y1(x) = a circle. ( r 2 – x 2 ) , the top half of In function graphing, you must define separate functions for the top and bottom halves of a circle. Press 8 # , 8 ¸ ¸ 2 ] jRZ2|XZ2d¸ 4. Define y2(x) = – r 2 – x 2 , the function for the bottom half of the circle.
Steps and keystrokes Display 5. Select the ZoomStd viewing window, which automatically graphs the functions. In the standard viewing window, both the x and y axes range from L10 to 10. However, this range is spread over a longer distance along the x axis than the y axis. Therefore, the circle appears as an ellipse. Notice slight gap between top and bottom halves. Press „ 6 6. Select ZoomSqr. ZoomSqr increases the range along the x axis so that circles and squares are shown in correct proportion.
Basic Function Graphing III Use the “Detect Discontinuities” graph format to eliminate faux asymptotes and connections in a jump discontinuity. Steps and keystrokes Display 1. Display the MODE dialog box. For Graph mode, select FUNCTION. For Angle mode, select RADIAN. Press 3 B 1 D D D B 1 ¸ 2. Open the Y= Editor and enter y1(x)=1/(x1). Press 8 # 1 e c X | 1 d ¸ 3.
Steps and keystrokes Display 4. Execute the Graph command, which automatically displays the Graph screen. Observe the “faux” asymptotes contained in the graph. Press 8 %q 5. Display the Graph Formats dialog box and set “Detect Discontinuities” to ON. Note: The second item on the Graph Format dialog is greyed out, which means the graph order is set to sequential “Seq”. Press 8 Í D D D D D D B 2 ¸ 6. Execute the Graph command, which automatically displays the Graph screen.
Parametric Graphing Graph the parametric equations describing the path of a ball kicked at an angle (q) of 60¡ with an initial velocity (v 0) of 15 meters/sec. The gravity constant g = 9.8 meters/sec 2. Ignoring air resistance and other drag forces, what is the maximum height of the ball and when does it hit the ground? Steps and keystrokes Display 1. Display the MODE dialog box. For Graph mode, select PARAMETRIC. Press 3 B 2 ¸ 2. Display and clear the Y= Editor.
Steps and keystrokes Display 3. Define the vertical component yt1(t) = v 0t sin q N (g/2)t 2. Enter values for v 0, q, and g. Press ¸ 15T p 2 W 60 2 “ d | c 9.8 e 2 d T Z 2 ¸ 4. Display the Window Editor. Enter Window variables appropriate for this example. You can press either D or ¸ to enter a value and move to the next variable. Press 8 $ 0 D 3 D .02 D ? 2 D 25 D 5 D ? 2 D 10 D 5 5. Graph the parametric equations to model the path of the ball. Press 8 % 6. Select Trace.
Polar Graphing The graph of the polar equation r1(q) = A sin Bq forms the shape of a rose. Graph the rose for A=8 and B=2.5. Then explore the appearance of the rose for other values of A and B. Steps and keystrokes Display 1. Display the MODE dialog box. For Graph mode, select POLAR. For Angle mode, select RADIAN. Press 3 B 3 D D D B 1 ¸ 2. Display and clear the Y= Editor. Then define the polar equation r1(q) = A sin Bq. Enter 8 and 2.5 for A and B, respectively. Press 8 # , 8 ¸ ¸ 8 2 W 2.
Steps and keystrokes Display 3. Select the ZoomStd viewing window, which graphs the equation. • The graph shows only five rose petals. - • In the standard viewing window, the Window variable qmax = 2p. The remaining petals have q values greater than 2p. The rose does not appear symmetrical. - Both the x an y axes range from L10 to 10. However, this range is spread over a longer distance along the x axis than the y axis. Press „ 6 4. Display the Window Editor, and change qmax to 4p.
Steps and keystrokes Display 5. Select ZoomSqr, which regraphs the equation. ZoomSqr increases the range along the x axis so that the graph is shown in correct proportion. Press „ 5 You can change values for A and B as necessary and regraph the equation. Sequence Graphing A small forest contains 4000 trees. Each year, 20% of the trees will be harvested (with 80% remaining) and 1000 new trees will be planted. Using a sequence, calculate the number of trees in the forest at the end of each year.
Steps and keystrokes Display 1. Display the MODE dialog box. For Graph mode, select SEQUENCE. Press 3 B 4 ¸ 2. Display and clear the Y= Editor. Then define the sequence as u1(n) = iPart(.8…u1(nN1)+1000). Use iPart to take the integer part of the result. No fractional trees are harvested. To access iPart(, you can use 2 I, simply type it, or select it from the CATALOG. Press 8 # , 8 ¸ ¸ 2 I 1 4 . 8 j U1 c j N | 1 d « 1000 d ¸ 3. Define ui1 as the initial value that will be used as the first term.
Steps and keystrokes Display 5. Set the x and y Window variables to appropriate values for this example. Press 0 D 50 D 10 D 0 D 6000 D 1000 6. Display the Graph screen. Press 8 % 7. Select Trace. Move the cursor to trace year by year. How many years (nc) does it take the number of trees (yc) to stabilize? Trace begins at nc=0. nc is the number of years. xc = nc since n is plotted on the x axis. yc = u1(n), the number of trees at year n. By default, sequences use the Square display style.
3D Graphing Graph the 3D equation z(x,y) = (x3y N y3x) / 390. Animate the graph by using the cursor to interactively change the eye Window variable values that control your viewing angle. Then view the graph in different graph format styles. Steps and keystrokes Display 1. Display the MODE dialog box. For Graph mode, select 3D. Press 3 B 5 ¸ 2. Display and clear the Y= Editor. Then define the 3D equation z1(x,y) = (x3y N y3x) / 390. Notice that implied multiplication is used in the keystrokes.
Steps and keystrokes Display 4. Select the ZoomStd viewing cube, which automatically graphs the equation. As the equation is evaluated (before it is graphed), “evaluation percentages” are shown in the upper-left part of the screen. Press „ 6 Note: If you have already used 3D graphing, the graph may be shown in expanded view. When you animate the graph, the screen returns to normal view automatically. (Except for animation, you can do the same things in normal and expanded view.
Steps and keystrokes Display 6. Return the graph to its initial orientation. Then move the viewing angle along the “viewing orbit” around the graph. Press 0 (zero, not the letter O) A A A 7. View the graph along the x axis, the y axis, and then the z axis. Press X This graph has the same shape along the y axis and x axis. Press Y Press Z 8. Return to the initial orientation.
Steps and keystrokes Display 9. Display the graph in different graph format styles.
Note: You can also display the graph as an implicit plot by using the GRAPH FORMATS dialog box (8 Í). If you press Í to switch between styles, the implicit plot is not displayed. Differential Equation Graphing Graph the solution to the logistic 1st-order differential equation y' = .001y…(100Ny). Start by drawing only the slope field. Then enter initial conditions in the Y= Editor and interactively from the Graph screen. Steps and keystrokes Display 1. Display the MODE dialog box.
Steps and keystrokes Display 2. Display and clear the Y= Editor. Then define the 1st-order differential equation: y1'(t)=.001y1…(100Ny1) Press p to enter the … shown above. Do not use implied multiplication between the variable and parentheses. If you do, it is treated as a function call. Leave the initial condition yi1 blank. Note: With y1' selected, the device will graph the y1 solution curve, not the derivative y1'. Press 8 # , 8 ¸ ¸ .001 Y1 p c 100 | Y1 d ¸ 3. Display the GRAPH FORMATS dialog box.
Steps and keystrokes Display 4. Display the Window Editor, and set the Window variables as shown to the right. Press 8 $ 0 D 10 D .1 D 0 D ? 10 D 110 D 10 D ? 10 D 120 D 10 D 0 D .001 D 20 5. Display the Graph screen. Because you did not specify an initial condition, only the slope field is drawn (as specified by Fields=SLPFLD in the GRAPH FORMATS dialog box). Press 8 % 6. Return to the Y= Editor and enter an initial condition: yi1=10 Press 8 # ¸ 10 ¸ 7. Return to the Graph screen.
Steps and keystrokes Display 8. Return to the Y= Editor and change yi1 to enter two initial conditions as a list: yi1={10,20} Press 8 # C ¸ 2 [ 10 b 20 2\¸ 9. Return to the Graph screen.
Steps and keystrokes Display 10. To select an initial condition interactively, press: 2Š When prompted, enter t=40 and y1=45. When selecting an initial condition interactively, you can specify a value for t other than the t0 value entered in the Y= Editor or Window Editor. Instead of entering t and y1 after pressing 2Š you can move the cursor to a point on the screen and then press ¸. You can use … to trace curves for initial conditions specified in the Y= Editor.
Additional Graphing Topics From the Home screen, graph the piecewise defined function: y = Lx when x < 0 and y = 5 cos(x) when x ‚ 0. Draw a horizontal line across the top of the cosine curve. Then save a picture of the displayed graph. Steps and keystrokes Display 1. Display the MODE dialog box. For Graph mode, select FUNCTION. For Angle mode, select RADIAN. Press 3 B 1 D D D B 1 ¸ 2. Display the Home screen. Use the Graph command and the when function to specify the piecewise defined function.
Steps and keystrokes Display 4. Draw a horizontal line across the top of the cosine curve. The calculator remains in “horizontal” mode until you select a different operation or press N. Press 2 ‰ 5 C (until the line is positioned) ¸ 5. Save a picture of the graph. Use PIC1 as the variable name for the picture. Be sure to set Type = Picture. By default, it is set to GDB. Press , 2 B 2 D D PIC j 1 ¸ ¸ 6. Clear the drawn horizontal line. You can also press † to regraph.
Steps and keystrokes Display 7. Open the saved picture variable to redisplay the graph with the line. Be sure to set Type = Picture. By default, it is set to GDB. Press , 1 B 2 (if not already shown, also set Variable = pic1) ¸ Tables Evaluate the function y=x 3N2x at each integer between M10 and 10. How many sign changes are there, and where do they occur? Steps and keystrokes Display 1. Display the MODE dialog box. For the Graph mode, select FUNCTION.
Steps and keystrokes Display 2. Display and clear the Y= Editor. Then define y1(x) = x 3 N 2x. Press 8 # , 8 ¸ ¸ X Z 3 | 2X¸ 3. Set the table parameters to: tblStart = M10 @tbl = 1 Graph < - > Table = OFF Independent = AUTO Press 8 & ? 10 D 1 D B 1 D B 1 ¸ 4. Display the Table screen. Press 8 ' 5. Scroll through the table. Notice that y1 changes sign at x = M1, 1, and 2. To scroll one page at a time, use 2 D and 2 C. Press D and C as necessary.
Steps and keystrokes Display 6. Zoom in on the sign change between x = L2 and x = L1 by changing the table parameters to: tblStart = L2 @tbl = .1 Press „ ? 2 D .1 ¸ ¸ Split Screens Split the screen to show the Y= Editor and the Graph screen. Explore the behavior of a polynomial as its coefficients change. Steps and keystrokes Display 1. Display the MODE dialog box. For Graph, select FUNCTION. For Split Screen, select LEFT-RIGHT. For Split 1 App, select Y= Editor. For Split 2 App, select Graph.
Steps and keystrokes Display 2. Clear the Y= Editor and turn off any stat data plots. Define y1(x) = .1x 3N2x+6. A thick border around the Y= Editor indicates it is active. When active, its entry line goes all the way across the display. Press , 8 ¸ ‡ 5 ¸ .1 X Z 3 | 2X«6¸ 3. Select the ZoomStd viewing window, which switches to the Graph screen and graphs the function. The thick border is now around the Graph screen. Press „ 6 4. Switch to the Y= Editor and edit y1(x) to change .1x 3 to .5x3.
Steps and keystrokes Display 5. Switch to the Graph screen, which regraphs the edited function. The thick border is around the Graph screen. Press 2 a 6. Switch to the Y= Editor and open the Window Editor in its place. Press 2 a 8 $ 7. Open the Home screen and then exit to a full-sized Home screen.
Data/Matrix Editor Use the Data/Matrix Editor to create a one-column list variable. Then add a second column of information. Notice that the list variable (which can have only one column) is automatically converted into a data variable (which can have multiple columns). Steps and keystrokes Display 1. Use O to display the Data/Matrix Editor. Create a new list variable named TEMP. Press 3 B 3 D D TEMP ¸ ¸ 2. Enter a column of numbers.
Steps and keystrokes Display 3. Move to column 2, and define its column header so that it is twice the value of column 1. DATA is shown in the upper-left corner to indicate that the list variable was converted to a data variable. Press B † 2 p j C 1 ¸ Œ means the cell is in a defined column. 4. Move to the column 2 header cell to show its definition in the entry line. When the cursor is on the header cell, you do not need to press † to define it. Simply begin typing the expression. Press 2 C C 5.
Statistics and Data Plots Based on a sample of seven cities, enter data that relates population to the number of buildings with more than 12 stories. Using Median-Median and linear regression calculations, find and plot equations to fit the data. For each regression equation, predict how many buildings of more than 12 stories you would expect in a city of 300,000 people. Steps and keystrokes Display 1. Display the MODE dialog box. For Graph mode, select FUNCTION. Press 3 B 1 ¸ 2.
Steps and keystrokes Display 3. Using the sample data below, enter the population in column 1. Pop. (in 1000s) 150 500 800 250 500 750 950 Bldgs > 12 stories 4 31 42 9 20 55 73 Press 150 ¸ 500 ¸ 800 ¸ 250 ¸ 500 ¸ 750 ¸ 950 ¸ 4. Move the cursor to row 1 in column 2 (r1c2). Then enter the corresponding number of buildings. 8 C moves the cursor to the top of the page. After typing data for a cell, you can press ¸ or D to enter the data and move the cursor down one cell.
Steps and keystrokes Display 5. Move the cursor to row 1 in column 1 (r1c1). Sort the data in ascending order of population. This sorts column 1 and then adjusts all other columns so that they retain the same order as column 1. This is critical for maintaining the relationships between columns of data. To sort column 1, the cursor can be anywhere in column 1. This example has you press 8C so that you can see the first four rows. Press A 8 C 2 ˆ 4 6. Display the Calculate dialog box.
Steps and keystrokes Display 8. Close the STAT VARS screen. The Data/Matrix Editor displays. Press ¸ 9. Display the Calculate dialog box. Set: Calculation Type = LinReg x = C1 y = C2 Store RegEQ to = y2(x) Press ‡ B 5 D D D B D ¸ 10. Perform the calculation to display the LinReg regression equation. This equation is stored in y2(x). Press ¸ 11. Close the STAT VARS screen. The Data/Matrix Editor displays. Press ¸ 12. Display the Plot Setup screen. Plot 1 is highlighted by default.
Steps and keystrokes Display 13. Define Plot 1 as: Plot Type = Scatter Mark = Box x = C1 y = C2 Notice the similarities between this and the Calculate dialog box. Press , B 1 D B 1 D C j 1 D j C2 14. Save the plot definition and return to the Plot Setup screen. Notice the shorthand notation for Plot 1’s definition.
Steps and keystrokes Display 15. Display the Y= Editor. For y1(x), the MedMed regression equation, set the display style to Dot. Note: Depending on the previous contents of your Y= Editor, you may need to move the cursor to y1. PLOTS 1 at the top of the screen means that Plot 1 is selected. Notice that y1(x) and y2(x) were selected when the regression equations were stored. Press 8 # 2 ˆ 2 16. Scroll up to highlight Plot 1. The displayed shorthand definition is the same as on the Plot Setup screen.
Steps and keystrokes Display 18. Return to the current session of the Data/Matrix Editor. Press O D ¸ ¸ 19. Enter a title for column 3. Define column 3’s header as the values predicted by the MedMed line. To enter a title, the cursor must highlight the title cell at the very top of the column. † lets you define a header from anywhere in a column. When the cursor is on a header cell, pressing † is not required. Press B B C C 2 ™ MED j ¸ † Y1 c j C1 d ¸ 20. Enter a title for column 4.
Steps and keystrokes Display 22. Enter a title for column 6. Define column 6’s header as the residuals for LinReg. Press B C 2 ™ RESID j ¸ † j C2 | j C5 ¸ 23. Display the Plot Setup screen and deselect Plot 1. Press „ † 24. Highlight Plot 2 and define it as: Plot Type = Scatter Mark = Box x = C1 y = C4 (MedMed residuals) Press D , D D C j 1 D j C4 ¸¸ 25.
Steps and keystrokes Display 26. Display the Y= Editor and turn all the y(x) functions off. From ‡, select 3:Functions Off, not 1:All Off. Plots 2 and 3 are still selected. Press 8 # ‡ 3 27. Use ZoomData to graph the residuals. › marks the MedMed residuals; + marks the LinReg residuals. Press „ 9 28. Display the Home screen. Press " 29. Use the MedMed (y1(x)) and LinReg (y2(x)) regression equations to calculate values for x = 300 (300,000 population).
Programming Write a program that prompts the user to enter an integer, sums all integers from 1 to the entered integer, and displays the result. Steps and keystrokes Display 1. Use O to display the Program Editor. Create a new program. Press 3 2. Type PROG1 (with no spaces) as the name of the new program variable. Press D D PROG j 1 3. Display the “template” for a new program. The program name, Prgm, and EndPrgm are shown automatically.
Steps and keystrokes Display 4. Type the following program lines. Request "Enter an integer",n Displays a dialog box that prompts “Enter an integer”, waits for the user to enter a value, and stores it (as a string) to variable n. expr(n)!n Converts the string to a numeric expression. 0!temp Creates a variable named temp and initializes it to 0. For i,1,n,1 Starts a For loop based on variable i. First time through the loop, i = 1. At end of loop, i is incremented by 1. Loop continues until i > n.
Steps and keystrokes 5. Go to the Home screen. Enter the program name, followed by a set of parentheses. Display prog1() You must include ( ) even when there are no arguments for the program. The program displays a dialog box with the prompt specified in the program. Press " 2 ™ PROG j 1 c d¸ 6. Type 5 in the displayed dialog box. Press 5 7. Continue with the program. The Disp command displays the result on the Program I/O screen. The result is the sum of the integers from 1 through 5.
Steps and keystrokes Display 8. Leave the Program I/O screen and return to the Home screen. You can also press N, 2 K, or " to return to the Home screen. Press ‡ Text Operations Start a new Text Editor session. Then practice using the Text Editor by typing whatever text you want. As you type, practice moving the text cursor and correcting any typos you may enter. Steps and keystrokes Display 1. Start a new session of the Text Editor. Press 3 2.
Steps and keystrokes Display 3. Type some sample text. • To type a single uppercase letter, press 7 and then the letter. - To type a space, press j (alpha function of the ? key). To type a period, press j to turn alpha-lock off, press ¶, and then press 2 ™ to turn alpha-lock on again. Practice editing your text by using: • The cursor pad to move the text cursor. • 0 or 8 . to delete the character to the left or right of the cursor, respectively. Press 2 ™ and type anything you want. 4.
Steps and keystrokes Display 5. Return to the current session on the Text Editor. Notice that the displayed session is exactly the same as you left it. Press 2 a Numeric Solver Consider the equation a=(m2Nm1)/(m2+m1)…g, where the known values are m2=10 and g=9.8. If you assume that a=1/3 g, find the value of m1. Steps and keystrokes Display 1. Use O to display the Numeric Solver. 2. Enter the equation. When you press ¸ or D, the screen lists the variables used in the equation.
Steps and keystrokes Display 3. Enter values for each variable, except the unknown variable m1. Define m2 and g first. Then define a. (You must define g before you can define a in terms of g.) Accept the default for bound. If a variable has been defined previously, its value is shown as a default. Press D 10 D D 9.8 C C C j G e 3 4. Move the cursor to the unknown variable m1. Optionally, you can enter an initial guess for m1.
Steps and keystrokes Display 6. Graph the solution using a ZoomStd viewing window. The graph is displayed in a split screen. You can explore the graph by tracing, zooming, etc. The variable marked by the cursor (unknown variable m1) is on the x axis, and left-rt is on the y axis. Press … 3 7. Return to the Numeric Solver and exit the split screen. You can press ¸ or D to redisplay the list of variables.
Number Bases Calculate 10 binary (base 2) + F hexadecimal (base 16) + 10 decimal (base 10). Then, use the 4 operator to convert an integer from one base to another. Finally, see how changing the Base mode affects the displayed results. Steps and keystrokes Display 1. Display the MODE dialog box, Page 2. For Base mode, select DEC as the default number base. Integer results are displayed according to the Base mode. Fractional and floatingpoint results are always displayed in decimal form.
Steps and keystrokes Display 3. Add 1 to the result and convert it to binary. 2 4 displays the 4 conversion operator. Press « 1 2 4 2 ™ BIN j ¸ 4. Add 1 to the result and convert it to hexadecimal. Press « 1 2 4 2 ™ HEX j ¸ 5. Add 1 to the result and leave it in the default decimal base. Results use the 0b or 0h prefix to identify the base. Press « 1 ¸ 6. Change the Base mode to HEX. When Base = HEX or BIN, the magnitude of a result is restricted to certain size limitations.
Steps and keystrokes Display 8. Change the Base mode to BIN. Press 3 „ (use D to move to Base mode) B 3 ¸ 9. Re-enter 0b10+0hF+10. Press ¸ Memory and Variable Management Assign values to a variety of variable data types. Use the VAR-LINK screen to view a list of the defined variables. Then move a variable to the user data archive memory and explore the ways in which you can and cannot access an archived variable.
variables are locked automatically.) Finally, unarchive the variable and delete the unused variables so that they will not take up memory. Steps and keystrokes Display 1. From the Home screen, assign variables with the following variable types. Expression: 5 !x1 Function: x2+4 !f(x) List: {5,10} !L1 Matrix: [30,25] !m1 Press " M 5 9 X1 ¸ X Z 2«49jFcXd¸2[ 5 b 10 2 \ 9 j L1 ¸ 2 g 30 b 25 2 h 9 j M1 ¸ 2. Suppose you start to perform an operation using a function variable but can’t remember its name.
Steps and keystrokes Display 4. Change the screen’s view to show only function variables. Although this may not seem particularly useful in an example with four variables, consider how useful it could be if there were many variables of all different types. Press „ D D B 5 ¸ 5. Highlight the f function variable, and view its contents. Notice that the function was assigned using f(x) but is listed as f on the screen. Press D 2 ˆ 6. Close the Contents window. Press N 7.
Archiving a variable Steps and keystrokes Display 1. Redisplay VAR-LINK, and highlight the variable you want to archive. The previous change in view is no longer in effect. The screen lists all defined variables. Press 2 ° (use D to highlight x1) 2. Use the , Manage toolbar menu to archive the variable. û indicates the variable is archived. Press , 8 3. Return to the Home screen and use the archived variable in a calculation.
Steps and keystrokes Display 4. Attempt to store a different value to the archived variable. Press 10 9 X1 ¸ 5. Cancel the error message. Press N 6. Use VAR-LINK to unarchive the variable. Press 2 ° (use D to highlight x1) , 9 7. Return to the Home screen and store a different value to the unarchived variable.
Deleting variables Steps and keystrokes Display 1. Display VAR-LINK, and use the ‡ All toolbar menu to select all variables. A Ÿ mark indicates items that are selected. Notice that this also selected the MAIN folder. Note: Instead of using ‡ (if you don’t want to delete all your variables), you can select individual variables. Highlight each variable to delete and press †. Press ‡ 1 2. Use , to delete. Note: You can press 0 (instead of , 1) to delete the marked variables. Press , 1 3.
Steps and keystrokes Display 4. Because ‡ 1 also selected the MAIN folder, an error message states that you cannot delete the MAIN folder. Acknowledge the message. When VAR-LINK is redisplayed, the deleted variables are not listed. Press ¸ 5. Close VAR-LINK and return to the current application (Home screen in this example). When you use N (instead of ¸) to close VAR-LINK, the highlighted name is not pasted to the entry line.
Operating the Calculator Turning the Calculator On and Off You can turn your graphing calculator on and off manually by using the ´ and 2 ® (or 8 ®) keys. To prolong battery life, the APD™ (Automatic Power Down™) feature lets the calculator turn itself off automatically. Turning the Calculator On Press ´. • If you turned the unit off by pressing 2 ®, the unit returns to either the Apps desktop or the Home screen.
Turning the Calculator Off You can use either of the following keys to turn off your graphing calculator. Press: Description 2® (press 2 and then press ®) Settings and memory contents are retained by the Constant Memory™ feature. However: • You cannot use 2 ® if an error message is displayed. • When you turn the calculator on again, it displays either the Home screen or the Apps desktop (regardless of the last application you used).
APD does not occur if a calculation or program is in progress, unless the program is paused. If a program is running, but waiting for a key press, APD will occur after several minutes of inactivity. Setting the Display Contrast The brightness and contrast of the display depend on room lighting, battery freshness, viewing angle, and the adjustment of the display contrast. The contrast setting is retained in memory when the graphing calculator is turned off.
When to Replace Batteries As the batteries get low, the display begins to dim (especially during calculations) and you must increase the contrast. If you have to increase the contrast frequently, replace the four alkaline batteries. Note: The display may be very dark after you change batteries. Use 8 | to lighten the display. The status line along the bottom of the display also gives battery information. Indicator in status line Description Batteries are low. Replace batteries as soon as possible.
Ê Ë Í Î Ì Ï Ê ƒ – 2 Š open toolbar menus. Select applications (when used with 8) Ë 2, 8, ¤, and j add functionality by increasing the available key commands. Ì X, Y, and Z are often used in symbolic calculations. Í A, B, C, and D move the cursor. Î O lets you select an application. Ï ¸ evaluates an expression, executes an instruction, selects a menu item, etc.
Modifier Keys Modifier Keys Modifier Description 2 Accesses the second function of the next key you press. On the keyboard, these are printed in the same color as the 2 key. (second) 8 (diamond) ¤ (shift) j Activates keys that select certain applications, menu items, and other operations from the keyboard. On the keyboard, these are printed in the same color as the 8 key. Types an uppercase character for the next letter key you press.
2 K accesses QUIT PASTE ESC QUIT, which is the same color as the 2 key. 8 7 accesses PASTE, which is the same color as the 8 key. N accesses the key’s primary function. Some keys perform only one additional operation, which may require either 2 or 8, depending on the color in which the operation is printed on the keyboard and where it is positioned above the key. CUT 2nd On the TI-89 Titanium, 8 5 accesses CUT, which is the same color as the 8 key.
Key Description 8' Displays the Table screen. @: 85 86 87 These keys let you edit entered information by performing a cut, copy, or paste operation. 2a Toggles between the last two chosen Apps or between split screen portions. 2¾ Toggles the custom menu on and off. 2 Converts measurement units. @ Designates a measurement unit. 8 0 Deletes the character to the left of the cursor (backspaces). 2/ Toggles between insert and overtype mode for entering information. 8.
Key Description 2¯ Displays the MEMORY screen. 2° Displays the VAR-LINK screen for managing variables and Flash applications. 2£ Recalls the contents of a variable. @ Displays the UNITS dialog box. 29 2¿ Displays the CHAR menu, which lets you select Greek letters, international accented characters, etc. 2 `, 2± Recalls the previous entry and the last answer, respectively.
Other letters are available as the j function of another key, similar to the 2 and 8 modifiers described in the previous section. For example: 2 È types ′, which is the same color as the 2 key. ′ A j [A] displays an A, which is the same color as the j key. = Typing Alphabetic Characters on the TI-89 Titanium To: Press: Type a single lowercase alpha character. j and then the letter key (status line shows ) Type a single uppercase alpha character.
• On the TI-89 Titanium, you do not need j or alpha-lock to type x, y, z, or t. But you must use ¤ or uppercase ALPHA-lock for X, Y, Z, or T. • On the TI-89 Titanium, alpha-lock is always turned off when you change applications, such as going from the Text Editor to the Home screen. On the TI-89 Titanium, while either type of alpha-lock is on: • To type a period, comma, or other character that is the primary function of a key, you must turn alpha-lock off.
Note: To type a number, press j to turn alpha-lock off. Press j or 2 ™ to resume typing letters. Alpha-lock is not turned on in dialog boxes that require numeric-only entries. The dialog boxes that accept only numeric entries are: Resize Matrix, Zoom Factors, and Table Setup. For Special Characters Use the 2 ¿ menu to select from a variety of special characters. For more information, refer to “Entering Special Characters” in the Text Editor module.
module. For example, it is important to know that functions such as x2 are evaluated before negation. Use c and d to include parentheses if you have any doubt about how a negation will be evaluated. Evaluated as M(22) If you use | instead of · (or vice versa), you may get an error message or you may get unexpected results. For example: • 9 p · 7 = M63 – but – 9 p | 7 displays an error message. • 6|2=4 – but – 6 · 2 = M12 since it is interpreted as 6(M2), implied multiplication.
2. Press: ^ í appears in the display. 3. Type the exponent as an integer with up to 3 digits. You can use a negative exponent. Entering a number in scientific notation does not cause the answers to be displayed in scientific or engineering notation. The display format is determined by the mode settings and the magnitude of the number. Represents 123.45 × 10-2 Entering Expressions and Instructions You perform a calculation by evaluating an expression.
Definitions Expression Consists of numbers, variables, operators, functions, and their arguments that evaluate to a single answer. For example: pr2+3. Operator • Enter an expression in the same order that it normally is written. • In most places where you are required to enter a value, you can enter an expression. Performs an operation such as +, –, ù, ^. • Function Returns a value. • Instruction Operators require an argument before and after the operator. For example: 4+5 and 5^2.
• This guidebook uses the word command as a generic reference to both functions and instructions. Implied Multiplication The graphing calculator recognizes implied multiplication, provided it does not conflict with a reserved notation.
Entering an Expression Type the expression, and then press ¸ to evaluate it. To enter a function or instruction name on the entry line, you can: • Press its key, if available. For example, press:2 W – or – • Select it from a menu, if available. For example, select 2:abs from the Number submenu of the MATH menu. – or – • Type the name letter-by-letter from the keyboard. (On the TI-89 Titanium, use j and 2 ™ to type letters.) You can use any mixture of uppercase or lowercase letters.
TI-89 Titanium Press 3.76 e c · 7.9 « 2] 5dd Display 3.76/( M7.9+‡( 2 ] inserts ‡( because its argument must be in parentheses. 3.76/( M7.9+‡(5)) Use d once to close ‡(5) and again to close (M7.9 + ‡5). «2 2 ™ LOG j c 45 d 3.76/( M7.9+‡(5))+2log(45) log requires ( ) around its argument.
Entering Multiple Expressions on a Line Ê To enter more than one expression or instruction at a time, separate them with a colon by pressing 2 Ë. Ê Displays last result only. Ë ! is displayed when you press § to store Ë a value to a variable. If an Entry or Answer Is Too Long for One Line In the history area, if both the entry and its answer cannot be displayed on one line, the answer is displayed on the next line.
2. As necessary, use C and D to highlight the entry or answer you want to view. For example, C moves from answer to entry, up through the history area. 3. Use B and A or 2 B and 2 A to scroll right and left. Note: When you scroll to the right, 7 is displayed at the beginning of the line. 4. To return to the entry line, press N. Continuing a Calculation When you press ¸ to evaluate an expression, the graphing calculator leaves the expression on the entry line and highlights it.
TI-89 Titanium Press Display 3.76 e c · 7.9 « 2]5dd ¸ « 2 2 ™ LOG j c 45 d ¸ When you press «, the entry line is replaced with the variable ans(1), which contains the last answer. Stopping a Calculation When a calculation is in progress, BUSY appears on the right end of the status line. To stop the calculation, press ´. There may be a delay before the Break message is displayed. Press N to return to the current application.
Pretty Print Mode By default, Pretty Print = ON. Exponents, roots, fractions, etc., are displayed in the same form in which they are traditionally written. You can use 3 to turn pretty print off and on. Pretty Print ON π p2, --- , 2 OFF x–3 ----------2 p^2, p/2, ‡((x–3)/2) The entry line does not show an expression in pretty print. If pretty print is turned on, the history area will show both the entry and its result in pretty print after you press ¸. Exact/Approx Mode By default, Exact/Approx = AUTO.
EXACT — Any result that is not a whole number is displayed in a fractional or symbolic form (1/2, p, 2 , etc.). Shows whole-number results. Shows simplified fractional results. Shows symbolic p. Shows symbolic form of roots that cannot be evaluated to a whole number. Press 8 ¸ to temporarily override the EXACT setting and display a floating-point result.
APPROXIMATE — All numeric results, where possible, are displayed in floating-point (decimal) form. Note: Results are rounded to the precision of your graphing calculator and displayed according to current mode settings. Fractional results are evaluated numerically. Symbolic forms, where possible, are evaluated numerically Because undefined variables cannot be evaluated, they are treated algebraically. For example, if the variable r is undefined, pr2= 3.14159⋅r2.
Note: To retain an EXACT form, use fractions instead of decimals. For example, use 3/2 instead of 1.5. The following chart compares the three settings. Entry Exact Result Approximate Result Auto Result 8/4 2 2. 2 8/6 4/3 1.33333 4/3 8.5ù3 51/2 25.5 ‡(2)/2 2 ------2 .707107 pù2 2⋅p 6.28319 2⋅p pù2. 2⋅p 6.28319 6.28319 25.5 — A decimal in the entry forces a floating-point result 2 ------in AUTO.
Internally, the calculator calculates and retains all decimal results with up to 14 significant digits (although a maximum of 12 are displayed). Setting Example Description FIX (0–12) 123. 123.5 123.46 123.457 FLOAT 123.456789012 Number of decimal places varies, depending on the result. FLOAT (1–12) 1.E 2 1.2E 2 123. 123.5 123.46 123.457 Results are rounded to the total number of selected digits.
Setting Example Description NORMAL 12345.6 If a result cannot be displayed in the number of digits specified by the Display Digits mode, the calculator switches from NORMAL to SCIENTIFIC for that result only. SCIENTIFIC 1.23456E 4 1.23456 × 104 Ê ENGINEERING Ë 1.23456E 3 Ì 12.3456 × 103 Í Ê Always 1 digit to the left of the decimal point. Ë Exponent (power of 10). Ì May have 1, 2, or 3 digits to the left of the decimal point. Í Exponent is a multiple of 3.
Removing the Highlight from the Previous Entry After you press ¸ to evaluate an expression, the calculator leaves that expression on the entry line and highlights it. To edit the expression, you must first remove the highlight; otherwise, you may clear the expression accidentally by typing over it. To remove the highlight, move the cursor toward the side of the expression you want to edit. A B A moves the cursor to the beginning. B moves the cursor to the end of the expression.
Deleting a Character To delete: Press: The character to the left of the cursor. 0 The character to the right of the cursor. 80 All characters to the right of the cursor. M (once only) Hold 0 to delete multiple characters. If there are no characters to the right of the cursor, M erases the entire entry line. Clearing the Entry Line To clear the entry line, press: • M if the cursor is at the beginning or end of the entry line.
Inserting or Overtyping a Character The calculator has both an insert and an overtype mode. By default, the calculator is in the insert mode. To toggle between the insert and overtype modes, press 2 /. If in: The next character you type: Thin cursor between characters Cursor highlights a character Will be inserted at the cursor. Will replace the highlighted character. Note: Look at the cursor to see if you’re in insert or overtype mode.
To highlight multiple characters: 1. Move the cursor to either side of the characters you want to highlight. To replace sin( with cos(, place the cursor beside sin. 2. Hold ¤ and press A or B to highlight characters left or right of the cursor. Hold ¤ and press B B B B. To replace or delete the highlighted characters: 1. Type the new characters. 2. Press 0. Note: When you highlight characters to replace, remember that some function keys automatically add an open parenthesis.
are described in the appropriate modules. Displaying a Menu Press: To display: ƒ, „, etc. A toolbar menu — Drops down from the toolbar at the top of most application screens. Lets you select operations useful for that application. O Apps desktop or APPLICATIONS menu — Lets you select from a list of applications. 2¿ CHAR menu — Lets you select from categories of special characters (Greek, math, etc.). 2I MATH menu — Lets you select from categories of math operations.
Selecting an Item from a Menu To select an item from the displayed menu, either: • Press the number or letter shown to the left of that item. For a letter on the TI-89 Titanium, press j and then a letter key. – or – • Use the cursor pad D and C to highlight the item, and then press ¸. (Note that pressing C from the first item moves the highlight to the last item, and vice versa.) 6 indicates that a menu will drop down from the toolbar when you press „. To select factor, press 2 or D ¸.
Because of limited screen size, the TI-89 Titanium overlaps these menus. $ indicates that you can For example, List displays a submenu that lets you select a specific List function. use the cursor pad to scroll down for additional items. For items that have a submenu, you can use the cursor pad as described below. • To display the submenu for the highlighted item, press B. (This is the same as selecting that item.) • To cancel the submenu without making a selection, press A.
Items Containing “. . .” (Dialog Boxes) If you select a menu item containing “...” (ellipsis marks), a dialog box is displayed for you to enter additional information. For example, Save Copy As ... displays a dialog box that prompts you to select a folder name and type a variable name. " indicates that you can press B to display and select from a menu. An input box indicates that you must type a value. (Alpha-lock is automatically turned on for the TI-89 Titanium.
Moving from One Toolbar Menu to Another To move from one toolbar menu to another without making a selection, either: • Press the key (ƒ, „, etc.) for the other toolbar menu. – or – • Use the cursor pad to move to the next (press B) or previous (press A) toolbar menu. Pressing B from the last menu moves to the first menu, and vice versa. When using B, be sure that an item with a submenu is not highlighted. If so, B displays that item’s submenu instead of moving to the next toolbar menu.
Selecting an Application The graphing calculator has different applications that let you solve and explore a variety of problems. You can select an application from a menu, the Apps desktop, or you can access commonly used applications directly from the keyboard. From the APPLICATIONS Menu 1. If the Apps desktop is off, press O to display a menu that lists the applications. Note: To cancel the menu without making a selection, press N. 2. Select an application.
Application: Lets you: Table Display a table of variable values that correspond to an entered function. Data/Matrix Editor Enter and edit lists, data, and matrices. You can perform statistical calculations and graph statistical plots. Program Editor Enter and edit programs and functions. Text Editor Enter and edit a text session. Numeric Solver Enter an expression or equation, define values for all but one variable, and then solve for the unknown variable.
The most common dialog box lists these options for the application: Option Description Current Returns the screen displayed when you last viewed the App. (If there is no current file/variable for the selected App, this option defaults to New if you press ¸.) Open Lets you select an existing file. New Creates a new file with the name typed in the field. Select an option and press ¸. The application appears.
From the Keyboard Operating the Calculator 184
You can access commonly used applications from the keyboard. On the TI-89 Titanium for example, 8 # is the same as pressing 8 and then ƒ. This guidebook uses the notation 8 #, similar to the notation used in second functions. Application: Press: Home " " Y= Editor 8# Window Editor 8$ Graph 8% Table Setup 8& Table Screen 8' Applications listed above ƒ, „ etc., are printed in the same color as 8. Setting Modes Modes control how numbers and graphs are displayed and interpreted.
Ê Ì Ë Ê There are three pages of mode listings. Press ƒ, „, or … to quickly display a particular page. Ë Indicates you can scroll down to see additional modes. Ì ! indicates that you can press B or A to display and select from a menu. Note: Modes that are not currently valid are dimmed. For example, on Page 2, Split 2 App is not valid when Split Screen = FULL. When you scroll through the list, the cursor skips dimmed settings. Changing Mode Settings From the MODE dialog box: 1.
• Press the number or letter for that setting. Note: To cancel a menu and return to the MODE dialog box without making a selection, press N. 4. Change other mode settings, if necessary. 5. When you finish all your changes, press ¸ to save the changes and exit the dialog box. Important: If you press N instead of ¸ to exit the MODE dialog box, any mode changes you made will be canceled.
Mode Description Exponential Format Notation used to display results: NORMAL, SCIENTIFIC, or ENGINEERING. Complex Format Format used to display complex results, if any: REAL (complex results are not displayed unless you use a complex entry), RECTANGULAR, or POLAR. Vector Format Format used to display 2- and 3-element vectors: RECTANGULAR, CYLINDRICAL, or SPHERICAL. Pretty Print Turns the pretty print display feature OFF or ON.
Mode Description Unit System Lets you select from three systems of measurement to specify the default units for displayed results: SI (metric or MKS); Eng/US (feet, pounds, etc.); or Custom. Custom Units Lets you select custom defaults. The mode is dimmed until you select Unit System, 3:CUSTOM. Language Lets you localize the calculator into one of several languages, depending on which language Flash applications are installed. Apps Desktop Turns the Apps desktop ON or OFF.
Menu Item Description Clear a–z Clears (deletes) all single-character variable names in the current folder, unless the variables are locked or archived. You will be prompted to press ¸ to confirm the action. Single-character variable names are often used in symbolic calculations such as: solve(a¦x2+b¦x+c=0,x) If any of the variables have already been assigned a value, your calculation may produce misleading results. To prevent this, you can select 1:Clear a–z before beginning the calculation.
• When defining a variable that you want to retain, use more than one character in the name. This prevents it from being deleted inadvertently by 1:Clear a–z. • For information about checking and resetting memory or other system defaults, refer to Memory and Variable Management. Using the Catalog Dialog Box The CATALOG provides a way to access any built-in command (functions and instructions) from one convenient list.
Ê Defaults to „ Built-in. Ë ƒ Help displays a command’s parameters in a dialog box. Ì … and † allow access to Flash application functions and User-Defined functions and programs. Note: Options that are not currently valid are dimmed. For example, … Flash Apps is dimmed if you have not installed a Flash application. † User-Defined is dimmed if you have not created a function or a program.
3. Move the 8 indicator to the command, and press ¸. To move the 8 indicator: Press or type: One function or program at a time D or C One page at a time 2 D or 2 C To the first function that begins with a specified letter The letter key. (On the TI-89 Titanium, do not press j first. If you do, you need to press j or 2 ™ again before you can type a letter.) Note: From the top of the list, press C to move to the bottom. From the bottom, press D to move to the top.
From the example above, the syntax for factor is: factor(expression) required – or – factor(expression,variable) optional Note: For details about the parameters, refer to that command’s description in the Technical Reference module. Viewing CATALOG Help You can display a command's parameters in a dialog box by pressing ƒ Help. The parameters are the same as those displayed on the status line. Indicated command and its parameters. Some commands, such as ClrDraw, do not require parameters.
Selecting a Flash Application Function A Flash application may contain one or more functions. When you select a function, its name is inserted in the entry line at the cursor location. Therefore, you should position the cursor as necessary before selecting the function. 1. Press: ½ 2. Press … Flash Apps. (This option is dimmed if no Flash applications are installed.) • The list is alphabetized by function name. The left column lists functions.
Selecting a User-Defined Function or Program You can create your own functions or programs and then use † User-Defined to access them. For instructions on how to create functions, see “Creating and Evaluating User-Defined Functions” in Calculator Home Screen, and “Overview of Entering a Function” in the Programming module. See Programming for instructions on how to create and run a program. When you select a function or program, its name is inserted in the entry line at the cursor location.
3. Move the 8 indicator to the function or program, and press ¸. To move the 8 indicator: Press or type: One function or program at a time D or C One page at a time 2 D or 2 C To the first function or program that The letter key. (On the TI-89 begins with a specified letter Titanium, do not press j first. If you do, you need to press j or 2 ™ again before you can type a letter.) Storing and Recalling Variable Values When you store a value, you store it as a named variable.
• Cannot be the same as a name that is preassigned by the calculator. Preassigned names include: - Built-in functions (such as abs) and instructions (such as LineVert). Refer to the Technical Reference module. System variables (such as xmin and xmax, which are used to store graphrelated values). Refer to the Technical Reference module for a list. Examples Variable Description myvar OK a OK Log Not OK, name is preassigned to the log function. Log1 OK 3rdTotal Not OK, starts with a digit.
DataTypes Examples Matrices Character strings 10 0 10 0 , 34 6 “Hello”, “The answer is:”, “xmin/10” Pictures Functions myfunc(arg), ellipse(x,y,r1,r2) Storing a Value in a Variable 1. Enter the value you want to store, which can be an expression. 2. Press §. The store symbol (!) is displayed. 3. Type the variable name. Note: TI-89 Titanium users should use j as necessary when typing variable names. 4. Press ¸. To store to a variable temporarily, you can use the “with” operator.
Displaying a Variable 1. Type the variable name. 2. Press ¸. If the variable is undefined, the variable name is shown in the result. In this example, the variable a is undefined. Therefore, it is used as a symbolic variable. Note: Refer to Symbolic Manipulation for information about symbolic manipulation. Using a Variable in an Expression 1. Type the variable name into the expression. 2. Press ¸ to evaluate the expression.
Recalling a Variable’s Value In some cases, you may want to use a variable’s actual value in an expression instead of the variable name. 1. Press 2 £ to display a dialog box. 2. Type the variable name. 3. Press ¸ twice. In this example, the value stored in num1 will be inserted at the cursor position in the entry line. Status Line Indicators in the Display The status line is displayed at the bottom of all application screens.
Í Î Ï Ð Ñ Exact/Approx Mode Graph Number Graph Mode Replace Batteries History Pairs, Busy/Pause, Locked Variable Indicator Meaning Current Folder Shows the name of the current folder. Refer to “Using Folders to Store Independent Sets of Variables” in Calculator Home Screen. MAIN is the default folder. Modifier Key Shows which modifier key is in effect, as described below. 2nd 2 — will use the second function of the next key you press. 2 8 — will use the diamond feature of the next key you press.
Indicator Meaning Angle Mode Shows the units in which angle values are interpreted and displayed. To change the Angle mode, use the 3 key. RAD Radians DEG Degrees GRAD Gradian Exact/Approx Mode Shows how answers are calculated and displayed. To change the Exact/Approx mode, use the 3 key. AUTO Auto EXACT Exact APPROX Approximate Graph Number If the screen is split to show two independent graphs, this indicates which graph is active — G1 or G2.
Indicator Meaning Battery Displayed only when the batteries are getting low. If BATT is shown with a black background, change the batteries as soon as possible. History Pairs, Busy/Pause, Archived The information shown in this part of the status line depends on the application you are using. 23/30 Displayed on the Home screen to show the number of entry/answer pairs in the history area. Refer to History Information on the Status Line in the Calculator Home Screen module.
Calculator Home Screen Calculator Home Screen The calculator Home screen is the starting point for math operations, including executing instructions, evaluating expressions, and viewing results. A blank calculator Home screen This module describes the parts of the calculator Home screen, how to scroll through or modify the history area; how to use cut, copy, and paste, and more. Note: The term “calculator Home screen” is used in this module. Other modules use the term “Home screen.
Parts of the Calculator Home Screen The following example contains previously entered data and describes the main parts of the calculator Home screen. Entry/answer pairs in the history area are displayed in “pretty print.” Pretty print displays expressions in the same form in which they are written on the board or in textbooks. Ê Ë Ì Í Ï Î Ê Toolbar Lets you display menus for selecting operations applicable to the calculator Home screen. To display a toolbar menu, press ƒ, „, etc.
Ï Last Answer Result of your last entry. Note that results are not displayed on the entry line. Note: 8 ¸ (Approx) was used in this example. The following example shows an answer that is not on the same line as the expression. Note that the answer is longer than the screen width. An arrow (8) indicates the answer is continued. The entry line contains ellipsis (…). Ellipsis indicates the entry is longer than the screen width. Ê Ë Ì Í Ê Last Entry "Pretty print" is ON. Exponents, roots, fractions, etc.
History Area The history area shows up to eight previous entry/answer pairs (depending on the complexity and height of the displayed expressions). When the display is filled, information scrolls off the top of the screen. You can use the history area to: • Review previous entries and answers. You can use the cursor to view entries and answers that have scrolled off the screen. • Recall or auto-paste a previous entry or answer onto the entry line so that you can re-use or edit it.
To: Do this: Return the cursor to the entry line Press N, or press D until the cursor is back on the entry line. Note: An example of viewing a long answer is available. History Information on the Status Line Use the history indicator on the status line for information about the entry/answer pairs. For example: If the cursor is on the entry line: Total number of pairs that are currently saved. Maximum number of pairs that can be saved.
Modifying the History Area To: Do this: Change the number of pairs that can be saved Press ƒ and select 9:Format, or press @ 8Í Then press B, use C or D to highlight the new number, and press ¸ twice. Clear the history area and delete all saved pairs Press ƒ and select 8:Clear Home, or enter ClrHome on the entry line. Delete a particular entry/answer pair Move the cursor to either the entry or answer. Press 0 or M.
2. Specify a folder and text variable that you want to use to store the entries. Note: Only the entries are saved, not the answers. Item Description Type Automatically set as Text and cannot be changed. Folder Shows the folder in which the text variable will be stored. To use a different folder, press B to display a menu of existing folders. Then select a folder. Variable Type a valid, unused variable name. Note: For information about folders, see the Memory and Variable Management module. 3.
1. Use the Text Editor to open the variable containing the saved calculator Home screen entries. The saved entries are listed as a series of command lines that you can execute individually, in any order. 2. Starting with the cursor on the first line of the script, press † repeatedly to execute the commands line by line. 3. Display the restored calculator Home screen. This split screen shows the Text Editor (with the command line script) and the restored calculator Home screen.
1. Use C and D to highlight the item in the history area. 2. Press ¸ to auto-paste that item to the entry line. To copy or move information in the entry line, you must use a cut, copy, or paste operation. (You can perform a copy operation in the history area, but not a cut or paste.) Cutting or Copying Information to the Clipboard When you cut or copy information, that information is placed in the clipboard.
Clipboard = (empty or the previous contents) After cut Clipboard = x^4–3x^3–6x^2+8x After copy Clipboard = x^4–3x^3–6x^2+8x Note: You can cut, copy or paste without having to use the ƒ toolbar menu. Press: @ 8 5, 8 6, or 8 7 Cutting is not the same as deleting. When you delete information, it is not placed in the clipboard and cannot be retrieved. Note: When you cut or copy information, it replaces the clipboard’s previous contents, if any.
2. Press ƒ and select 6:Paste, or use the key shortcut: @ 87 Example: Copying and Pasting Suppose you want to reuse an expression without retyping it each time. 1. Copy the applicable information. a) Use ¤ B or ¤ A to highlight the expression. b) Press: @ 86 c) For this example, press ¸ to evaluate the entry. 2. Paste the copied information into a new entry. a) Begin a new entry and place the cursor where you want to paste the copied information.
b) Press … 1 to select the d (differentiate) function. c) Press: @ 87 to paste the copied expression. d) Complete the new entry, and press ¸. Note: You can also reuse an expression by creating a user-defined function. 3. Paste the copied information into a different application. a) Press 8 # to display the Y= Editor. b) Press ¸ to define y1(x). c) Press: @ 87 to paste. d) Press ¸ to save the new definition. Note: By copying and pasting, you can easily transfer information from one application to another.
Reusing a Previous Entry or the Last Answer You can reuse a previous entry by reexecuting the entry “as is” or by editing the entry and then reexecuting it. You can also reuse the last calculated answer by inserting it into a new expression. Reusing the Expression on the Entry Line When you press ¸ to evaluate an expression, the TI-89 Titanium leaves that expression on the entry line and highlights it. You can type over the entry, or you can reuse it as necessary.
TI-89 Titanium Display ¸¸ Note: Reexecuting an entry “as is” is useful for iterative calculations that involve variables. Using the equation A=pr2, use trial and error to find the radius of a circle that covers 200 square centimeters. Note: Editing an entry lets you make minor changes without retyping the entire entry. The example below uses 8 as the first guess and then displays the answer in its approximate floating-point form. You can edit and reexecute using 7.
TI-89 Titanium Display A88 7.95 ¸ Note: When the entry contains a decimal point, the result is automatically displayed in floating-point. Recalling a Previous Entry You can recall any previous entry that is stored in the history area, even if the entry has scrolled off the top of the screen. The recalled entry replaces whatever is currently shown on the entry line. You can then reexecute or edit the recalled entry.
If the entry line contains the last entry, 2 ` recalls this entry. If the entry line is edited or cleared, 2 ` recalls this entry. Recalling the Last Answer Each time you evaluate an expression, the TI-89 Titanium stores the answer to the variable ans(1). To insert this variable in the entry line, press 2 ±. For example, calculate the area of a garden plot that is 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes. 1. Find the area. 1.7 p 4.
Auto-Pasting an Entry or Answer from the History Area You can select any entry or answer from the history area and “auto-paste” a duplicate of it on the entry line. This lets you insert a previous entry or answer into a new expression without having to retype the previous information. Why Use Auto-Paste The effect of using auto-paste is similar to 2 ` and 2 ± as described in the previous section, but there are differences.
Auto-Pasting an Entry or Answer 1. On the entry line, place the cursor where you want to insert the entry or answer. 2. Press C to move the cursor up into the history area. This highlights the last answer. 3. Use C and D to highlight the entry or answer to auto-paste. • C moves from answer to entry up through the history area. • You can use C to highlight items that have scrolled off the screen Note: To cancel auto-paste and return to the entry line, press N.
Creating and Evaluating User-Defined Functions User-defined functions can be a great time-saver when you need to repeat the same expression (but with different values) multiple times. User-defined functions can also extend your TI-89 Titanium’s capabilities beyond the built-in functions. Format of a Function The following examples show user-defined functions with one argument and two arguments. You can use as many arguments as necessary.
Arguments (x and y in these examples) are placeholders that represent whatever values you pass to the function. They do not represent the variables x and y unless you specifically pass x and y as the arguments when you evaluate the function. Creating a User-Defined Function Use one of the following methods. Method Description § Store an expression to a function name (including the argument list). Define command Define a function name (including the argument list) as an expression.
Creating a Multi-Statement Function You can also create a user-defined function whose definition consists of multiple statements. The definition can include many of the control and decision-making structures (If, ElseIf, Return, etc.) used in programming. Note: For information about similarities and differences between functions and programs, refer to Programming.
Ì Returns a message if nn is not an integer or if nn{0. Í Sums the reciprocals. Î Returns the sum. When entering a multi-statement function on the calculator Home screen, you must enter the entire function on a single line. Use the Define command just as you would for a single-statement function. Use a colon to separate each statement. Define sumrecip(nn)=Func:Local temp,i: ... :EndFunc Use argument names that will never be used when calling the function or program.
Evaluating a Function You can use a user-defined function just as you would any other function. Evaluate it by itself or include it in another expression. Displaying and Editing a Function Definition To: Do this: Display a list of all Press 2 ° to display the VAR-LINK user-defined functions screen. You may need to use the „ View toolbar menu to specify the Function variable type. (Refer to Memory and Variable Management.
To: Do this: Display the definition of a user-defined function From the VAR-LINK screen, highlight the function and display the Contents menu. @ 2ˆ – or – From the calculator Home screen, press 2 £. Type the function name but not the argument list (such as xroot), and press ¸ twice. – or – From the Program Editor, open the function. (Refer to Programming.) Edit the definition From the calculator Home screen, use 2 £ to display the definition. Edit the definition as necessary.
If an Entry or Answer Is “Too Long” Move the cursor into the history area, and highlight the entry or answer. Then use the cursor pad to scroll. For example: • The following shows an answer that is too long for one line. Press A or 2 A to scroll left. • Press B or 2 B to scroll right. The following shows an answer that is both too long and too tall to be displayed on the screen. Note: This example uses the randMat function to generate a 25 x 25 matrix.
For example: Note: This example uses the seq function to generate a sequential list of integers from 1 to 2500. When you see the << ...>> symbol, the answer cannot be displayed even if you highlight it and try to scroll. In general, you can try to: • Free up additional memory by deleting unneeded variables and/or Flash applications. Use 2 ° as described in Memory and Variable Management. • If possible, break the problem into smaller parts that can be calculated and displayed with less memory.
Turning the Custom Menu On and Off When you turn on the custom menu, it replaces the normal toolbar menu. When you turn it off, the normal menu returns. For example, from the calculator Home screen’s normal toolbar menu, press 2 ½ to toggle the custom menu on and off. 2¾ Calculator Home screen normal toolbar menu Custom menu Note: You can also turn the custom menu on and off by entering CustmOn or CustmOff in the entry line and pressing ¸.
Menu Function International Commonly accented characters such as è, é,and ê. Tool ClrHome, NewProb, and CustmOff. @ @ 2ˆ 2‰ Note: A custom menu can give you quick access to commonly used items. The Programming module shows you how to create custom menus for the items you use most often. Restoring the Default Custom Menu If a custom menu other than the default is displayed and you want to restore the default: 1.
Finding the Software Version and ID Number In some situations, you may need to find out information about your TI-89 Titanium, particularly the software version and the unit’s ID number. Displaying the “About” Screen 1. From either the calculator Home screen or the Apps desktop, press ƒ and then select A:About. Your screen will be different from the one shown to the right. 2. Press ¸ or N to close the screen.
The About screen displays the following information about your calculator: • Hardware version • OS (Advanced Mathematics Software) version • Product identifier (Product ID) • Unit ID • Apps certificate revision number (Cert. Rev.) Ê Ë Ì Í Î Ê OS version Ë Product identifier Ì Apps certificate revision number Í Hardware version Î Unit ID (required to obtain certificates for installing purchased Apps) Your screen will be different from the one shown above.
Symbolic Manipulation Using Undefined or Defined Variables When performing algebraic or calculus operations, it is important that you understand the effect of using undefined and defined variables. Otherwise, you may get a number for a result instead of the algebraic expression that you anticipated. How Undefined and Defined Variables Are Treated When you enter an expression that contains a variable, the TI-89 Titanium treats the variable in one of two ways.
• If x is defined, the result may be in a form you did not expect. Note: When defining a variable, it’s a good practice to use more than one character in the name. Leave one-character names undefined for symbolic calculations. Unless you knew that 5 had been stored to x previously, the answer 75 could be misleading. Determining If a Variable Is Exists Method: Enter the variable name. Example: If defined, the variable’s value is displayed. If undefined, the variable name is displayed.
Method: Use the getType function. Example: If defined, the variable’s type is displayed. If undefined, “NONE” is displayed. Note: Use 2 ° to view a list of defined variables, as described in Memory and Variable Management.
Deleting a Defined Variable You can “undefine” a defined variable by deleting it. To delete: Do this: One or more specified variables Use the DelVar function. You can also delete variables by using the VAR-LINK screen (2 °) as described in Memory and Variable Management. All variables of a specific type Use the Deltype function. Note: The Deltype function deletes all variables of the specified type in all folders.
To delete: Do this: All one-letter variables (a – z) in the current folder. From the Home screen Clean Up menu, select 1:Clear a-z. You will be prompted to press ¸ to confirm the deletion. Note: For information about folders, refer to the Calculator Home Screen module. Temporarily Overriding a Variable By using the “with” operator ( | ), you can: • Temporarily override a variable’s defined value. • Temporarily define a value for an undefined variable.
Using Exact, Approximate, and Auto Modes The Exact/Approx mode settings, which are described briefly in Operating the Handheld, directly affect the precision and accuracy with which the TI-89 Titanium calculates a result. This section describes these mode settings as they relate to symbolic manipulation. EXACT Setting When Exact/Approx = EXACT, the handheld uses exact rational arithmetic with up to 614 digits in the numerator and 614 digits in the denominator.
• With this kind of equation, EXACT will not compute approximate solutions. For example, 2Lx = x has an approximate solution x ≈ 0.641186, but it is not displayed in the EXACT setting. Advantages Disadvantages Results are exact. As you use more complicated rational numbers and irrational constants, calculations can: • Use more memory, which may exhaust the memory before a solution is completed. • Take more computing time.
Functions such as solve and ‰ (integrate) can use both exact symbolic and approximate numeric techniques. These functions skip all or some of their exact symbolic techniques in the APPROXIMATE setting. Advantages Disadvantages If exact results are not needed, this might save time and/or use less memory than the EXACT setting. Approximate results are sometimes more compact and comprehensible than exact results. Results with undefined variables or functions often exhibit incomplete cancellation.
converting any rational operands to floating-point. In other words, floating-point is “infectious.” For example: 1/2 - 1/3 transforms to 1/6 but 0.5 - 1/3 transforms to .16666666666667 This floating-point infection does not leap over barriers such as undefined variables or between elements of lists or matrices. For example: (1/2 - 1/3) x + (0.5 - 1/3) y transforms to x/6 + .16666666666667 y and {1/2 - 1/3, 0.5 - 1/3} transforms to {1/6, .
Automatic Simplification When you type an expression on the entry line and press ¸, the TI-89 Titanium automatically simplifies the expression according to its default simplification rules. Default Simplification Rules All of the following rules are applied automatically. You do not see intermediate results. • If a variable has a defined value, that value replaces the variable.
• Numeric subexpressions are combined. • Products and sums are sorted into order. Products and sums involving undefined variables are sorted according to the first letter of the variable name. - Undefined variables r through z are assumed to be true variables, and are placed in alphabetical order at the beginning of a sum. Undefined variables a through q are assumed to represent constants, and are placed in alphabetical order at the end of a sum (but before numbers).
• Polynomial greatest common divisors are canceled. • Polynomials are expanded unless no key cancellation can occur. No key cancellation • Common denominators are formed unless no key cancellation can occur. No key cancellation • Functional identities are exploited.
Delayed Simplification for Certain Built-In Functions Usually, variables are automatically simplified to their lowest possible level before they are passed to a function. For certain functions, however, complete simplification is delayed until after the function is performed. Functions that Use Delayed Simplification Functions that use delayed simplification have a required var argument that performs the function with respect to a variable.
Note: You may or may not want to define a numeric value for var, depending on the situation. For example: x cannot be simplified. x is not simplified. The function uses x3, and then substitutes 5 for x. Note: The example to the right finds the derivative of x3 at x=5. If x3 was initially simplified to 75, you would find the derivative of 75, which is not what you want. x is simplified to t. The function uses t3. x is simplified to t. The function uses t3, and then substitutes 5 for t.
Substituting Values and Setting Constraints The “with” operator ( | ) lets you temporarily substitute values into an expression or specify domain constraints. Typing the “With” Operator To type the “with” operator ( | ), press: @ Í Substituting for a Variable For every occurrence of a specified variable, you can substitute a numeric value or an expression. First derivative of x3 at x = 5 To substitute for multiple variables at the same time, use the Boolean and operator.
Substituting for a Simple Expression For every occurrence of a simple expression, you can substitute a variable, numeric value, or another expression. Substituting s for sin(x) shows that the expression is a polynomial in terms of sin(x). By replacing a commonly used (or long) term, you can display results in a more compact form. Note: acos(x) is different from a*cos(x). Substituting Complex Values You can substitute complex values just as you would for other values.
Note: • For an overview of complex numbers, refer to the Technical Reference module. • To get the complex i, press 2 ). Do not simply type the letter i on the keyboard. Be Aware of the Limitations of Substitutions • Substitution occurs only where there is an exact match for the substitution. Only x 2 was replaced, not x 4. Define the substitution in simpler terms for a more complete substitution.
• Infinite recursions can occur when you define a substitution variable in terms of itself. Substitutes sin(x+1), sin(x+1+1), sin(x+1+1+1), etc sin(x)|x=x+1 When you enter a substitution that causes an infinite recursion: • - An error message is displayed. - When you press N, an error is shown in the history area. Internally, an expression is sorted according to the automatic simplification rules. Therefore, products and sums may not match the order in which you entered them.
- Substituting for more general expressions (either møc2=e or c2øm=e) may not work as you anticipate. No match for substitution Note: Use the solve function to help determine the single-variable substitution. Specifying Domain Constraints Many identities and transformations are valid for only a particular domain. For example: ln(x†y) = ln(x) + ln(y) only if x and/or y is not negative Sin-1(sin(q)) = q only if q ‚ Lp/2 and q p/2 radians Use the “with” operator to specify the domain constraint.
Note: Enter ln(x†y) instead of ln(xy); otherwise, xy is interpreted as a single variable named xy. Because sinL1(sin(q)) = q is not always valid, the expression is not simplified. With a constraint, the expression can be simplified. Note: For ‚ or , press 8 Ã or 8 Â. You can also use 2 I 8 or 2 G 2 to select them from a menu. Using Substitutions vs. Defining a Variable In many cases, you can achieve the same effect as a substitution by defining the variable.
Storing 1!x affects the subsequent calculations.calculation. Caution: After x is defined, it can affect all calculations that involve x (until you delete x). Overview of the Algebra Menu You can use the „ Algebra toolbar menu to select the most commonly used algebraic functions. The Algebra Menu From the Home screen, press „ to display: This menu is also available from the MATH menu. Press 2 I and then select 9:Algebra.
Note: For a complete description of each function and its syntax, refer to the Technical Reference module. Menu Item Description solve Solves an equation for a specified variable. This returns real solutions only, regardless of the Complex Format mode setting. Displays answers with "and" and "or" connecting solutions. (For complex solutions, select A:Complex from the Algebra menu.) factor Factors an expression with respect to all its variables or with respect to only a specified variable.
Menu Item Description Trig Displays the submenu: tExpand — Expands trig expressions with angle sums and multiple angles. TCollect — Collects the products of integer powers of trig functions into angle sums and multiple angles. tCollect is the opposite of tExpand. Complex Displays the submenu: These are the same as solve, factor, and zeros; but they also compute complex results. Extract Displays the submenu: getNum — Applies comDenom and then returns the resulting numerator.
Menu Item Description right — Returns the right-hand side of an equation or inequality. Note: The left and right functions are also used to return a specified number of elements or characters from the left or right side of a list or character string. Common Algebraic Operations This section gives examples for some of the functions available from the „ Algebra toolbar menu. For complete information about any function, refer to the Technical Reference module.
Factoring and Expanding Polynomials Use the factor („ 2) and expand („ 3) functions. factor(expression [,var]) for factoring with respect to a variable expand(expression [,var]) for partial expansion with respect to a variable Factor x5 N 1. Then expand the result. Notice that factor and expand perform opposite operations. Finding Prime Factors of a Number The factor („ 2) function lets you do more than simply factor an algebraic polynomial.
Finding Partial Expansions With the expand („ 3) function’s optional var value, you can do a partial expansion that collects similar powers of a variable. Do a full expansion of (x2Nx) (y2Ny) with respect to all variables. Then do a partial expansion with respect to x. Solving an Equation Use the solve („ 1) function to solve an equation for a specified variable. solve(equation, var) Solve x + y N 5 = 2x N 5y for x. Notice that solve displays only the final result.
To see intermediate results, you can manually solve the equation step-by-step. x « y | 5 Á 2x | 5y |2x |y «5 p?1 Note: An operation such as | 2 p subtracts 2x from both sides. Solving a System of Linear Equations Consider a set of two equations with two unknowns: 2x N 3y = 4 Lx + 7y = L12 To solve this system of equations, use any of the following methods. Method Example Use the solve function for a one-step solve(2xN3y=4 and Lx+7y=L12,{x,y}) solution.
Method Example Use the simult function with a matrix. Enter the coefficients as a matrix and the results as a constant column matrix. Use the rref function with a matrix. Enter the coefficients as an augmented matrix. Note: The simult and rref matrix functions are not on the „ Algebra menu. Use 2 I 4 or the Catalog.
Finding the Zeros of an Expression Use the zeros („ 4) function. zeros(expression, var) Use the expression x sin(x) + cos(x). Find the zeros with respect to x in the interval 0 x and x 3. Use the “with” operator to specify the interval. Note: For ‚ or , type 8 Ã or 8 Â.You can also use 2 I 8 or 2 G 2 to select them from a menu.
Finding Proper Fractions and Common Denominators Use the propFrac („ 7) and comDenom („ 6) functions. propFrac(rational expression [,var]) for proper fractions with respect to a variable comDenom(expression [,var]) for common denominators that collect similar powers of this variable Find a proper fraction for the expression (x4 N 2x2 + x) / (2x2 + x + 4). Then transform the answer into a ratio of a fully expanded numerator and a fully expanded denominator.
• 31x + 60 --------------------- is the remainder of x4N2x2+x divided by 2x2+x+4. 8 • x x ----- – --- – 15/8 is the quotient. 2 4 2 Overview of the Calc Menu You can use the … Calc toolbar menu to select commonly used calculus functions. The Calc Menu From the Home screen, press … to display: This menu is also available from the MATH menu. Press 2 I and then select A:Calculus. Note: For a complete description of each function and its syntax, refer to the Technical Reference module.
‰ integrate Integrates an expression with respect to a specified variable. limit Calculates the limit of an expression with respect to a specified variable. G sum Evaluates an expression at discrete variable values within a range and then calculates the sum. Π product Evaluates an expression at discrete variable values within a range and then calculates the product. fMin Finds candidate values of a specified variable that minimize an expression.
Note: The d symbol for differentiate is a special symbol. It is not the same as typing the letter D on the keyboard. Use … 1 or 2 =. Common Calculus Operations This section gives examples for some of the functions available from the … Calc toolbar menu. For complete information about any calculus function, refer to the Technical Reference module. Integrating and Differentiating Use the ‰ integrate (… 2) and d differentiate (… 1) functions.
Note: You can integrate an expression only; you can differentiate an expression, list, or matrix. Finding a Limit Use the limit (… 3) function. limit(expression, var, point [,direction]) negative number = from left positive number= from right omitted number or 0 = both Find the limit of sin(3x) / x as x approaches 0. Note: You can find a limit for an expression, list, or matrix.
Finding a Taylor Polynomial Use the taylor (… 9) function. taylor(expression, var, order [,point]) if omitted, expansion point is 0 Find a 6th order Taylor polynomial for sin(x) with respect to x. Store the answer as a user-defined function named y1(x). Then graph sin(x) and the Taylor polynomial. Graph sin(x):Graph y1(x) Important: Degree-mode scaling by p/180 may cause calculus application results to appear in a different form.
For Information about Creating a User-Defined Function Refer to: • “Creating and Evaluating User-Defined Functions” in the Calculator Home Screen module. • “Graphing a Function Defined on the Home Screen” and “Graphing a Piecewise Defined Function” in the Calculator Home Screen module. • “Overview of Entering a Function” in the Programming module. Undefined Functions You can use functions such as f(x), g(t), r(q), etc., that have not been assigned a definition.
• Use 9 to create a user-defined secant function, where: 1 sec x = ----------cos x Then find the limit of sec(x) as x approaches p/4. Note: To select limit from the Calc toolbar menu, press … 3. • Use Define to create a user-defined function h(x), where: x sin -t h ( x ) = ∫ -------t Define h(x)= ‰(sin(t)/t,t,0,x). 0 Then find a 5th order Taylor polynomial for h(x) with respect to x. Note: To select ‰ from the Calc toolbar menu, press … 2 (or press 2 < on the keyboard). To select taylor, press … 9.
In some cases, you may be able to create an equivalent single-statement function. For example, consider a piecewise function with two pieces. When: Use expression: x<0 x|0 Lx • 5 cos(x) If you were to create a multi-statement user-defined function with the form: Func If x<0 Then Return ëx Else Return 5cos(x) EndIf EndFunc Define y1(x)=Func:If x<0 Then: ... :EndFunc Then numerically integrate y1(x) with respect to x. Note: To select nInt from the Calc toolbar menu, press … B:nInt.
• Create an equivalent single-statement user-defined function. Use the TI-89 Titanium’s built-in when function. Then integrate y1(x) with respect to x. Define y1(x)=when(x<0, Lx, 5cos(x)) Note: To select ‰ from the Calc toolbar menu, press … 2 (or press 2 < on the keyboard). Press 8 ¸ for a floating-point result. If You Get an Out-of-Memory Error The TI-89 Titanium stores intermediate results in memory and then deletes them when the calculation is complete.
• Clear the history area (, 8) or delete unneeded history pairs. You can also use , 9 to reduce the number of history pairs that will be saved. Use 3 to set Exact/Approx = APPROXIMATE. (For results that have a large number of digits, this uses less memory than AUTO or EXACT. For results that have only a few digits, this uses more memory.) Simplifying Problems • Split the problem into parts. - • Split solve(a†b=0,var) into solve(a=0,var) and solve(b=0,var). Solve each part and combine the results.
• Reformulate a problem to avoid fractional powers. • Omit relatively small terms to find an approximation. Special Constants Used in Symbolic Manipulation The result of a calculation may include one of the special constants described in this section. In some cases, you may also need to enter a constant as part of your entry. true, false These indicate the result of an identity or a Boolean expression. x=x is true for any value of x. 5<3 is false.
@n1 ... @n255 This notation indicates an “arbitrary integer” that represents any integer. When an arbitrary integer occurs multiple times in the same session, each occurrence is numbered consecutively. After it reaches 255, arbitrary integer consecutive numbering restarts at @n0. Use Clean Up 2:NewProb to reset to @n1. Note: For @, press: 8 9 Symbolic Manipulation A solution is at every integer multiple of p.
@1 ... @255 This notation indicates an “arbitrary constant” that represents any integer. When an arbitrary constant occurs multiple times in the same session, each occurrence is numbered consecutively. After it reaches 255, arbitrary integer consecutive numbering restarts at @0. Use Clean Up 2:NewProb to reset to @1. Note: For @, press: 8 9 ˆ,, e ˆ represents infinity, and e represents the constant 2.71828... (base of the natural logarithms). These constants are often used in entries as well as results.
undef This indicates that the result is undefined.
Constants and Measurement Units Entering Constants or Units You can use a menu to select from a list of available constants and units, or you can type them directly from the keyboard. From a Menu The following shows how to select a unit, but you can use the same general procedure to select a constant. From the Home screen: 1. Type the value or expression. 6.3 2. Display the UNITS dialog box. Press: 29 3. Use D and C to move the cursor to the applicable category.
4. To select the highlighted (default) unit, press ¸. – or – To select a different unit from the category, press B. Then highlight the applicable unit, and press ¸. Note: If you created a user-defined unit for an existing category, it is listed in the menu. The selected unit is placed in the entry line. Constant and unit names always begin with an underscore ( _ ). You can also move the cursor by typing the first letter of a unit. 6.
Combining Multiple Units You may need to combine two or more units from different categories. For example, suppose you want to enter a velocity in meters per second. In the UNITS dialog box, however, the Velocity category does not contain this unit. You can enter meters per second by combining _m and _s from the Length and Time categories, respectively. 3†9.8_m/_s Combine the units _m and _s. There is no pre-defined m/_s unit. Note: Create a user-defined unit for frequently used combinations.
Using Parentheses with Units in a Calculation In a calculation, you may need to use parentheses ( ) to group a value and its units so that they are evaluated properly. This is particularly true for division problems. For example: To calculate: 100_m ----------------2_s Enter: _m _s 100_m/(2_s) 50 • ------You must use parentheses for (2_s). This is important for division. If you omit the parentheses, you will get unexpected units. For example: 100_m/2_s 50.
Converting from One Unit to Another You can convert from one unit to another in the same category, including any userdefined units. For All Units Except Temperature If you use a unit in a calculation, it is converted and displayed automatically in the current default unit for that category, unless you use the 4 conversion operator as described later. The following examples assume that your default units are set to the SI system of metric units. Notes: • Refer to the list of pre-defined units.
If you want to convert to a unit other than the default, use the 4 conversion operator. expression_unit1 4 _unit2 For 4, press 2 4.
If an expression uses a combination of units, you can specify a conversion for some of the units only. Any units for which you do not specify a conversion will be displayed according to your defaults. To convert 186000 miles/second from miles to kilometers: 186000_mi/_s 4 _km Because a Time conversion is not specified, it is shown in its default unit (_s in this example).
For Temperature Values To convert a temperature value, you must use tmpCnv( ) instead of the 4 operator. tmpCnv(expression_¡tempUnit1, _¡tempUnit2) For ¡, press 2 v“ .
For Temperature Ranges To convert a temperature range (the difference between two temperature values), use @tmpCnv( ). @tmpCnv(expression_¡tempUnit1, _¡tempUnit2) For example, to convert a 100_¡C range to its equivalent range in _¡F: @tmpCnv(100_¡c, _¡f) 100_oC 0 100 32 212 Note: For @, press: 8 c 7 [D] _oC _oF 180_oF Setting the Default Units for Displayed Results All results involving units are displayed in the default unit for that category.
If You’re Using the SI or ENG/US System The SI and ENG/US systems of measurement (set from Page 3 of the MODE screen) use built-in default units, which you cannot change. The default units for these systems are available. If Unit System=SI or ENG/US, the Custom Units item is dimmed. You cannot set a default for individual categories. Setting Custom Defaults To set custom defaults: 1. Press 3 … B 3 to set Unit System = CUSTOM. 2. Press D to highlight SET DEFAULTS. 3.
4. For each category, you can highlight its default, press B, and select a unit from the list. 5. Press ¸ twice to save your changes and exit the MODE screen. You can also move the cursor by typing the first letter of a unit. Notes: • You can also use setUnits( ) or getUnits( ) to set or return information about default units. Refer to the Technical Reference module. • When the CUSTOM UNIT DEFAULTS dialog box first appears, it shows the current default units.
• If the defaults are Area = _acre and Length = _m (meters), area results are shown with _acre units. • If you set Area = NONE, area results are shown with _m2 units. Note: NONE is not available for base categories such as Length and Mass that have no components. Creating Your Own User-Defined Units In any category, you can expand the list of available units by defining a new unit in terms of one or more pre-defined units. You can also use “standalone” units.
Rules for User-Defined Unit Names The naming rules for units are similar to variables. • Can have up to 8 characters. • First character must be an underscore. For _, press: 85 • Second character can be any valid variable name character except _ or a digit. For example, _9f is not valid. • Remaining characters (up to 6) can be any valid variable name character except an underscore. Defining a Unit Define a unit the same way you store to a variable.
definition !_newUnit For !, press 9 For example, to define a dekameter unit: 10_m !_dm To define an acceleration unit: _m/_s^2 !_ms2 Assuming unit defaults for Length and Time are set to _m and _s. To calculate 195 blinks in 5 minutes as _blinks/_min: 195_blinks/(5_min) Assuming unit default for Time is set to _s. Notes: • User-defined units are displayed in lowercase characters, regardless of the case you use to define them. • User-defined units such as _dm are stored as variables.
List of Pre-Defined Constants and Units This section lists the pre-defined constants and units by category. You can select any of these from the UNITS dialog box. If you use 3 to set default units, note that categories with only one defined unit are not listed. Defaults for SI and ENG/US The SI and ENG/US systems of measurement use built-in default units. In this section, the built-in defaults are indicated by (SI) and (ENG/US). In some categories, both systems use the same default.
Description Value _Mn neutron rest mass 1.67492728E‘M27_kg _Mp proton rest mass 1.67262171E‘M27_kg _Na Avogadro’s number 6.0221415E23 /_mol _q electron charge 1.60217653E‘M19_coul _Rb Bohr radius 5.291772108E‘M11_m _Rc molar gas constant 8.314472_J/_mol/_¡K _Rdb Rydberg constant 10973731.568525 /_m _Vm molar volume 2.2413996E‘M2_m3/_mol _H0 permittivity of a vacuum 8.8541878176204E‘M12_F/_m _s Stefan-Boltzmann constant 5.670400E‘M8_W/_m2/_¡K4 _f0 magnetic flux quantum 2.
• These values represent the most up-to-date constants available at time of printing from the CODATA Internationally recommended values of the Fundamental Physical Constants available on the National Institute of Standards and Technology (NIST) web site. (http://physics.nist.gov/cuu/Constants/index.html).
Volume _cup cup _ml milliliter _floz fluid ounce _pt pint _flozUK British fluid ounce _qt quart _gal gallon _tbsp tablespoon _galUK British gallon _tsp teaspoon _l liter NONE (SI) (ENG/US) Time _day day _s second (SI) (ENG/US) _hr hour _week week _min minute _yr year _ms millisecond _ms microsecond _ns nanosecond Velocity _knot knot _mph _kph kilometers per hour NONE (SI) (ENG/US) Constants and Measurement Units miles per hour 296
Acceleration no pre-defined units Temperature _¡C ¡Celsius (For ¡, press 2 “.
_mg milligram _mton metric ton _tonUK long ton Force _dyne dyne _N newton (SI) _kgf kilogram force _tonf ton force _lbf pound force (ENG/US) Energy _Btu British thermal unit (ENG/US) _J joule (SI) _cal calorie _kcal kilocalorie _erg erg _kWh kilowatt-hour _eV electron volt _latm liter-atmosphere _ftlb foot-pound Power _hp horsepower (ENG/US) _kW kilowatt Constants and Measurement Units _W watt (SI) 298
Pressure _atm atmosphere _mmHg millimeters of mercury _bar bar _Pa pascal (SI) _inH2O inches of water _psi pounds per square inch (ENG/US) _inHg inches of mercury _torr millimeters of mercury _mmH2O millimeters of water Viscosity, Kinematic _St stokes Viscosity, Dynamic _P poise Frequency _GHz gigahertz _kHz kilohertz _Hz hertz (SI) (ENG/US _MHz megahertz Constants and Measurement Units 299
Electric Current _A ampere (SI) (ENG/US) _mA milliampere _kA kiloampere _mA microampere Charge _coul coulomb (SI) (ENG/US) Potential _kV kilovolt _V volt (SI) (ENG/US) _mV millivolt _volt volt Resistance _kJ kilo ohm _ohm ohm _MJ megaohm _J ohm (SI) (ENG/US) Conductance _mho mho (ENG/US) _siemens siemens (SI) _mmho millimho _mmho micromho Constants and Measurement Units 300
Capacitance _F farad (SI) (ENG/US) _pF picofarad _nF nanofarad _mF microfarad Mag Field Strength _Oe oersted NONE (SI) (ENG/US) Mag Flux Density _Gs gauss _T tesla (SI) (ENG/US) Magnetic Flux _Wb weber (SI) (ENG/US) Inductance _henry henry (SI) (ENG/US) _nH nanohenry _mH millihenry _mH microhenry Constants and Measurement Units 301
Basic Function Graphing Overview of Steps in Graphing Functions To graph one or more y(x) functions, use the general steps shown below. For a detailed description of each step, refer to the following pages. You may not need to do all the steps each time you graph a function. Graphing Functions 1. Set Graph mode (3) to FUNCTION. Also set Angle mode, if necessary. 2. Define x and y components on Y= Editor (8 #). 3. Select (†) which defined functions to graph.
4. Set the display style for a function. 2ˆ This is optional. For multiple equations, this helps visually distinguish one from another. 5. Define the viewing window (8 $). „ Zoom also changes the viewing window. 6. Change the graph format if necessary. ƒ9 – or – 8Í 7. Graph the selected functions (8 %). Exploring the Graph From the Graph screen, you can: • Display the coordinates of any pixel by using the free-moving cursor, or of a plotted point by tracing a function.
• Use the ‡ Math toolbar menu to find a zero, minimum, maximum, etc. Setting the Graph Mode Before graphing y(x) functions, you must select FUNCTION graphing. You may also need to set the Angle mode, which affects how the TI-89 Titanium graphs trigonometric functions. Graph Mode 1. Press 3 to display the MODE dialog box, which shows the current mode settings. 2. Set the Graph mode to FUNCTION. Refer to “Setting Modes” in Operating the Calculator.
Graph Mode Setting Description POLAR r(q) polar equations SEQUENCE u(n) sequences 3D z(x,y) 3D equations DIFFERENTIAL EQUATION y'(t) differential equations Angle Mode When using trigonometric functions, set the Angle mode for the units (RADIAN, DEGREE or GRADIAN) in which you want to enter and display angle values. Checking the Status Line To see the current Graph mode and Angle mode, check the status line at the bottom of the screen.
the current graphing mode. For example, in POLAR graphing mode, function names are r1(q), r2(q), etc.) Defining a New Function 1. Press 8 # to display the Y= Editor. Plots — You can scroll above y1= to see a list of stat plots. Function List — You can scroll through the list of functions and definitions. Entry Line — Where you define or edit the function highlighted in the list. Note: The function list shows abbreviated function names such as y1, but the entry line shows the full name y1(x). 2.
The function list now shows the new function, which is automatically selected for graphing. Note: If you accidentally move the cursor to the entry line, press N to move it back to the function list. Editing a Function From the Y= Editor: 1. Press D and C to highlight the function. 2. Press ¸ or … to move the cursor to the entry line. 3. Do any of the following: • Use B and A to move the cursor within the expression and edit it.
Clearing a Function From the Y= Editor: To erase: Do this: A function from the function list Highlight the function and press 0 or M. A function from the entry line Press M once or twice (depending on the cursor’s location) and then press ¸. All functions Press ƒ and then select 8:Clear Functions. When prompted for confirmation, press ¸. Note: ƒ 8 does not erase any stat plots. You don’t have to clear a function to prevent it from being graphed. You can select the functions you want to graph.
From the Home Screen or a Program You can also define and evaluate a function from the Home screen or a program. • Use the Define and Graph commands. Refer to: - • “Graphing a Function Defined on the Home Screen” and “Graphing a Piecewise Defined Function” in Additional Graphing Topics. “Overview of Entering a Function” in Programming. Store an expression directly to a function variable. Refer to: - “Storing and Recalling Variable Values” in Operating the Calculator.
Selected If PLOT numbers are displayed, those stat plots are selected. Deselected In this example, Plots 1 and 2 are selected. To view them, scroll above y1=. To select or deselect: Do this: A specified function • Move the cursor to highlight the function. • Press †. This procedure selects a deselected function or deselects a selected function. All functions • Press ‡ to display the All toolbar menu. • Select the applicable item.
• Use the FnOn and FnOff commands (available from the Home screen’s † Other toolbar menu) for functions. Refer to the Technical Reference module. • Use the PlotsOn and PlotsOff commands for stat plots. Refer to the Technical Reference module. Setting the Display Style for a Function For each defined function, you can set a style that specifies how that function will be graphed. This is useful when graphing multiple functions. For example, set one as a solid line, another as a dotted line, etc.
3. To make a change, select the applicable style. Style Description Line Connects plotted points with a line. This is the default. Dot Displays a dot at each plotted point. Square Displays a solid box at each plotted point. Thick Connects plotted points with a thick line. Animate A round cursor moves along the leading edge of the graph but does not leave a path. Path A round cursor moves along the leading edge of the graph and does leave a path. Above Shades the area above the graph.
From the Home Screen or a Program You can also set a function’s style from the Home screen or a program. Refer to the Style command in the Technical Reference module. Defining the Viewing Window The viewing window represents the portion of the coordinate plane displayed on the Graph screen. By setting Window variables, you can define the viewing window’s boundaries and other attributes. Function graphs, parametric graphs, etc., have their own independent set of Window variables.
Variable Description xscl, yscl Distance between tick marks on the x and y axes. xres Sets pixel resolution (1 through 10) for function graphs. The default is 2. • At 1, functions are evaluated and graphed at each pixel along the x axis. • At 10, functions are evaluated and graphed at every 10th pixel along the x axis. To turn off tick marks, set xscl=0 and/or yscl=0. Small values of xres improve the graph’s resolution but may reduce the graphing speed.
From the Home Screen or a Program You can also store values directly to the Window variables from the Home screen or a program. Refer to “Storing and Recalling Variable Values” in Operating the Calculator. Changing the Graph Format You can set the graph format to show or hide reference elements such as the axes, a grid, and the cursor’s coordinates. Function graphs, parametric graphs, etc., have their own independent set of graph formats.
Format Description Graph Order Graphs functions one at a time (SEQ) or all at the same time (SIMUL). Not available when Discontinuity Detection is set to ON. Grid Shows (ON) or hides (OFF) grid points that correspond to the tick marks on the axes. Axes Shows (ON) or hides (OFF) the x and y axes. Leading Cursor Shows (ON) or hides (OFF) a reference cursor that tracks the functions as they are graphed. Labels Shows (ON) or hides (OFF) labels for the x and y axes.
4. After changing all applicable format settings, press ¸ to save your changes and close the GRAPH FORMATS dialog box. Note: To cancel a menu or exit the dialog box without saving any changes, use N instead of ¸. Graphing the Selected Functions When you are ready to graph the selected functions, display the Graph screen. This screen uses the display style and viewing window that you previously defined. Displaying the Graph Screen Press 8 %. The TI-89 Titanium automatically graphs the selected functions.
• To pause graphing temporarily, press ¸. (The PAUSE indicator replaces BUSY.) To resume, press ¸ again. • To cancel graphing, press ´. To start graphing again from the beginning, press † (ReGraph). If You Need to Change the Viewing Window Depending on various settings, a function may be graphed such that it is too small, too large, or offset too far to one side of the screen. To correct this: • Redefine the viewing window with different boundaries. • Use a Zoom operation.
• Changed a stat plot definition. Displaying Coordinates with the Free-Moving Cursor To display the coordinates of any location on the Graph screen, use the free-moving cursor. You can move the cursor to any pixel on the screen; the cursor is not confined to a graphed function. Free-Moving Cursor When you first display the Graph screen, no cursor is visible. To display the cursor, press a cursor pad arrow. The cursor moves from the center of the screen, and its coordinates are displayed.
To move the free-moving cursor: Press: In increments of 10 pixels 2 and then a cursor pad arrow. Note: To hide the cursor and its coordinates temporarily, press M, N, or ¸. The next time you move the cursor, it moves from its last position. When you move the cursor to a pixel that appears to be “on” the function, it may be near the function but not on it. Cursor coordinates are for the center of the pixel, not the function.
Tracing a Function To display the exact coordinates of any plotted point on a graphed function, use the … Trace tool. Unlike the free-moving cursor, the trace cursor moves only along a function’s plotted points. Beginning a Trace From the Graph screen, press …. The trace cursor appears on the function, at the middle x value on the screen. The cursor’s coordinates are displayed at the bottom of the screen.
To move the trace cursor: Do this: To a specified x value on the function Type the x value and press ¸. Note: If you enter an x value, it must be between xmin and xmax. The trace cursor moves only from plotted point to plotted point along the function, not from pixel to pixel. Function number being traced. For example: y3(x). Trace coordinates are those of the function, not the pixel. If your screen does not show coordinates, set the graph format so that Coordinates = RECT or POLAR.
Moving from Function to Function Press C or D to move to the previous or next selected function at the same x value. The new function number is shown on the screen. The “previous or next” function is based on the order of the selected functions in the Y= Editor, not the appearance of the functions as graphed on the screen. Automatic Panning If you trace a function off the left or right edge of the screen, the viewing window automatically pans to the left or right.
Using QuickCenter If you trace a function off the top or bottom of the viewing window, you can press ¸ to center the viewing window on the cursor location. Before using QuickCenter After using QuickCenter After QuickCenter, the cursor stops tracing. If you want to continue tracing, press …. You can use QuickCenter at any time during a trace, even when the cursor is still on the screen. Canceling Trace To cancel a trace at any time, press N.
Using Zooms to Explore a Graph The „ Zoom toolbar menu has several tools that let you adjust the viewing window. You can also save a viewing window for later use. Overview of the Zoom Menu Press „ from the Y= Editor, Window Editor, or Graph screen. Procedures for using ZoomBox, ZoomIn, ZoomOut, ZoomStd, Memory, and SetFactors are given later in this section. For more information about the other items, refer to the Technical Reference module.
Zoom Tool Description ZoomStd Sets Window variables to their default values. xmin = L10 ymin = L10 xres = 2 xmax = 10 ymax = 10 xscl = 1 yscl = 1 ZoomTrig Sets Window variables to preset values that are often appropriate for graphing trig functions. Centers the origin and sets: @x = p/24 (.130899... radians ymin = -4 or 7.5 degrees) ymax = 4 xscl = p/2 (1.570796... radians yscl = 0.5 or 90 degrees) ZoomInt Lets you select a new center point, and then sets @x and @y to 1 and sets xscl and yscl to 10.
Zooming In with a Zoom Box 1. From the „ Zoom menu, select 1:ZoomBox. The screen prompts for 1st Corner? 2. Move the cursor to any corner of the box you want to define, and then press ¸. y1(x)=2øsin(x) The cursor changes to a small square, and the screen prompts for 2nd Corner? Note: To move the cursor in larger increments, use 2 B, 2 D, etc. 3. Move the cursor to the opposite corner of the zoom box. As you move the cursor, the box stretches. 4.
Zooming In and Out on a Point 1. From the „ Zoom menu, select 2:ZoomIn or 3:ZoomOut. A cursor appears, and the screen prompts for New Center? 2. Move the cursor to the point where you want to zoom in or out, and then press ¸. The TI-89 Titanium adjusts the Window variables by the Zoom factors defined in SetFactors. • For a ZoomIn, the x variables are divided by xFact, and the y variables are divided by yFact. new xmin = xmin/xFact , etc.
1. From the „ Zoom menu, select C:SetFactors to display the ZOOM FACTORS dialog box. Zoom factors must be ‚ 1, but they do not have to be integers. The default setting is 4. Note: To exit without saving any changes, press N. 2. Use D and C to highlight the value you want to change. Then: • Type the new value. The old value is cleared automatically when you begin typing. – or – • Press A or B to remove the highlighting, and then edit the old value. 3.
Select: To: 1:ZoomPrev Return to the viewing window displayed before the previous zoom. 2:ZoomSto Save the current viewing window. (The current Window variable values are stored to the system variables zxmin, zxmax, etc.) 3:ZoomRcl Recall the viewing window last stored with ZoomSto. Note: You can store only one set of Window variable values at a time. Storing a new set overwrites the old set.
Overview of the Math Menu Press ‡ from the Graph screen. On the Derivatives submenu, only dy/dx is available for function graphing. The other derivatives are available for other graphing modes (parametric, polar, etc.). Math Tool Description Value Evaluates a selected y(x) function at a specified x value. Zero, Minimum, Maximum Finds a zero (x-intercept), minimum, or maximum point within an interval. Intersection Finds the intersection of two functions.
Math Tool Description Shade Depends on the number of functions graphed. • If only one function is graphed, this shades the function’s area above or below the x axis. • If two or more functions are graphed, this shades the area between any two functions within an interval. Note: For Math results, cursor coordinates are stored in system variables xc and yc (rc and qc if you use polar coordinates). Derivatives, integrals, distances, etc., are stored in the system variable sysMath.
You can also display function coordinates by tracing the function (…), typing an x value, and pressing ¸. Finding a Zero, Minimum, or Maximum within an Interval 1. From the Graph screen, press ‡ and select 2:Zero, 3:Minimum, or 4:Maximum. 2. As necessary, use D and C to select the applicable function. Note: Typing x values is a quick way to set bounds. 3. Set the lower bound for x. Either use A and B to move the cursor to the lower bound or type its x value. 4. Press ¸.
5. Press ¸. A 4 at the top of the screen marks the lower bound. 6. Set the upper bound, and press ¸. The cursor moves to the intersection, and its coordinates are displayed. y2(x)=2xN7 Finding the Derivative (Slope) at a Point 1. From the Graph screen, press ‡ and select 6:Derivatives. Then select 1:dy/dx from the submenu. 2. As necessary, use D and C to select the applicable function. 3. Set the derivative point. Either move the cursor to the point or type its x value. 4. Press ¸.
3. Set the lower limit for x. Either use A and B to move the cursor to the lower limit or type its x value. 4. Press ¸. A 4 at the top of the screen marks the lower limit. Note: To erase the shaded area, press † (ReGraph). 5. Set the upper limit, and press ¸. The interval is shaded, and its approximate numerical integral is displayed. Finding an Inflection Point within an Interval 1. From the Graph screen, press ‡ and select 8:Inflection. 2. As necessary, use D and C to select the applicable function. 3.
2. As necessary, use D and C to select the function for the first point. 3. Set the first point. Either use A or B to move the cursor to the point or type its x value. 4. Press ¸. A + marks the point. 5. If the second point is on a different function, use D and C to select the function. 6. Set the second point. (If you use the cursor to set the point, a line is drawn as you move the cursor.) 7. Press ¸. The distance between the two points is displayed, along with the connecting line.
Finding an Arc Length 1. From the Graph screen, press ‡ and select B:Arc. 2. As necessary, use D and C to select the applicable function. 3. Set the first point of the arc. Either use A or B to move the cursor or type the x value. 4. Press ¸. A + marks the first point. 5. Set the second point, and press ¸. A + marks the second point, and the arc length is displayed. Shading the Area between a Function and the x Axis You must have only one function graphed.
3. Set the lower bound for x. Either use A and B to move the cursor to the lower bound or type its x value. Note: If you do not press A or B, or type an x value when setting the lower and upper bound, xmin and xmax will be used as the lower and upper bound, respectively. 4. Press ¸. A 4 at the top of the screen marks the lower bound. 5. Set the upper bound, and press ¸. The bounded area is shaded. To erase the shaded area, press † (ReGraph).
6. Set the lower bound for x. Either use A and B to move the cursor to the lower bound or type its x value. Note: If you do not press A or B, or type an x value when setting the lower and upper bound, xmin and xmax will be used as the lower and upper bound, respectively. 7. Press ¸. A 4 at the top of the screen marks the lower bound. 8. Set the upper bound, and press ¸. The bounded area is shaded. To erase the shaded area, press † (ReGraph).
Polar Graphing Overview of Steps in Graphing Polar Equations To graph polar equations, use the same general steps used for y(x) functions as described in Basic Function Graphing. Any differences that apply to polar equations are described on the following pages. Graphing Polar Equations 1. Set Graph mode (3) to POLAR. Also set Angle mode, if necessary. 2. Define x and y components on Y= Editor (8 #). 3. Select (†) which defined equations to graph. Select the x or y component, or both.
4. Set the display style for an equation. You can set either the x or y component. 2ˆ This is optional. For multiple equations, this helps visually distinguish one from another. 5. Define the viewing window (8 $). „ Zoom also changes the viewing window. 6. Change the graph format if necessary. ƒ9 – or – 8Í 7. Graph the selected equations (8 %).
• Use the „ Zoom toolbar menu to zoom in or out on a portion of the graph. • Use the ‡ Math toolbar menu to find derivatives, tangents, etc. Some menu items are not available for polar graphs. Differences in Polar and Function Graphing This module assumes that you already know how to graph y(x) functions as described in Basic Function Graphing. This section describes the differences that apply to polar equations.
You can use the Define command from the Home screen (see the Technical Reference module) to define functions and equations for any graphing mode, regardless of the current mode. The Y= Editor maintains an independent function list for each Graph mode setting. For example, suppose: • In FUNCTION graphing mode, you define a set of y(x) functions. You change to POLAR graphing mode and define a set of r(q) equations.
Variable Description qstep Increment for the q value. Polar equations are evaluated at: r(qmin) r(qmin+qstep) r(qmin+2(qstep)) ... not to exceed ... r(qmax) xmin, xmax, ymin, ymax Boundaries of the viewing window. xscl, yscl Distance between tick marks on the x and y axes. Note: You can use a negative qstep. If so, qmin must be greater than qmax. Standard values (set when you select 6:ZoomStd from the „ Zoom toolbar menu) are: qmin = 0. xmin = L10. ymin = L10. xmax = 10. ymax = 10.
ƒ9 – or – 8Í to set Coordinates = POLAR. If Coordinates = RECT, the polar equations will be graphed properly, but coordinates will be displayed as x and y. When you trace a polar equation, the q coordinate is shown even if Coordinates = RECT. Exploring a Graph As in function graphing, you can explore a graph by using the following tools. Any displayed coordinates are shown in polar or rectangular form as set in the graph format.
Tool For Polar Graphs: … Trace Lets you move the cursor along a graph one qstep at a time. ‡ Math • When you begin a trace, the cursor is on the first selected equation at qmin. • QuickCenter applies to all directions. If you move the cursor off the screen (top or bottom, left or right), press ¸ to center the viewing window on the cursor location. • Automatic panning is not available.
Parametric Graphing Overview of Steps in Graphing Parametric Equations To graph parametric equations, use the same general steps used for y(x) functions as described in Basic Function Graphing. Any differences that apply to parametric equations are described on the following pages. Graping Parametic Equations 1. Set Graph mode (3) to PARAMETRIC. Also set Angle mode, if necessary. 2. Define x and y components on Y= Editor (8 #). 3. Select (†), which defined equations to graph.
4. Set the display style for an equation. You can set either the x or y component. 2ˆ This is optional. For multiple equations, this helps visually distinguish one from another. 5. Define the viewing window (8 $). „ Zoom also changes the viewing window. 6. Change the graph format if necessary. ƒ9 – or – 8Í 7. Graph the selected equations (8 %).
• Use the „ Zoom toolbar menu to zoom in or out on a portion of the graph. • Use the ‡ Math toolbar menu to find derivatives, tangents, etc. Some menu items are not available for parametric graphs. Differences in Parametric and Function Graphing This module assumes that you already know how to graph y(x) functions as described in Basic Function Graphing. This section describes the differences that apply to parametric equations.
Be careful when using implied multiplication with t. For example: Enter: Instead of: Because: tùcos(60) tcos(60) tcos is interpreted as a user-defined function called tcos, not as implied multiplication. In most cases, this refers to a nonexistent function. So the TI-89 Titanium simply returns the function name, not a number. Note: When using t, be sure implied multiplication is valid for your situation.
Selecting the Display Style You can set the style for either the x or y component. For example, if you set the x component to Dot, the TI-89 Titanium automatically sets the y component to Dot. Note: Use the Animate and Path styles for interesting projectile-motion effects. The Above and Below styles are not available for parametric equations and are dimmed on the Y= Editor’s Style toolbar menu.
Variable Description xscl, yscl Distance between tick marks on the x and y axes. Standard values (set when you select 6:ZoomStd from the „ Zoom toolbar menu) are: tmin = 0 xmin = L10. ymin = L10. tmax = 2p (6.2831853... radians or 360 degrees) xmax = 10. ymax = 10. tstep =p/24 (.1308996... radians or 7.5 degrees) xscl = 1. yscl = 1. You may need to change the standard values for the t variables (tmin, tmax, tstep) to ensure that enough points are plotted.
Tool For Parametric Graphs: „ Zoom Works just as it does for function graphs, with the following exceptions: … Trace ‡ Math • Only x (xmin, xmax, xscl) and y (ymin, ymax, yscl) Window variables are affected. • The t Window variables (tmin, tmax, tstep) are not affected unless you select 6:ZoomStd (which sets tmin = 0, tmax = 2p, and tstep = p/24). Lets you move the cursor along a graph one tstep at a time. • When you begin a trace, the cursor is on the first selected parametric equation at tmin.
Sequence Graphing Overview of Steps in Graphing Sequences To graph sequences, use the same general steps used for y(x) functions as described in Basic Function Graphing. Any differences are described on the following pages. Graphing Sequences 1. Set Graph mode (3) to SEQUENCE. Also set Angle mode, if necessary. 2. Define sequences and, if needed, initial values on Y= Editor (8 #). 3. Select (†) which defined sequences to graph. Do not select initial values.
5. Define the viewing window (8 $). „ Zoom also changes the viewing window. 6. Change the graph format if necessary. ,9 — or — 8Í 7. Graph the selected equations (8 %). Exploring the Graph From the Graph screen, you can: • Display the coordinates of any pixel by using the free-moving cursor, or of a plotted point by tracing a sequence. • Use the „ Zoom toolbar menu to zoom in or out on a portion of the graph. • Use the ‡ Math toolbar menu to evaluate a sequence.
Differences in Sequence and Function Graphing This module assumes that you already know how to graph y(x) functions as described in Basic Function Graphing. This section describes the differences that apply to sequences. Setting the Graph Mode Use 3 to set Graph = SEQUENCE before you define sequences or set Window variables. The Y= Editor and the Window Editor let you enter information for the current Graph mode setting only.
If a sequence requires an initial value but you do not enter one, you will get an error when graphing. On the Y= Editor, Axes lets you select the axes that are used to graph the sequences. Optionally, for sequences only, you can select different axes for the graph. TIME is the default. Axes Description TIME Plots n on the x axis and u(n) on the y axis. WEB Plots u(n-1) on the x axis and u(n) on the y axis. CUSTOM Lets you select the x and y axes.
Selecting Sequences With TIME and WEB axes, the TI-89 Titanium graphs only the selected sequences. If you entered any sequences that require an initial value, you must enter the corresponding ui value. Note: With TIME and CUSTOM axes, all defined sequences are evaluated even if they are not plotted. You can select a sequence You cannot select its initial value. With CUSTOM axes, when you specify a sequence in the custom settings, it is graphed regardless of whether it is selected.
Window Variables The Window Editor maintains an independent set of Window variables for each Graph mode setting (just as the Y= Editor maintains independent function lists). Sequence graphs use the following Window variables. Variable Description nmin, nmax Smallest and largest n values to evaluate. Sequences are evaluated at: u(nmin) u(nmin+1) u(nmin+2) ... not to exceed ... u(nmax) plotStrt The term number that will be the first one plotted (depending on plotstep).
Standard values (set when you select 6:ZoomStd from the „ Zoom toolbar menu) are: nmin = 1. nmax = 10. plotstrt = 1. plotstep = 1. xmin = L10. xmax = 10. xscl = 1. ymin = L10. ymax = 10. yscl = 1. You may need to change the standard values for the n and plot variables to ensure that sufficient points are plotted. To see how plotstrt affects graph, look at the following examples of a recursive sequence. This graph is plotted beginning with the 1st term.
With TIME axes (from Axes on the Y= Editor), you can set plotstrt = 1 and still graph only a selected part of the sequence. Simply define a viewing window that shows only the area of the coordinate plane you want to view. You could set: • xmin = first n value to graph • xmax = nmax (although you can use other values) • plotStrt= nma ymin and ymax = expected values for the sequence Changing the Graph Format The Graph Order format is not available.
Tool For Sequence Graphs: „ Zoom Works just as it does for function graphs. … Trace • Only x (xmin, xmax, xscl) and y (ymin, ymax, yscl) Window variables are affected. • The n and plot Window variables (nmin, nmax, plotStrt, plotStep) are not affected unless you select 6:ZoomStd (which sets all Window variables to their standard values). Depending on whether you use TIME, CUSTOM, or WEB axes, Trace operates very differently.
During a trace, you can evaluate a sequence by typing a value for n and pressing ¸. You can use QuickCenter at any time during a trace, even if the cursor is still on the screen. Setting Axes for Time, Web, or Custom Plots For sequences only, you can select different types of axes for the graph. Examples of the different types are given later in this module. Displaying the AXES Dialog Box From the Y= Editor, Axes: • Depending on the current Axes setting, some items may be dimmed.
Item Description X Axis and Y Axis Active only when Axes = CUSTOM, these let you select the value or sequence to plot on the x and y axes. To change any of these settings, use the same procedure that you use to change other types of dialog boxes, such as the MODE dialog box. Using Web Plots A web plot graphs u(n) vs. u(nN1), which lets you study the long-term behavior of a recursive sequence. The examples in this section also show how the initial value can affect a sequence’s behavior.
• Draws a y=x reference line. • Plots the selected sequence definitions as functions, with u(nN1) as the independent variable. This effectively converts a recursive sequence into a nonrecursive form for graphing. For example, consider the sequence u1(n) = 5 – u1 ( n – 1 ) and an initial value of ui1=1. The TI-89 Titanium draws the y=x reference line and then plots y = y = 5–x.
3. Moves horizontally to the y=x reference line. 4. Repeats this vertical and horizontal movement until n=nmax. Note: The web starts at plotstrt. The value of n is incremented by 1 each time the web moves to the sequence (plotStep is ignored). Example: Convergence 1. On the Y= Editor (8 #), define u1(n) = L.8u1(nN1) + 3.6. Set initial value ui1 = L4. 2. Set Axes = TIME. 3. On the Window Editor (8 $), set the Window variables.
6. On the Window Editor, change the Window variables. nmin=1 nmax=25 plotstrt=1 plotstep=1 xmin= L10 xmax=10 xscl=1 ymin=L10 ymax=10 yscl=1 7. Regraph the sequence. Web plots are always shown as lines, regardless of the selected display style. Note: During a trace, you can u(n) y=L.8x + 3.6 u(nN1) y=x move the cursor to a specified n value by typing the value and pressing ¸. 8. Press …. As you press B, the trace cursor follows the web.
Example: Divergence 1. On the Y= Editor (8 #), define u1(n) = 3.2u1(nN1) N .8(u1(nN1)) 2. Set initial value ui1 = 4.45. 2. Set Axes = TIME. 3. On the Window Editor (8 $), set the Window variables. nmin=0 nmax=10 plotstrt=1 plotstep=1 xmin=0 xmax=10 xscl=1 ymin=L75 ymax=10 yscl=1 4. Graph the sequence (8 %). u(n) Because the sequence quickly diverges to large negative values, only a few points are plotted. n 5. On the Y= Editor, set Axes = WEB and Build Web = AUTO. 6.
7. Regraph the sequence. u(n The web plot shows how quickly the sequence diverges to large negative values. u(nN1) y=x y=3.2xN.8x2 Example: Oscillation This example shows how the initial value can affect a sequence. 1. On the Y= Editor (8 #), use the same sequence defined in the divergence example: u1(n) = 3.2u1(nN1) N .8(u1(nN1)) 2. Set initial value ui1 = 0.5. 2. Set Axes = TIME. 3. On the Window Editor (8 $), set the Window variables.
6. On the Window Editor (8 $), set the Window variables. nmin=1 nmax=100 plotstrt=1 plotstep=1 xmin=2.68 xmax=6.47 xscl=1 ymin=4.7 ymax=47 yscl=1 7. Regraph the sequence. u(n) u(nN1) Note: The web moves to an orbit oscillating between two stable points. y=x y=3.2xN.8x2 8. Press …. Then use B to trace the web. As you trace to larger values of nc, notice that xc and yc oscillate between 2.05218 and 3.19782. 9. On the Window Editor, set plotstrt=50. Then regraph the sequence.
Example: Predator-Prey Model Using the predator-prey model in biology, determine the numbers of rabbits and foxes that maintain population equilibrium in a certain region. R = Number of rabbits M = Growth rate of rabbits if there are no foxes (use .05) K = Rate at which foxes can kill rabbits (use .001) W = Number of foxes G = Growth rate of foxes if there are rabbits (use .0002) D = Death rate of foxes if there are no rabbits (use .
3. On the Window Editor (8 $), set the Window variables. nmin=0 nmax=400 plotstrt=1 plotstep=1 xmin=0 xmax=400 xscl=100 4. Graph the sequence (8 %). Note: Use … to individually trace the number of rabbits ymin=0 ymax=300 yscl=100 u(n) u1(n) u2(n) u1(n) and foxes u2(n) over time (n). 5. On the Y= Editor, set Axes = CUSTOM, X Axis = u1, and Y Axis = u2. 6. On the Window Editor (8 $), set the Window variables. nmin=0 nmax=400 plotstrt=1 plotstep=1 xmin=84 xmax=237 xscl=50 ymin=25 ymax=75 yscl=10 7.
Using a Sequence to Generate a Table Previous sections described how to graph a sequence. You can also use a sequence to generate a table. Refer to Tables for detailed information. Example: Fibonacci Sequence In a Fibonacci sequence, the first two terms are 1 and 1. Each succeeding term is the sum of the two immediately preceding terms. 1. On the Y= Editor (8 #), define the sequence and set the initial values as shown. You must enter {1,1}, although {1 1} is shown in the sequence list. 2.
3. Set Window variables (8 $) so that nmin has the same value as tblStart. 4. Display the table (8 '). Fibonacci sequence is in column 2. 5. Scroll down the table (D or 2 D) to see more of the sequence.
3D Graphing Overview of Steps in Graphing 3D Equations To graph 3D equations, use the same general steps used for y(x) functions as described in Basic Function Graphing. Any differences that apply to 3D equations are described on the following pages. Graphing 3D Equations 1. Set Graph mode (3) to 3D. Also set Angle mode, if necessary. 2. Define 3D equations on Y= Editor (8 #). 3. Select (†) which equation to graph. You can select only one 3D equation.
5. Change the graph format if necessary. ƒ9 – or 8Í Note: To help you see the orientation of 3D graphs, turn on Axes and Labels. 6. Graph the selected equations (8 %). Note: Before displaying the graph, the screen shows the “percent evaluated.” Exploring the Graph From the Graph screen, you can: • Trace the equation. • Use the „ Zoom toolbar menu to zoom in or out on a portion of the graph. Some of the menu items are dimmed because they are not available for 3D graphs.
Differences in 3D and Function Graphing This module assumes that you already know how to graph y(x) functions as described in Basic Function Graphing. This section describes the differences that apply to 3D equations. Setting the Graph Mode Use 3 to set Graph = 3D before you define equations or set Window variables. The Y= Editor and the Window Editor let you enter information for the current Graph mode setting only.
• When you return to FUNCTION graphing mode, your y(x) functions are still defined in the Y= Editor. When you return to 3D graphing mode, your z(x,y) equations are still defined. Note: You can use the Define command from the Home screen (see the Technical Reference module) to define functions and equations for any graphing mode, regardless of the current mode. Selecting the Display Style Because you can graph only one 3D equation at a time, display styles are not available.
Variable Description xmin, xmax, ymin, ymax, zmin, zmax Boundaries of the viewing cube. xgrid, ygrid The distance between xmin and xmax and between ymin and ymax is divided into the specified number of grids. The z(x,y) equation is evaluated at each grid point where the grid lines (or grid wires) intersect.
Note: If you enter a fractional number for xgrid or ygrid, it is rounded to the nearest whole number | 1. The 3D mode does not have scl Window variables, so you cannot set tick marks on the axes. Standard values (set when you select 6:ZoomStd from the „ Zoom toolbar menu) are: eyeq = 20. eyef = 70. eyeψ = 0. xmin = L10. xmax = 10. xgrid = 14. ymin = L10. ymax = 10. ygrid = 14. zmin = L10. zmax = 10. ncontour = 5.
8Í to set Coordinates = POLAR. Tool For 3D Graphs: Free-Moving Cursor The free-moving cursor is not available. „ Zoom Works essentially the same as it does for function graphs, but remember that you are now using three dimensions instead of two. … Trace 3D Graphing • Only the following zooms are available: 2:ZoomIn, 3:ZoomOut, 5:ZoomSqr, 6:ZoomStd, A:ZoomFit, B:Memory, C:SetFactors • Only x (xmin, xmax), y (ymin, ymax), and z (zmin, zmax) Window variables are affected.
Tool For 3D Graphs: ‡ Math Only 1:Value is available for 3D graphs. This tool displays the z value for a specified x and y value. After selecting 1:Value, type the x value and press ¸. Then type the y value and press ¸. Note: During a trace, you can also evaluate z(x,y). Type the x value and press ¸; then type the y value and press ¸. Moving the Cursor in 3D When you move the cursor along a 3D surface, it may not be obvious why the cursor moves as it does.
Note: You can move the cursor only within the x and y boundaries set by Window variables xmin, xmax, ymin, and ymax. Although the rules are straightforward, the actual cursor movement can be confusing unless you know the orientation of the axes. In 2D graphing, the x and y axes always have the same orientation relative to the Graph screen. In 3D graphing, x and y have a different orientation relative to the Graph screen. Also, you can rotate and/or elevate the viewing angle.
When you press …, the trace cursor appears at the midpoint of the xy grid. Use the cursor pad to move the cursor to any edge. B moves in a positive D moves in a negative x direction, up to xmax. y direction, back to ymin. C moves in a positive y direction, up to ymax. A moves in a negative x direction, back to xmin. By displaying and labeling the axes, you can more easily see the pattern in the cursor movement. To move grid points closer together, you can increase Window variables xgrid and ygrid.
For example, consider a saddle shape z1(x,y) = (x2Ny2) / 3. The following graph shows the view looking down the y axis. Now look at the same shape at 10¡ from the x axis (eyeq = 10). You can move the cursor so that it does not appear to be on a grid point. If you cut away the front side, you can see the cursor is actually on a grid point on the hidden back side. Note: To cut away the front of the saddle in this example, set xmax=0 to show only negative x values.
For example, suppose you trace the paraboloid z(x,y) = x2 + .5y2 graphed with the indicated Window variables. You can easily move the cursor to a position such as: Trace cursor Valid trace coordinates Although the cursor is actually tracing the paraboloid, it appears off the curve because the trace coordinates: • xc and yc are within the viewing cube. – but – • zc is outside the viewing cube. Note: QuickCenter lets you center the viewing cube on the cursor’s location. Simply press ¸.
How the Viewing Angle Is Measured The viewing angle has three components: • Z eyef eyeq — angle in degrees from the positive x axis. • eyef — angle in degrees from the eye X positive z axis. • Y eyeq eyeψ — angle in degrees by which the graph is rotated counter-clockwise around the line of sight set by eyeq and eyef. Do not enter a ¡symbol. For example, type 20, 70, and 0, not 20¡, 70¡ and 0¡. Note: When eyeψ=0, the z axis is vertical on the screen.
Effect of Changing eyeq eye theta The view on the Graph screen is always oriented along the viewing angle. From this point of view, you can change eyeq to rotate the viewing angle around the z axis. z1(x,y) = (x3y – y3x) / 390 In this example eyef = 70 eyeq = 20 eyeq = 50 eyeq = 80 Note: This example increments eyeq by 30.
Effect of Changing eyef eye phi By changing eyef, you can elevate your viewing angle above the xy plane. If 90 < eyef < 270, the viewing angle is below the xy plane. z1(x,y) = (x 3y – y 3x) / 390 In this example eyeq = 20 eyef = 90 eyef = 70 eyef = 50 Note: This example starts on the xy plane (eyef = 90) and decrements eyef by 20 to elevate the viewing angle. Effect of Changing eyeψ eye psi The view on the Graph screen is always oriented along the viewing angles set by eyeq and eyef.
Note: During rotation, the axes expand or contract to fit the screen’s width and height. This causes some distortion as shown in the example. 3 In this example, eyeq=20 and eyef=70 3 z1(x,y)=(x y–y x) / 390 eyeψ = 0 eyeψ = 45 eyeψ = 90 When eyeψ=0, the z axis runs the height of the screen. z=10 z=ë10 When eyeψ=90, the z axis runs the width of the screen.
As the z axis rotates 90¡, its range (L10 to 10 in this example) expands to almost twice its original length. Likewise, the x and y axes expand or contract. From the Home Screen or a Program The eye values are stored in the system variables eyeq, eyef, and eyeψ. You can access or store to these variables as necessary. @ To type f or ψ, press 8 c j [F] or 8 c Ú, respectively. You can also press 2 G and use the Greek menu.
Note: The viewing orbit affects the eye Window variables in differing amounts. Animating the Graph To: Do this: Animate the graph incrementally. Press and release the cursor quickly. Move along the viewing orbit. A or B Change the viewing orbit’s elevation. C or D (primarily increases or decreases eyef) Animate the graph continuously. Press and hold the cursor for about 1 second, and then release it. To stop, press N, ¸, ´, or 8 (space).
• After animating the graph, you can stop and then re-start the animation in the same direction by pressing: ¸ or j • During an animation, you can switch to the next graph format style by pressing: Í • You can view a graphic that shows the eye angles. Animating a Series of Graph Pictures You can also animate a graph by saving a series of graph pictures and then flipping (or cycling) through those pictures. Refer to “Animating a Series of Graph Pictures” Additonal Graphing Topics.
– or 8Í • The dialog box shows the current graph format settings. • To exit without making a change, press N. To change any of these settings, use the same procedure that you use to change other types of dialog boxes, such as the MODE dialog box. Examples of Axes Settings To display the valid Axes settings, highlight the current setting and press B. z1(x,y) = x2+.5y2 • AXES — Shows standard xyz axes. • BOX — Shows 3-dimensional box axes.
Note: Setting Labels = ON is helpful when you display either type of 3D axes. Examples of Style Settings Note: WIRE FRAME is faster to graph and may be more convenient when you’re experimenting with different shapes. To display the valid Style settings, highlight the current setting and press B. • WIRE FRAME — Shows the 3D shape as a transparent wire frame. • HIDDEN SURFACES — Uses shading to differentiate the two sides of the 3D shape.
Optical illusions may be more noticeable with box axes. For example, it may not be immediately obvious which is the “front” of the box. Looking down from above the xy plane Looking up from below the xy plane eyeq = 20, eyef = 55, eyeψ = 0 eyeq = 20, eyef = 120, eyeψ= 0 Note: The first two examples show the graphs as displayed on the screen. The second two examples use artificial shading (which is not displayed on the screen) to show the front of the box.
Selecting the Graph Format Style In 3D graphing mode, define an equation and graph it as you would any 3D equation, with the following exception. Display the GRAPH FORMATS dialog box by pressing ƒ 9 from the Y= Editor, Window editor, or Graph screen. Then set: Style = CONTOUR LEVELS – or – Style = WIRE AND CONTOUR • For CONTOUR LEVELS, only the contours are shown. - • The viewing angle is set initially so that you are viewing the contours by looking down the z axis.
format as it does if you use: 8Í Style z1(x,y)=(x3y–y3x) / 390 z1(x,y)=x2+.5y2–5 Looking down z axis CONTOUR LEVELS Using eyeq=20, eyef=70, eyeψ=0 CONTOUR LEVELS WIRE AND CONTOUR Note: These examples use the same x, y, and z Window variable values as a ZoomStd viewing cube. If you use ZoomStd, press Z to look down the z axis. Do not confuse the contours with the grid lines. The contours are darker.
How Are Z Values Determined? You can set the ncontour Window variable (8 $) to specify the number of contours that will be evenly distributed along the displayed range of z values, where: zmax – zmin increment = -------------------------------- ncontour + 1 The z values for the contours are: zmin + increment zmin + 2(increment) zmin + 3(increment) © zmin + ncontour(increment) The default is 5. You can set this to 0 through 20.
Drawing a Contour for the Z Value of a Selected Point Interactively If a contour graph is currently displayed, you can specify a point on the graph and draw a contour for the corresponding z value. 1. To display the Draw menu, press: 2ˆ 2. Select 7:Draw Contour. 3. Either: • Type the point’s x value and press ¸, and then type the y value and press ¸. – or – • Move the cursor to the applicable point. (The cursor moves along the grid lines.) Then press ¸.
Drawing Contours for Specified Z Values From the Graph screen, display the Draw menu and then select 8:DrwCtour. The Home screen is displayed automatically with DrwCtour in the entry line. You can then specify one or more z values individually or generate a sequence of z values. Some examples are: DrwCtour 5 Draws a contour for z=5. DrwCtour {1,2,3} Draws contours for z=1, 2, and 3. DrwCtour seq(n,n,L10,10,2) Draws contours for a sequence of z values from L10 through 10 in steps of 2 (L10, L8, L6, etc.
• Because of possible long evaluation times, you first may want to experiment with your 3D equation by using Style=WIRE FRAME. The evaluation time is much shorter. Then, after you’re sure you have the correct Window variable values, display the Graph Formats dialog box and set Style=CONTOUR LEVELS or WIRE AND CONTOUR. 8Í Example: Contours of a Complex Modulus Surface The complex modulus surface given by z(a,b) = abs(f(a+bi)) shows all the complex zeros of any polynomial y=f(x).
4. Display the Graph Formats dialog box: 8 Í Turn on the axes, set Style = CONTOUR LEVELS, and return to the Window editor. 5. Press 8 % to graph the equation. It will take awhile to evaluate the graph; so be patient. When the graph is displayed, the complex modulus surface touches the xy plane at exactly the complex zeros of the polynomial: 1 3 1 3 L 1 , --- + ------- i, and --- – ------- i 2 2 2 2 6. Press …, and move the trace cursor to the zero in the fourth quadrant. The coordinates let you estimate .
Notes: • For more accurate estimates, increase the xgrid and ygrid Window variables. However, this increases the graph evaluation time. • When you animate the graph, the screen changes to normal view. Use p to toggle between normal and expanded views. Implicit Plots An implicit plot is used primarily as a way to graph 2D implicit forms that cannot be graphed in function graphing mode. Technically, an implicit plot is a 3D contour plot with a single contour drawn for z=0 only.
By using implicit plots in 3D graphing mode, you can graph these implicit forms without solving for y or x. Rearrange the implicit form as an equation set to zero. f(x,y)–g(x,y)=0 In the Y= Editor, enter the non-zero side of the equation. This is valid because an implicit plot automatically sets the equation equal to zero. z1(x,y)=f(x,y)–g(x,y) For example, given the ellipse equation shown to the right, enter the implicit form in the Y= Editor. If x2+.5y2=30, then z1(x,y)=x2+.5y2–30.
Note: From the Graph screen, you can switch to the other graph format styles by and then set Style = IMPLICIT PLOT. pressing: Í However, to return to IMPLICIT PLOT press: 8Í • The viewing angle is set initially so that you are viewing the plot by looking down the z axis. You can change the viewing angle as necessary. • The plot is shown in expanded view. To switch between expanded and normal view, press p. • The Labels format is set to OFF automatically.
Note: These examples use the same x, y, and z Window variable values as a ZoomStd viewing cube. If you use ZoomStd, press Z to look down the z axis. Notes About Implicit Plots For an implicit plot: • The ncontour Window variable has no affect. Only the z=0 contour is drawn, regardless of the value of ncontour. The displayed plot shows where the implicit form intersects the xy plane. • You can use the cursor keys to animate the plot. • You cannot trace (…) the implicit plot itself.
Example Graph the equation sin(x 4+y–x3 y) = .1. 1. Use 3 to set Graph=3D. 2. Press 8 #, and define the equation: z1(x,y)=sin(x^4+y– x^3y)–.1 3. Press 8 $, and set the Window variables as shown. 4. Press: 8 ÍTurn on the axes, set Style = IMPLICIT PLOT, and return to the Window editor. 5. Press 8 % to graph the equation. It will take awhile to evaluate the graph; so be patient. The graph shows where sin(x 4+y–x 3y) = .
6. Use the cursor keys to animate the graph and view it from different eye angles. Note: For more detail, increase the xgrid and ygrid Window variables. However, In expanded view, this this increases the graph evaluation time. example shows eyeq=L127.85, eyef=52.86, and eyeψ=L18.26. Note: When you animate the graph, the screen changes to normal view. Press p to switch between normal and expanded views.
Differential Equation Graphing Overview of Steps in Graphing Differential Equations To graph differential equations, use the same general steps used for y(x) functions as described in Basic Function Graphing. Any differences are described on the following pages. Graphing Differential Equations 1. Set Graph mode (3) to DIFF EQUATIONS. Also set Angle mode, if necessary. 2. Define equations and, optionally, initial conditions on Y= Editor (8 #). 3. Select (†) which defined functions to graph.
4. Set the display style for a function. @ 2ˆ 5. Set the graph format. Solution Method and Fields are unique to differential equations. ,9 — or — @ 8Í Note: The Fields format is critical, depending on the order of the equation. 6. Set the axes as applicable, depending on the Fields format. @ 2‰ Note: Valid Axes settings depend on the Fields format. 7. Define the viewing window (8 $). Note: Depending on the Solution Method and Fields formats, different Window variables are displayed.
8. Graph the selected functions (8 %). Differences in Diff Equations and Function Graphing This module assumes that you already know how to graph y(x) functions as described in Basic Function Graphing. This section describes the differences. Setting the Graph Mode Use 3 to set Graph = DIFF EQUATIONS before you define differential equations or set Window variables. The Y= Editor and the Window Editor let you enter information for the current Graph mode setting only.
Note: You can use the Define command from the Home screen to define functions and equations. When entering equations in the Y= Editor, do not use y(t) formats to refer to results. For example: Do not use implied multiplication between a variable and parenthetical expression. If you do, it is treated as a function call. Enter: y1' = .001y1ù(100Ny1) Not: y1' = .001y1(t)ù(100Ny1(t)) Only 1st-order equations can be entered in the Y= Editor.
Selecting the Display Style With the Style menu, only the Line, Dot, Square, Thick, Animate, and Path styles are available. Dot and Square mark only those discrete values (in tstep increments) at which a differential equation is plotted. @ 2ˆ Setting Graph Formats From the Y= Editor, Window Editor, or Graph screen, press: ,9 — or — @ 8Í The formats affected by differential equations are: Graph format Description Graph Order Not available.
Graph format Description Fields Specifies whether to draw a field for the differential equation. • SLPFLD — Draws a slope field for only one 1st-order equation, with t on the x axis and the solution on the y axis. • DIRFLD — Draws a direction field for only one 2ndorder equation (or system of two 1st-order equations), with axes determined by the custom axes settings. • FLDOFF — Does not display a field. This is valid for equations of any order, but you must use it for 3rd- or higher-order.
Axes Description TIME Plots t on the x axis and y (the solutions to the selected differential equations) on the y axis. CUSTOM Lets you select the x and y axes. Window Variables Differential equation graphs use the following Window variables. Depending on the Solution Method and Fields graph formats, not all of these variables are listed in the Window Editor (8 $) at the same time. Variable Description t0 Time at which the initial conditions entered in the Y= Editor occur.
Variable Description tplot First t value plotted. If this is not a tstep increment, plotting begins at the next tstep increment. In some situations, the first points evaluated and plotted starting at t0 may not be interesting visually. By setting tplot greater than t0, you can start the plot at the interesting area, which speeds up the graphing time and avoids unnecessary clutter on the Graph screen. Note: If tmax < t0, tstep must be negative.
Variable Description When ncurves is used, t0 is set temporarily at the middle of the screen and initial conditions are distributed evenly along the y axis, where: ymax – ymin increment = -------------------------------ncurves + 1 The y values for the initial conditions are: ymin + increment ymin + 2ù(increment) © ymin + ncurvesù(increment) diftol (Solution Method = RK only) Tolerance used by the RK method to help select a step size for solving the equation; must be ‚1EL14.
Standard values (set when you select 6:ZoomStd from the „ Zoom toolbar menu) are: t0 = 0. tmax = 10. tstep = .1 tplot = 0. xmin = L1. xmax = 10. xscl = 1. ymin = L10. ymax = 10. yscl = 1. ncurves = 0. diftol = .001 Estep = 1. fldres = 14. dtime = 0. You may need to change the standard values for the t variables to ensure that sufficient points are plotted.
Tool For Differential Equation Graphs: „ Zoom Works just as it does for function graphs. … Trace • Only x (xmin, xmax, xscl) and y (ymin, ymax, yscl) Window variables are affected. • The t Window variables (t0, tmax, tstep, tplot) are not affected unless you select 6:ZoomStd (which sets all Window variables to their standard values). Lets you move the cursor along the curve one tstep at a time. To move approximately ten plotted points at a time, press 2 B or 2 A.
Setting the Initial Conditions You can enter initial conditions in the Y= Editor, let the TI-89 Titanium calculate initial conditions automatically, or select them interactively from the Graph screen. Entering Initial Conditions in the Y= Editor You can specify one or more initial conditions in the Y= Editor. To specify more than one, enter them as a list enclosed in braces { } and separated by commas. To enter initial conditions for the y1' equation, use the yi1 line, etc.
If You Do Not Enter an Initial Condition in the Y= Editor If you do not enter initial conditions, the ncurves Window variable (8 $) specifies the number of solution curves graphed automatically. By default, ncurves = 0. You can enter a value from 0 through 10. However, the Fields graph format and the Axes setting determine whether ncurves is used. If Fields = Then: SLPFLD Uses ncurves, if not set to 0, to graph curves. DIRFLD Ignores ncurves. Does not graph any curves.
Selecting an Initial Condition Interactively from the Graph Screen When a differential equation is graphed (regardless of whether a solution curve is displayed), you can select a point on the Graph screen and use it as an initial condition. If Fields = Do this: SLPFLD – or – DIRFLD Press: @ 2Š Specify an initial condition. Either: • Move the cursor to the applicable point and press ¸. – or – • For each of the two coordinates, type a value and press ¸.
If Fields = Do this: FLDOFF • Press: @ 2Š You are prompted to select the axes for which you want to enter initial conditions. t is a valid selection. It will let you specify a value for t0. Your selections will be used as the axes for the graph. • You can accept the defaults or change them. Then press ¸. • Specify an initial condition as described for SLPFLD or DIRFLD.
Defining a System for Higher-Order Equations In the Y= Editor, you must enter all differential equations as 1st-order equations. If you have an nth-order equation, you must transform it into a system of n 1st-order equations. Transforming an Equation into a 1st-Order System A system of equations can be defined in various ways, but the following is a general method. 1. Rewrite the original differential equation as necessary. y'' + y' + y = ex a) Solve for the highest-ordered derivative.
In place of: Substitute: y y' y'' y''' y(4) y1 y2 y3 y4 y5 © © y'' = et N y2 N y1 Do not substitute on the left side at this time. d) On the left side of the equation, substitute for the derivative value as shown below.
2. On the applicable lines in the Y= Editor, define the system of equations as: y1' = y2 y2' = y3 y3' = y4 – up to – yn ' = your nth-order equation Note: Based on the above substitutions, the y' lines in the Y= Editor represent: y1' = y' y2' = y'' etc. Therefore, this example’s 2nd-order equation is entered on the y2' line. In a system such as this, the solution to the y1' equation is the solution to the nth-order equation. You may want to deselect any other equations in the system.
Example 1. Press 3 and set Graph=DIFF EQUATIONS. 2. Define a system of equations for the 2ndorder equation. Rewrite the equation and make the necessary substitutions. 3. In the Y= Editor (8 #), enter the system of equations. y'' + y = 0 y'' = Ly y'' = Ly1 y2' = Ly1 yi1 is the initial condition for y(0). 4. Enter the initial conditions: yi1=0 and yi2=1 Note: t0 is the time at which the initial conditions occur. It is also the first t evaluated for the graph. By default, t0=0.
6. In the Y= Editor, press: @ 2 ‰and make sure Axes = CUSTOM with y1 and y2 as the axes. Important: Fields=DIRFLD cannot plot a time axis. An Invalid Axes error occurs if Axes=TIME or if t is set as a CUSTOM axis. 7. In the Window Editor (8 $), set the Window variables. t0=0 tmax=10 tstep=.1 tplot=0 xmin=L2 xmax=2 xscl=1 ymin=L2 ymax=2 yscl=1 ncurves=0 diftol=.001 fldres=14 dtime=0 8. Display the Graph screen (8 %).
To examine this harmonic oscillator in more detail, use a split screen to graph the manner in which y and y' change with respect to time (t). 9. Press 3 and change the mode settings on Page 2 as shown. Then close the MODE dialog box, which redraws the graph. Note: To display different graphs in both parts of a split screen, you must use the 2-graph mode. 10. Press 2 a to switch to the right side of the split screen. 11. Use † to select y1' and y2'. The right side uses the same equations as the left side.
14. In the Window Editor, change ymin and ymax as shown to the right. ymin=L2. ymax=2. Note: When you enter 2-graph mode, Window variables for the right side are set to their defaults. 15. Press 8 % to display the Graph screen for graph #2. The left side shows the phase-plane orbit. The right side shows the solution curve and its derivative. 16. To return to a full screen of the original graph, press 2 a to switch to the left side. Then press 3 and change the Split Screen setting.
Example 1. Press 3 and set Graph=DIFF EQUATIONS. 2. Define a system of equations for the 3rdorder equation. Rewrite the equation and make the necessary substitutions. y''' + 2y'' + 2y' + y = sin(x) y''' = sin(x) N 2y'' N 2y' Ny y''' = sin(t) N 2y'' N 2y' Ny y''' = sin(t) N 2y3 N 2y2 N y1 y3' = sin(t) N 2y3 N 2y2 N y1 3. In the Y= Editor (8 #), enter the system of equations. 4. Enter the initial conditions: yi1=0, yi2=1, and yi3=1 Note: t0 is the time at which the initial conditions occur.
6. Press: ,9 — or — @ 8 ÍSet Axes = ON, Labels = ON, Solution Method = RK, and Fields = FLDOFF. Important: For 3rd- or higher-order equations, you must set Fields=FLDOFF. Otherwise, an Undefined variable error occurs when graphing. 7. In the Y= Editor, press: @ 2 ‰ Set Axes = TIME. Note: With Axes=TIME, the solution to the selected equation is plotted against time (t). 8. In the Window Editor (8 $), set the Window variables. t0=0 tmax=10 tstep=.1 tplot=0 xmin=L1 xmax=10 xscl=1.
9. Display the Graph screen (8 %). Note: To find the solution at a particular time, use … to trace the graph. Setting Axes for Time or Custom Plots Setting the axes can give you great flexibility in graphing differential equations. Custom axes are particularly effective for showing different kinds of relationships. Displaying the AXES Dialog Box From the Y= Editor, press: @ 2‰ If Fields = SLPFLD, Axes is unavailable.
Item Description X Axis, Y Axis Active only when Axes = CUSTOM, these let you select what you want to plot on the x and y axes. t — time y — solutions (y1, y2, etc.) of all selected differential equations y' — values of all selected differential equations (y1', y2', etc.) y1, y2, etc. — the solution to the corresponding differential equation, regardless of whether that equation is selected y1', y2', etc.
Predator-Prey Model Use the two coupled 1st-order differential equations: y1' = Ly1 + 0.1y1 ùy2 and y2' = 3y2 Ny1 ùy2 where: y1 = Population of foxes yi1 = Initial population of foxes (2) y2 = Population of rabbits yi2 = Initial population of rabbits (5) 1. Use 3 to set Graph = DIFF EQUATIONS. 2. In the Y= Editor (8 #), define the differential equations and enter the initial conditions. Note: To speed up graphing times, clear any other equations in the Y= Editor.
4. In the Y= Editor, press: @ 2 ‰ Set Axes = TIME. 5. In the Window Editor (8 $), set the Window variables. t0=0 tmax=10 tstep=p/24 tplot=0 xmin=L1 xmax=10 xscl=5 ymin=L10 ymax=40 yscl=5 ncurves=0 diftol=.001 6. Graph the differential equations (8 %). 7. Press … to trace. Then press 3 ¸ to see the number of foxes (yc for y1) and rabbits (yc for y2) at t=3. y2(t) Note: Use C and D to move the trace cursor between the curves for y1 and y2.
8. Return to the Y= Editor. Press: ,9 — or — @ 8Í Set Fields = DIRFLD. Note: In this example, DIRFLD is used for two related differential equations that do not represent a 2nd-order equation. 9. Press: @ 2‰ Confirm that the axes are set as shown. 10. In the Y= Editor, clear the initial conditions for yi1 and yi2. 11. Return to the Graph screen, which displays only the direction field. 12. To graph a family of solutions, return to the Y= Editor and enter the initial conditions shown below.
13. Return to the Graph screen, which displays a curve for each pair of initial conditions. 14. Press … to trace. Then press 3 ¸ to see the number of foxes (xc) and rabbits (yc) at t=3. Because t0=0 and tmax=10, you can trace in the range 0 t 10. Note: Use C and D to move the trace cursor from one initial condition curve to another. Example Comparison of RK and Euler Consider a logistic growth model dP/dt = .001ùPù(100NP), with the initial condition P(0) = 10.
2. Express the 1st-order equation in terms of y1'=.001y1ù(100Ny1) y1' and y1. Do not use implied multiplication between the variable and parentheses. If you do, it is treated as a function call. 3. Enter the equation in the Y= Editor (8 #). 4. Enter the initial condition: yi1=10 t0 is the time at which the initial condition occurs. By default, t0=0. 5. Press: ,9 — or — @ 8Í Set Solution Method = RK and Fields = FLDOFF. Note: To speed up graphing times, clear any other equations in the Y= Editor.
t0=0. tmax=100. Ê tstep=1. tplot=0. xmin=L1. xmax=100. xscl=1. ymin=L10. ymax=10 yscl=1. ncurves=0. diftol=.001 Ê Important: Change tstep from .1 (its default) to 1. Otherwise, BldData calculates too many rows for the data variable and a Dimension error occurs. 7. In the Home screen @ "" use BldData to create a data variable containing the RK graphing points. BldData rklog 8. Return to the Y= Editor, press: ,9 — or — @ 8Í Set Solution Method = EULER.
10. Use the Data/Matrix Editor (O) to create a new data variable named errorlog. Note: errorlog lets you combine the data in rklog and eulerlog so that you can view the two sets of data side by side. 11. In this new data variable, define the c1, c2, and c3 column headers to refer to data in rklog and eulerlog. Also, enter column titles as shown. To define a column header, move the cursor to that column, press †, type the reference expression (such as rklog[1] for c1), and press ¸.
15. The exact solution to the differential equation is given below. Enter it as y1. y1 = (100ùe^(x/10))/(e^(x/10)+9) Note: You can use deSolve( ) to find this exact, general solution. , You can use C to scroll up to see Plot 1 and Plot 2. 16. In the Window Editor, set the Window variables. xmin=L10 xmax=100 xscl=10 ymin=L10. ymax=120. yscl=10. xres=2. 17. Display the Graph screen (8 %). Note: The fuzzy line on the graph indicates differences between the RK and Euler values. 18.
20. Press … to trace, and then press C or D until y1 is selected. (1 shows in upper right corner.) Then enter 40. Euler (Plot 2) RK (Plot 1) Exact solution (y1) y1 is selected when 1 shows here By moving the trace cursor to trace each solution to xc = 40, you can find that: • The exact solution (y1) is 85.8486, rounded to six digits. • The RK solution (Plot 1) is 85.8952. • The Euler solution (Plot 2) is 85.6527.
Example For a general solution, use the following syntax. For a particular solution, refer to the Technical Reference module. deSolve(1stOr2ndOrderODE, independentVar, dependentVar) Using the logistic 1st-order differential equation, find the general solution for y with respect to t. deSolve(y' = 1/1000 yù(100Ny),t,y) For ', type 2 È. Do not use implied multiplication between the variable and parentheses. If you do, it will be treated as a function call.
Before using deSolve( ), clear any existing t and y variables. Otherwise, an error occurs. 1. In the Home screen @ " "use deSolve( ) to find the general solution. @1 represents a constant. You may get a different constant (@2, etc.). 2. Use the solution to define a function. a) Press C to highlight the solution in the history area. Then press ¸ to autopaste it into the entry line. b) Insert the Define instruction at the beginning of the line. Then press ¸.
4. Evaluate the general solution (y) with the constant @1=9/100 to obtain the particular solution shown. You can also use deSolve( ) to solve this problem directly. Enter: deSolve(y' = 1/1000 yù(100Ny) and y(0)=10,t,y) Troubleshooting with the Fields Graph Format If you have difficulties graphing a differential equation, this section can help you correct the problem. Many problems may be related to your Fields graph format setting.
If the equation is: Valid Fields settings are: 2nd-order (system of two 1st-order equations) DIRFLD or FLDOFF 3rd- or higher-order FLDOFF (system of three or more 1st-order equations) Because Fields = SLPFLD is the default setting, a common error message is shown to the right. When you see this or any other error message: • For your order of equation, use the previous table to find the valid Fields settings. Change to the applicable setting.
Fields=SLPFLD In the Y= Editor Use † to select one and only one 1st-order equation. You can enter mulNotele equations, but only one at a time can be selected. The selected equation must not refer to any other equation in the Y= Editor. For example: If y1'=y2, an Undefined variable error occurs when you graph. In the Graph screen If the slope field is drawn but no solution curve is plotted, specify an initial condition.
Fields=DIRFLD In the Y= Editor Enter a valid system of two 1st-order equations. For information about defining a valid system for a 2nd-order equation, refer to Example of a 2nd-Order Equation. Set Axes = CUSTOM: @ 2 ‰ If Axes = TIME, an Invalid axes error occurs when you graph. If you enter initial conditions in the Y= Editor, the equations referenced by the custom axes must have the same number of initial conditions. Otherwise, a Dimension error occurs when you graph.
In the Graph screen If the direction field is drawn but no curve is plotted, enter initial conditions in the Y= Editor or select one interactively from the Graph screen. If you did enter initial conditions, select ZoomFit: @ „jA The ncurves Window variable is ignored with DIRFLD. Default curves are not drawn automatically. Notes With DIRFLD, the equations referenced by the custom axes determine which equations are graphed, regardless of which equations are selected in the Y= Editor.
With custom axes If X Axis is not t, you must enter at least one initial condition for each equation in the Y= Editor (whether the equation is selected or not). Otherwise, a Diff Eq setup error occurs when you graph. In the Graph screen If no curve is graphed, set an initial condition. If you did enter initial conditions in the Y= Editor, select ZoomFit: @ „jA A 1st-order equation may look different with FLDOFF than with SLPFLD.
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Tables Overview of Steps in Generating a Table To generate a table of values for one or more functions, use the general steps shown below. For specific information about setting table parameters and displaying the table, refer to the following pages. Generating a Table 1. Set Graph mode and, if necessary, Angle mode (3). Note: Tables are not available in 3D Graph mode. 2. Define functions on Y= Editor (8 #). 3. Select (†) which defined functions to display in the table.
5. Display the table (8 '). Exploring the Table From the Table screen, you can: • Scroll through the table to see values on other pages. • Highlight a cell to see its full value. • Change the table’s setup parameters. By changing the starting or incremental value used for the independent variable, you can zoom in or out on the table to see different levels of detail. • Change the cell width. • Edit selected functions.
Displaying the TABLE SETUP Dialog Box To display the TABLE SETUP dialog box, press 8 &. From the Table screen, you can also press „. Setup Parameter Description tblStart If Independent = AUTO and Graph < - > Table = OFF, this specifies the starting value for the independent variable. @tbl If Independent = AUTO and Graph < - > Table = OFF, this specifies the incremental value for the independent variable. @tbl can be positive or negative, but not zero.
Setup Parameter Description Independent AUTO — The TI-89 Titanium automatically generates a series of values for the independent variable based on tblStart, @tbl, and Graph < - > Table. ASK — Lets you build a table manually by entering specific values for the independent variable. Note: The table initially starts at tblStart, but you can use C to scroll to prior values.
1. Use D and C to highlight the value or setting to change. 2. Specify the new value or setting. To change: Do this: tblStart or @tbl Type the new value. The existing value is erased when you start to type. — or — Press A or B to remove the highlighting. Then edit the existing value. Graph < - > Table or Independent Press A or B to display a menu of valid settings. Then either: • Move the cursor to highlight the setting and press ¸. — or — • Press the number for that setting.
• Set Graph < - > Table and Independent by using the setTable function. Refer to the Technical Reference module. Displaying an Automatic Table If Independent = AUTO on the TABLE SETUP dialog box, a table is generated automatically when you display the Table screen. If Graph < - > Table = ON, the table matches the trace values from the Graph screen. If Graph < - > Table = OFF, the table is based on the values you entered for tblStart and @tbl.
First column shows values of the independent variable. Other columns show corresponding values of the functions selected in the Y= Editor. Header row shows names of independent variable (x) and selected functions (y1). Entry line shows full value of highlighted cell. Note: You can scroll back from the starting value by pressing C or 2 C.
Changing the Cell Width Cell width determines the maximum number of digits and symbols (decimal point, minus sign, and “í” for scientific notation) that can be displayed in a cell. All cells in the table have the same width. Note: By default, the cell width is 6. To change the cell width from the Table screen: 1. Press ƒ 9 — or — @ ¹Í 2. Press B or A to display a menu of valid widths (3–12). 3. Move the cursor to highlight a number and press ¸.
• If a number’s magnitude is too large for the current cell width, the number is rounded and shown in scientific notation. • If the cell width is too narrow even for scientific notation, “...” is shown. Notes: • If a function is undefined at a particular value, undef is displayed in the cell. • Use 3 to set the display modes. By default, Display Digits = FLOAT 6. With this mode setting, a number is shown with up to six digits, even if the cell is wide enough to show more.
If Results are Complex Numbers A cell shows as much as possible of a complex number (according to the current display modes) and then shows “...” at the end of the displayed portion. When you highlight a cell containing a complex number, the entry line shows the real and imaginary parts with a maximum of four digits each (FLOAT 4). Editing a Selected Function From a table, you can change a selected function without having to use the Y= Editor. 1. Move the cursor to any cell in the column for that function.
4. Press ¸ to save the edited function and update the table. The edited function is also saved in the Y= Editor. If You Want to Change the Setup Parameters After generating an automatic table, you can change its setup parameters as necessary. Press „ or ¹ & to display the TABLE SETUP dialog box. Then make your changes. Building a Manual (Ask) Table If Independent = ASK on the TABLE SETUP dialog box, the TI-89 Titanium lets you build a table manually by entering specific values for the independent variable.
Header row shows names of independent variable (x) and selected functions (y1). Enter a value here. If you first display an automatic table and then change it to Independent = ASK, the table continues to show the same values. However, you can no longer see additional values by scrolling up or down off the screen. Entering or Editing an Independent Variable Value You can enter a value in column 1 (independent variable) only. 1. Move the cursor to highlight the cell you want to enter or edit.
Enter values in any numerical order. Enter a new value here. Shows full value of highlighted cell. Note: In this example, you can move the cursor to column 2, but you can enter values in column 1 only. Entering a List in the Independent Variable Column 1. Move the cursor to highlight any cell in the independent variable column. 2. Press † to move the cursor to the entry line. 3. Type a series of values, enclosed in braces { } and separated by commas. For example: x={1,1.5,1.
Adding, Deleting, or Clearing To: Do this: Insert a new row above a specified row Highlight a cell in the specified row and press: @ 2ˆ The new row is undefined (undef) until you enter a value for the independent variable. Delete a row Highlight a cell in the row and press ‡. If you highlight a cell in the independent variable column, you can also press 0. Clear the entire table (but not the selected Y= functions) Press ƒ 8. When prompted for confirmation, press ¸.
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Additional Graphing Topics Collecting Data Points from a Graph From the Graph screen, you can store sets of coordinate values and/or math results for later analysis. You can store the information as a single-row matrix (vector) on the Home screen or as data points in a system data variable that can be opened in the Data/Matrix Editor. Collecting the Points 1. Display the graph. (This example shows y1(x)=5ùcos(x).) 2. Display the coordinates or math results you want to collect. 3.
8· Displayed coordinates are added to the Home screen’s history area (but not the entry line) as a single-row matrix or vector. 8b Displayed coordinates are stored in a data variable named sysData, which you can open in the Data/Matrix Editor. Note: Use a split screen to show a graph and the Home screen or Data/Matrix Editor at the same time. Notes about SysData Variable • When you press: 8b - • If sysData does not exist, it is created in the MAIN folder.
• If the Graph screen contains a function or stat plot that references the current contents of sysData, this command will not operate. Graphing a Function Defined on the Home Screen In many cases, you may create a function or expression on the Home screen and then decide to graph it. You can copy an expression to the Y= Editor, or graph it directly from the Home screen without using the Y= Editor.
Copying from the Home Screen to the Y= Editor If you have an expression on the Home screen, you can use any of the following methods to copy it to the Y= Editor. Method Description Copy and paste 1. Highlight the expression on the Home screen. Press ƒ and select 5:Copy. 2. Display the Y= Editor, highlight the desired function, and press ¸. 3. Press ƒ and select 6:Paste. Then press ¸. Note: Instead of using ƒ 5 or ƒ 6 to copy and paste, use:8 6 or 8 7 § Store the expression to a Y= function name.
Method Description 2£ If the expression is already stored to a variable: 1. Display the Y= Editor, highlight the desired function, and press ¸. 2. Press 2 £. Type the variable name that contains the expression, and press ¸ twice. Important: To recall a function variable such as f1(x), type only f1, not the full function name. 3. Press ¸ to save the recalled expression in the Y= Editor’s function list.
If the expression is in terms of: A non-native independent variable Use the Graph command as shown in this example: Graph 1.25aùcos(a),a Specify the independent variable; otherwise, you may get an error. Note: Graph uses the current Window variable settings and is available from the Home screen’s † toolbar menu. Graph does not work with sequence graphs or differential equations. For parametric, polar, and 3D graphs, use the following variations.
• Execute the ClrGraph command (available from the Home screen’s † Other toolbar menu). – or – • Display the Y= Editor. The next time you display the Graph screen, it will use the functions selected on the Y= Editor. Extra Benefits of User-Defined Functions You can define a user-defined function in terms of any independent variable. For example: Define f1(aa)=1.25aacos(aa). Define f1(aa)=1.25aaùcos(aa) Graph f1(x) Refers to the function by using the native independent variable. and: Define f1(aa)=1.
two-piece functions. For three or more pieces, it may be easier to create a multistatement, user-defined function. Using the When Function To define a two-piece function, use the syntax: when(condition, trueExpression, falseExpression) For example, suppose you want to graph a function with two pieces. When: Use expression: x<0 Mx x|0 5 cos(x) In the Y= Editor: The function is “pretty printed” in this form. Enter the function in this form. For three or more pieces, you can use nested when functions.
Note: To enter when, type it or use the CATALOG. When: Use expression: x < Mp 4 sin(x) x | M p and x < 0 2x + 6 x|0 6 – x2 In the Y= Editor: where: y1(x)=when(x<0,when(x< M p,4ùsin(x),2x+6),6Nx^2) This nested function is in effect when x<0. Nested functions quickly become complex and difficult to visualize. Using a Multi-Statement, User-Defined Function For three or more pieces, you may want to create a multi-statement, user-defined function.
For example, consider the previous three-piece function. When: Use expression: x < Mp 4 sin(x) x | M p and x < 0 2x + 6 x|0 6 – x2 Note: For information about similarities and differences between functions and programs, refer to Programming. A multi-statement, user-defined function can have many of the control and decisionmaking structures (If, ElseIf, Return, etc.) used in programming. When creating the structure of a function, it may be helpful to visualize it first in a block form.
Use a colon (:) to separate each statement. Func:If x< Mp Then:Return 4ùsin(x): ... :EndIf:EndFunc In the Y= Editor: Only Func is shown for a multi-statement function. Enter a multi-statement function on one line. Be sure to include colons. From the Home Screen or a Program From the Home screen, you can also use the Define command to create a multistatement, user-defined function. Information is available on copying a function from the Home screen to the Y= Editor.
Examples Using the Y= Editor Enter the expression {2,4,6} sin(x) and graph the functions. Note: Enclose list elements in braces (2 [ and 2 \) and separate them with commas. Graphs three functions: 2 sin(x), 4 sin(x), 6 sin(x) Enter the expression {2,4,6} sin({1,2,3} x) and graph the functions. Graphs three functions: 2 sin(x), 4 sin(2x), 6 sin(3x) Note: The commas are shown in the entry line but not in the function list.
graph {2,4,6}sin(x) graph {2,4,6}sin({1,2,3}x) Simultaneous Graphs with Lists When the graph format is set for Graph Order = SIMUL, the functions are graphed in groups according to the element number in the list. For these example functions, the TI-89 Titanium / Voyage™ 200 Graphing Calculator graphs three groups. • 2 sin(x), x+4, cos(x) • 4 sin(x), 2x+4 • 6 sin(x), 3x+4 The functions within each group are graphed simultaneously, but the groups are graphed sequentially.
Using the Two-Graph Mode In two-graph mode, the calculator’s graph-related features are duplicated, giving you two independent graphing calculators. The two-graph mode is only available in split screen mode. For more information about split screens, refer to Split Screens. Setting the Mode Several mode settings affect the two-graph mode, but only two settings are required. Both are on Page 2 of the MODE dialog box. 1. Press 3. Then press „ to display Page 2. 2. Set the following required modes.
Page 2: • • Split 1 App = application for top or left side Split 2 App = application for bottom or right side • Graph 2 = Graph mode for bottom or right side • 4. Press ¸ to close the dialog box. The Two-Graph Screen A two-graph screen is similar to a regular split screen.
• Window Editor variables. • Table setup parameters and Table screens. • Graph formats such as Coordinates, Axes, etc. • Graph screens. • Y= Editors. However, both graphs share common function and stat plot definitions. Note: The Y= Editor is completely independent only when the two sides use different graphing modes (as described below). Independent graph-related applications (Y= Editor, Graph screen, etc.) can be displayed on both sides of the screen at the same time.
• When both sides use the same graphing mode, each side shows the same function list. - • You can use † to select different functions and stat plots (indicated by Ÿ) for each side. If you set a display style for a function, that style is used by both sides.2 ˆ Suppose Graph 1 and Graph 2 are set for function graphing.
- Use 3 to set Number of Graphs = 1, or exit the split screen by setting Split Screen = FULL. – or – - Press 2 K twice. This always exits a split screen and returns to a full-sized Home screen. Note: You can display non-graph-related applications (such as the Home screen) on only one side at a time. Remember that the Two Sides Are Independent In two-graph mode, the two sides may appear to be related when, in fact, they are not. For example: For Graph 1, the Y= Editor lists y(x) functions.
To switch the active sides, press 2 a or use the switch function, switch(1) or switch(2). Drawing a Function or Inverse on a Graph For comparison purposes, you may want to draw a function over your current graph. Typically, the drawn function is some variation of the graph. You can also draw the inverse of a function. (These operations are not available for 3D graphs.) Drawing a Function, Parametric, or Polar Equation Execute DrawFunc, DrawParm, or DrawPol from the Home screen or a program.
2. On the Graph screen, press: 2 ˆ and select 2:DrawFunc. To display the Home screen and put DrawFunc in the entry line, press:2 ˆ 2 3. On the Home screen, specify the function to draw. DrawFunc y1(x)N6 4. Press ¸ to draw the function on the Graph screen. You cannot trace, zoom, or perform a math operation on a drawn function. Note: To clear the drawn function, press † – or – 2 ˆ and select 1:ClrDraw Drawing the Inverse of a Function Execute DrawInv from the Home screen or a program.
1. On the Graph screen, press: 2 ˆ and select 3:DrawInv To display the Home screen and put DrawInv in the entry line, press: 2ˆ3 2. On the Home screen, specify the inverse function. DrawInv y1(x) 3. Press ¸. The inverse is plotted as (y,x) instead of (x,y). Drawing a Line, Circle, or Text Label on a Graph You can draw one or more objects on the Graph screen, usually for comparisons. For example, draw a horizontal line to show that two parts of a graph have the same y value.
From the Graph screen: • 2ˆ and select 1:ClrDraw. – or – • Press † to regraph. Note: You can also enter ClrDraw on the Home screen’s entry line. You can also do anything that causes the Smart Graph feature to redraw the graph (such as change the Window variables or deselect a function on the Y= Editor).
Drawing a Point or a Freehand Line From the Graph screen: 1. 2 ‰ and select 1:Pencil. 2. Move the cursor to the applicable location. To draw a: Do this: Point (pixel-sized) Press ¸. Freehand line Press and hold ¤, and move the cursor to draw the line. Note: When drawing a freehand line, you can move the cursor diagonally. After drawing the point or line, you are still in Pencil mode. • To continue drawing, move the cursor to another point. • To quit, press N.
Erasing Individual Parts of a Drawing Object From the Graph screen: 1. 2 ‰ and select 2:Eraser. The cursor is shown as a small box. 2. Move the cursor to the applicable location. To erase: Do this: Area under the box Press ¸. Along a freehand line Press and hold ¤, and move the cursor to erase the line. Note: These techniques also erase parts of graphed functions. After erasing, you are still in Eraser mode. • To continue erasing, move the box cursor to another location. • To quit, press N.
2. Move the cursor to the 1st point, and press ¸. 3. Move to the 2nd point, and press ¸. (As you move, a line extends from the 1st point to the cursor.) Note: Use 2 to move the cursor in larger increments; 2 B, etc. After drawing the line, you are still in Line mode. • To continue drawing another line, move the cursor to a new 1st point. • To quit, press N. Drawing a Circle From the Graph screen: 1. 2 ‰ and select 4:Circle. 2. Move the cursor to the center of the circle, and press ¸. 3.
Drawing a Horizontal or Vertical Line From the Graph screen: 1. 2 ‰ and select 5:Horizontal or 6:Vertical. A horizontal or vertical line and a flashing cursor are displayed on the screen. If the line is initially displayed on an axis, it may be difficult to see. However, you can easily see the flashing cursor. 2. Use the cursor pad to move the line to the appropriate position. Then press ¸. After drawing the line, you are still in “line” mode. • To continue, move the cursor to another location.
2. As necessary, use D and C to select the applicable function. 3. Move the cursor to the tangent point, and press ¸. The tangent line is drawn, and its equation is displayed. Note: To set the tangent point, you can also type its x value and press ¸. Drawing a Line Based on a Point and a Slope To draw a line through a specified point with a specified slope, execute the DrawSlp command from the Home screen or a program. Use the syntax: DrawSlp x, y, slope You can also access DrawSlp from the Graph screen.
Typing Text Labels From the Graph screen: 1. 2 ‰ and select 7:Text. 2. Move the text cursor to the location where you want to begin typing. 3. Type the text label. After typing the text, you are still in “text” mode. • To continue, move the cursor to another location. • To quit, press ¸ or N. Note: The text cursor indicates the upper-left corner of the next character you type. From the Home Screen or a Program Commands are available for drawing any of the objects described in this section.
Saving and Opening a Picture of a Graph You can save an image of the current Graph screen in a PICTURE (or PIC) variable. Then, at a later time, you can open that variable and display the image. This saves the image only, not the graph settings used to produce it. Saving a Picture of the Whole Graph Screen A picture includes any plotted functions, axes, tick marks, and drawn objects. The picture does not include lower and upper bound indicators, prompts, or cursor coordinates.
Saving a Portion of the Graph Screen You can define a rectangular box that encloses only the portion of the Graph screen that you want to save. 1. @ 2‰ and select 8:Save Picture. A box is shown around the outer edge of the screen. Note: You cannot save a portion of a 3D graph. 2. Set the 1st corner of the box by moving its top and left sides. Then press ¸. Note: Use D and C to move the top or bottom, and use B and A to move the sides. 3. Set the 2nd corner by moving the bottom and right sides.
Opening a Graph Picture When you open a graph picture, it is superimposed over the current Graph screen. To display only the picture, use the Y= Editor to deselect any other functions before opening the graph picture. From the Graph screen: 1. Press ƒ and select 1:Open. 2. Select the type (Picture), folder, and variable that contain the graph picture you want to open. Note: If a variable name is not shown on the dialog box, there are no graph pictures in the folder. 3. Press ¸.
Deleting a Graph Picture Unwanted Picture variables take up calculator memory. To delete a variable, use the VAR-LINK screen (2 °) as described in Memory and Variable Management. From a Program or the Home Screen To save (store) and open (recall) a graph picture, use the StoPic, RclPic, AndPic, XorPic, and RplcPic commands as described in the Technical Reference module. To display a series of graph pictures as an animation, use the CyclePic command. For an example, refer to CyclePic Command.
CyclePic picNameString, n [,wait] [,cycles] [,direction] Ê Ê Ë Ì Í Ë Ì Í Î base name of pictures in quotes, such as "pic" # of pictures to cycle seconds between # of times to repeat cycle Example This example program (named cyc) generates 10 views of a 3D graph, with each view rotated 10¿¡ further around the Z axis.
Technical Reference module. For information about using the Program Editor, refer to Programming. Program Listing Every Other Graph from Program :cyc() :Prgm :local I :¦Set mode and Window variables :setMode(“graph”,”3d”) :70!eyef :M10!xmin :10!xmax :14!xgrid :M10!ymin :10!ymax :14!ygrid :M10!zmin :10!zmax :1!zscl :¦Define the function :(x^3ùy–y^3ùx)/390!z1(x,y) :¦Generate pics and rotate :For i,1,10,1 : iù10!eyeq : DispG : StoPic #("pic" & string(i)) :EndFor :¦Display animation :CyclePic "pic",10,.
Comments start with ¦. Press: 8d Note: Due to its complexity, this program takes several minutes to run. After entering this program on the Program Editor, go to the Home screen and enter cyc( ). Saving and Opening a Graph Database A graph database is the set of all elements that define a particular graph. By saving a graph database as a GDB variable, you can recreate that graph at a later time by opening its stored database variable.
A graph database does not include drawn objects or stat plots. Note: In two-graph mode, the elements for both graphs are saved in a single database. Saving the Current Graph Database From the Y= Editor, Window Editor, Table screen, or Graph screen: 1. Press ƒ and select 2:Save Copy As. 2. Specify the folder and a unique variable name. 3. Press ¸. After typing in an input box such as Variable, you must press ¸ twice. Note: If you start from the Graph screen, be sure to use Type=GDB.
From the Y= Editor, Window Editor, Table screen, or Graph screen: 1. Press ƒ and select 1:Open. 2. Select the folder and variable that contain the graph database you want to open. 3. Press ¸. Note: If you start from the Graph screen, be sure to use Type=GDB. Deleting a Graph Database Unused GDB variables take up calculator memory. To delete them, use the VAR-LINK screen (2 °) described in Memory and Variable Management.
Split Screens Setting and Exiting the Split Screen Mode To set up a split screen, use the MODE dialog box to specify the applicable mode settings. After you set up the split screen, it remains in effect until you change it. Setting the Split Screen Mode 1. Press 3 to display the MODE dialog box. 2. Because the modes related to split screens are listed on the second page of the MODE dialog box, either: • Use D to scroll down. — or — • Press „ to display Page 2. 3.
When you set Split Screen = TOP-BOTTOM or LEFT-RIGHT, previously dimmed modes such as Split 2 App become active. Setting the Initial Applications Before pressing ¸ to close the MODE dialog box, you can use the Split 1 App and Split 2 App modes to select the applications you want to use. Mode Specifies the application in the: Split 1 App Top or left part of the split screen. Split 2 App Bottom or right part of the split screen.
Other Modes that Affect a Split Screen Mode Description Number of Graphs Note: Leave this set to 1 unless you have read the applicable section in Additional Graphing Topics. Lets you set up and display two independent sets of graphs. This is an advanced graphing feature as described in “Using the TwoGraph Mode” in Additional Graphing Topics. Split Screens and Pixel Coordinates The calculator has commands that use pixel coordinates to draw lines, circles, etc., on the Graph screen.
Split 1 App Split 2 App Ratio x y x y TOP–BOTTOM 1:1 0 – 154 0 – 34 0 – 154 0 – 34 LEFT–RIGHT 1:1 0 – 76 0 – 72 0 – 76 0 – 72 Split Voyage™ 200: Split 1 App Split 2 App Split Ratio x y x y FULL N/A 0 – 238 0 – 102 N/A N/A TOP–BOTTOM 1:1 0 – 234 0 – 46 0 – 234 0 – 46 1:2 0 – 234 0 – 26 0 – 234 0 – 68 2:1 0 – 234 0 – 68 0 – 234 0 – 26 1:1 0 – 116 0 – 98 0 –116 0 – 98 1:2 0– 76 0 – 98 0 – 156 0 – 98 2:1 0 – 156 0 – 98 0 – 76 0 – 98 LEFT–RIGHT E
Method 2: Press 2 K twice to display a full-sized Home screen. When You Turn Off the Calculator Turning the calculator off does not exit the split screen mode. If the calculator is turned off: When you turn the calculator on again: When you press 2 : The split screen is still in effect, but the Home screen is always displayed in place of the application that was active when you pressed 2 :. By the Automatic Power Down™ The split screen is just as you left it. (APD™) feature, or when you press 8 :.
Split-screen indicator Names of open Apps Split screen indicator Description Top-bottom split screen • 1 indicates the application that will appear in the top portion of the screen. • 2 indicates the application that will appear in the bottom portion of the screen. The highlighted numeral indicates the active portion of the split screen. Left-right split screen • 1 indicates the application that will appear in the left portion of the screen.
Selecting the Active Application With a split screen, only one of the two applications can be active at a time. You can easily switch between existing applications, or you can open a different application. The Active Application • The active application is indicated by a thick border. • The toolbar and status line, which are always the full width of the display, are associated with the active application.
Toolbar is for Graph screen. Thick border indicates the Graph screen is active. Graph screen does not have an entry line. Opening a Different Application Method 1: 1. Use 2 a to switch to the application you want to replace. 2. Use O or 8 (such as 8 $) to select the new application. If you select an application that is already displayed, the calculator switches to that application. Method 2: 3. Press 3 and then „. 4. Change Split 1 App and/or Split 2 App.
Using 2nd QUIT to Display the Home Screen Note: Pressing 2 K twice always exits the split screen mode. If the Home screen: Pressing 2 K: Is not already displayed Opens the Home screen in place of the active application. Is displayed, but is not the active application Switches to the Home screen and makes it the active application. Is the active application Exits the split screen mode and displays a full-sized Home screen.
Note: Both Top-Bottom and Left-Right splits use the same methods to select an application.
Data/Matrix Editor Overview of List, Data, and Matrix Variables To use the Data/Matrix Editor effectively, you must understand list, data, and matrix variables. List Variable A list is a series of items (numbers, expressions, or character strings) that may or may not be related. Each item is called an element. In the Data/Matrix Editor, a list variable: • Is shown as a single column of elements, each in a separate cell. • Must be continuous; blank or empty cells are not allowed within the list.
On the Home screen (or anywhere else you can use a list), you can enter a list as a series of elements enclosed in braces { } and separated by commas. Although you must use commas to separate elements on the entry line, spaces separate the elements in the history area. To refer to a specified element in a list, use the format shown to the right.
Note: For stat calculations, columns must have the same length. From the Home screen or a program, you can use the NewData command to create a data variable that consists of existing lists. NewData data1,list1,list2 Ê Ë Ê Name of data variable to create Ë Names of existing list Although you cannot directly display a data variable on the Home screen, you can display a specified column or element.
Matrix Variable A matrix is a rectangular array of elements. When you create a matrix in the Data/Matrix Editor, you must specify the number of rows and columns (although you can add or delete rows and columns later). In the Data/Matrix Editor, a matrix variable: • Looks similar to a data variable, but all columns must have the same length. • Is initially created with 0 in each cell. You can then enter the applicable value in place of 0.
Starting a Data/Matrix Editor Session Each time you start the Data/Matrix Editor, you can create a new variable, resume using the current variable (the variable that was displayed the last time you used the Data/Matrix Editor), or open an existing variable. Creating a New Data, Matrix, or List Variable 1. Press O and then select the Data/Matrix icon. Press ¸. 2. Select 3:New. 3. Specify the applicable information for the new variable. Item Lets you: Type Select the type of variable to create.
Item Lets you: Variable Type a new variable name. If you specify a variable that already exists, an error message will be displayed when you press ¸. When you press N or ¸ to acknowledge the error, the NEW dialog box is redisplayed. Row dimension and Col dimension If Type = Matrix, type the number of rows and columns in the matrix. Note: If you do not type a variable name, your calculator displays the Home screen. 4.
Creating a New Variable from the Data/Matrix Editor From the Data/Matrix Editor: 1. Press ƒ and select 3:New. 2. Specify the type, folder, and variable name. For a matrix, also specify the number of rows and columns. Opening Another Variable You can open another variable at any time. 1. From the Data/Matrix Editor, press ƒ and select 1:Open. – or – From any application, launch Data/Matrix Editor again and select 2:Open. 2. Select the type, folder, and variable to open. 3. Press ¸.
Deleting a Variable Because all Data/Matrix Editor variables are saved automatically, you can accumulate quite a few variables, which take up memory. To delete a variable, use the VAR-LINK screen (2 °). For information about VAR-LINK, refer to Memory and Variable Management. Entering and Viewing Cell Values If you create a new variable, the Data/Matrix Editor is initially blank (for a list or data variable) or filled with zeros (for a matrix).
When values are entered, the entry line shows the full value of the highlighted cell. Note: Use the title cell at the very top of each column to identify the information in that column. Entering or Editing a Value in a Cell You can enter any type of expression in a cell (number, variable, function, string, etc.). 1. Move the cursor to highlight the cell you want to enter or edit. 2. Press ¸ or … to move the cursor to the entry line. 3. Type a new value or edit the existing one. 4.
Scrolling through the Editor To move the cursor: Press: One cell at a time D, C, B, or A One page at a time 2 and then D, C, B, or A Go to row 1 in the current column or to the last row that contains data for any column on the screen, respectively. If the cursor is in or past that last row, 8 D goes to row 999. 8 C or 8D Go to column 1 or to the last column that contains data, respectively. If the cursor is in or past that last column, 8 B goes to column 99.
• In a list variable, a cell in the gap is undefined until you enter a value for the cell. & Note: If you enter more than one column of elements in a list variable, it is converted automatically into a data variable. • In a data variable, gaps in a column are handled the same as a list. However, if you leave a gap between columns, that column is blank.
Changing the Cell Width The cell width affects how many characters are displayed in any cell. To change the cell width in the Data/Matrix Editor: 1. To display the FORMATS dialog box, press: ƒ9 – or – 8Í Cell width is the maximum number of characters that can be displayed in a cell. All cells have the same cell width. Note: Remember, to see a number in full precision, you can always highlight the cell and look at the entry line. 2.
Clearing a Column or all Columns This procedure erases the contents of a column. It does not delete the column. To clear: Do this: A column 1. Move the cursor to any cell in the column. 2. Press: 2 ˆ and select 5:Clear Column. (This item is not available for a matrix.) All columns Press ƒ and select 8:Clear Editor. When prompted for confirmation, press ¸ (or N to cancel). Note: For a list or data variable, a clear column is empty. For a matrix, a clear column contains zeros.
1. Move the cursor to any cell in the column and press †. – or – Move the cursor to the header cell (c1, c2, etc.) and press ¸. Notes: • ¸ is not required if you want to type a new definition or replace the existing one. However, if you want to edit the existing definition, you must press ¸. • To view an existing definition, press † or move the cursor to the header cell and look at the entry line. 2. Type the new expression, which replaces any existing definition.
• Press A or B to remove the highlighting. Then edit the old expression. Note: To cancel any changes, press N before pressing ¸. You can use an expression that: For example: Generates a series of numbers. c1=seq(x^2,x,1,5) c1={1,2,3,4,5} Refers to another column. c2=2ùc1 c4=c1ùc2–sin(c3) Note: The seq function is described in the Technical Reference module. If you refer to an empty column, you will get an error message unless Auto-calculate = OFF. Ê 3.
Clearing a Header Definition 1. Move the cursor to any cell in the column and press †. – or – Move the cursor to the header cell (c1, c2, etc.) and press ¸. 2. Press M to clear the highlighted expression. 3. Press ¸, D, or C. Using an Existing List as a Column Suppose you have one or more existing lists, and you want to use those existing lists as columns in a data variable. From the: Do this: Data/Matrix Editor In the applicable column, use † to define the column header.
Note: If you have a CBL 2™ or CBR™, use these techniques for your collected lists. Use 2 ° to see existing list variables. To Fill a Matrix with a List You cannot use the Data/Matrix Editor to fill a matrix with a list. However, you can use the list8mat command from the Home screen or a program. For information, refer to the Technical Reference module. The Auto-calculate Feature For list and data variables, the Data/Matrix Editor has an Auto-calculate feature. By default, Auto-calculate = ON.
If Auto-calculate = OFF and you make changes as described above, the header definitions are not recalculated until you set Auto-calculate = ON. Note: You may want to set Auto-calculate = OFF to make changes without recalculating each time, enter a definition such as c1=c2+c3 before you enter columns 2 and 3, or override any errors in a definition until you can debug the error.
Ê Ë Ì Î Í Ê c2=shift(c1,2) Ë c3=shift(c1,M2) Ì Shifted columns have the same length as the base Í Last two elements of c1 shift down and out the bottom; undefined elements shift into the top. Î First two elements of c1 shift up and out the top; undefined elements shift into the bottom. Note: To enter shift, type it from the keyboard or select it from the CATALOG. Using the CumSum Function The cumSum function returns a cumulative sum of the elements in a base column.
Sorting Columns After entering information in a data, list, or matrix variable, you can easily sort a specified column in numeric or alphabetical order. You can also sort all columns as a whole, based on a “key” column. Sorting a Single Column In the Data/Matrix Editor: 1. Move the cursor to any cell in the column. 2. Press: 2 ˆ and select 3:Sort Column. Numbers are sorted in ascending order. C1 Character strings are sorted in alphabetical order.
Sorting All Columns Based on a “Key” Column Consider a database structure in which each column along the same row contains related information (such as a student’s first name, last name, and test scores). In such a case, sorting only a single column would destroy the relationship between the columns. In the Data/Matrix Editor: 1. Move the cursor to any cell in the “key” column. 2. In this example, move the cursor to the second column (c2) to sort by last name.
Saving a Copy of a List, Data, or Matrix Variable You can save a copy of a list, data, or matrix variable. You can also copy a list to a data variable, or you can select a column from a data variable and copy that column to a list. Valid Copy Types You can copy a: To a: List List or data Data Data Data column List Matrix Matrix Note: A list is automatically converted to a data variable if you enter more than one column of information. Procedure From the Data/Matrix Editor: 1.
2. Press ƒ and select 2:Save Copy As. 3. In the dialog box: • Select the Type and Folder for the copy. • Type a variable name for the copy. • When available, select the column to copy from. Ê Note: If you type the name of an existing variable, its contents will be replaced. Ê Column is dimmed unless you copy a data column to a list. The column information is not used for other types of copies. 4. Press ¸ (after typing in an input box such as Variable, you must press ¸ twice).
Data/Matrix Editor 539
Statistics and Data Plots Overview of Steps in Statistical Analysis This section gives an overview of the steps used to perform a statistical calculation or graph a statistical plot. For detailed descriptions, refer to the following pages. 1. Set Graph mode (3) to FUNCTION. 2. Enter stat data in the Data/Matrix Editor. Note: Refer to the Data/Matrix Editor module for details on entering data in the Data/Matrix Editor. 3. Perform stat calculations to find stat variables or fit data to a model (‡). 4.
6. Change the graph format if necessary. 7. , 9 — or — @ 8Í Graph the selected equations (8 %). Performing a Statistical Calculation From the Data/Matrix Editor, use the ‡ Calc toolbar menu to perform statistical calculations. You can analyze one-variable or two-variable statistics, or perform several types of regression analyses. The Calculate Dialog Box You must have a data variable opened. The Data/Matrix Editor will not perform statistical calculations with a list or matrix variable.
From the Data/Matrix Editor: 1. Press ‡ to display the Calculate dialog box. Pathname of the data variable This example shows all items as active. On your calculator, items are active only if they are valid for the current settings of Calculation Type and Freq and Categories. Note: If an item is not valid for the current settings, it will appear dimmed.
2. Specify applicable settings for the active items. Item Description Calculation Type Select the type of calculation. x Type the column number in the Data/Matrix Editor (C1, C2, etc.) used for x values, the independent variable. Y Type the column number used for y values, the dependent variable. This is required for all Calculation Types except OneVar. Store RegEQ to If Calculation Type is a regression analysis, you can select a function name (y1(x), y2(x), etc.).
Note: To use an existing list variable for x, y, Freq, or Category, type the list name instead of a column number. An example using Freq, Category, and Include Categories is available. 3. Press ¸ after typing in an input box, press ¸ twice). The results are displayed on the STAT VARS screen. The format depends on the Calculation Type. For example: For Calculation Type = OneVar For Calculation Type = LinReg When : is shown instead of =, you can scroll for additional results.
Previous results are cleared when you: • Edit the data points or change the Calculation Type. • Open another data variable or reopen the same data variable (if the calculation referred to a column in a data variable). Results are also cleared if you leave and then reopen the Data/Matrix Editor with a data variable. • Change the current folder (if the calculation referred to a list variable in the previous folder).
Selecting the Calculation Type From the Calculate dialog box (‡), highlight the current setting for the Calculation Type and press B. You can then select from a menu of available types. If an item is dimmed, it is not valid for the current Calculation Type. Calc Type Description OneVar One-variable statistics — Calculates the statistical variables. TwoVar Two-variable statistics — Calculates the statistical variables.
Calc Type Description LinReg Linear regression — Fits the data to the model y=ax+b (where a is the slope, and b is the y-intercept) using a leastsquares fit and x and y. LnReg Logarithmic regression — Fits the data to the model equation y=a+b ln(x) using a least-squares fit and transformed values ln(x) and y. Logistic Logistic regression — Fits the data to the model y=a/(1+bùe^(cùx))+d and updates all the system statistics variables.
Calc Type Description QuartReg Quartic regression — Fits the data to the fourth-order polynomial y=ax4+bx3+cx2+ dx+e. You must have at least five data points. SinReg • For five points, the equation is a polynomial fit. • For six or more points, it is a polynomial regression. Sinusoidal regression — Calculates the sinusoidal regression and updates all the system statistics variables. The output is always in radians, regardless of the angle mode setting.
Management. All statistical variables are cleared when you edit the data or change the calculation type. Other conditions that clear the variables are listed. Calculated Variables Statistical variables are stored as system variables. However, regCoef and regeq are treated as a list and a function variable, respectively. One Var Two Var mean of x values ü ü sum of x values Gx Gx sum of x2 values Gx2 Gx2 sample std. deviation of x Sx Sx population std.
maximum of x values One Var Two Var maxX maxX minimum of y values minY maximum of y values maxY 1st quartile q1 median medStat 3rd quartile q3 Regressions regression equation regeq regression coefficients (a, b, c, d, e) regCoef correlation coefficient †† corr coefficient of determination †† R2 summary points (MedMed only) † medx1, medy1, medx2, medy2, medx3, medy3 †† corr is defined for a linear regression only; R2 is defined for all polynomial regressions.
• 1st quartile is the median of points between minX and medStat, and 3rd quartile is the median of points between medStat and maxX. Defining a Statistical Plot From the Data/Matrix Editor, you can use the entered data to define several types of statistical plots. You can define up to nine plots at a time. Procedure From the Data/Matrix Editor: 1. Press „ to display the Plot Setup screen. Initially, none of the plots are defined. 2. Move the cursor to highlight the plot number that you want to define. 3.
4. Specify applicable settings for the active items. Item Description Plot Type Select the type of plot. Mark Select the symbol used to plot the data points: Box (›), Cross (x), Plus (+), Square (0), or Dot (¦). x Type the column number in the Data/Matrix Editor (C1, C2, etc.) used for x values, the independent variable. y Type the column number used for y values, the dependent variable. This is active only for Plot Type = Scatter or xyline. Hist.
• Plots defined with column numbers always use the last data variable in the Data/Matrix Editor, even if that variable was not used to create the definition. • To use an existing list variable for x, y, Freq, or Category, type the list name instead of the column number. • An example using Freq, Category, and Include Categories is available. 5. Press ¸ (after typing in an input box, press ¸ twice). The Plot Setup screen is redisplayed. The plot you just defined is automatically selected for graphing.
• Execute a Graph command. • Open a different variable in the Data/Matrix Editor. Copying a Plot Definition From Plot Setup: 1. Highlight the plot and press „. 2. Press B and select the plot number that you want to copy to. 3. Press ¸. Note: If the original plot was selected (Ÿ), the copy is also selected. Clearing a Plot Definition From Plot Setup, highlight the plot and press ….
Scatter Data points from x and y are plotted as coordinate pairs. Therefore, the columns or lists that you specify for x and y must be the same length. • Plotted points are shown with the symbol that you select as the Mark. • If necessary, you can specify the same column or list for both x and y. Xyline This is a scatter plot in which data points are plotted and connected in the order in which they appear in x and y. You may want to sort all the columns in the Data/Matrix Editor before plotting.
Box Plot This plots one-variable data with respect to the minimum and maximum data points (minX and maxX) in the set. • A box is defined by its first quartile (Q1), median (Med), and third quartile (Q3). • Whiskers extend from minX to Q1 and from Q3 to maxX. Q1 minx Med Q3 maxX • When you select multiple box plots, they are plotted one above the other in the same order as their plot numbers. • Use NewPlot to show statistical data as a modified box plot.
Histogram This plots one-variable data as a histogram. The x axis is divided into equal widths called buckets or bars. The height of each bar (its y value) indicates how many data points fall within the bar’s range. • When defining the plot, you can specify the Hist. Bucket Width (default is 1) to set the width of each bar. • A data point at the edge of a bar is counted in the bar to the right. xmax – xmin Number of bars = ---------------------------------------------Hist. Bucket Width xmin + Hist.
• When you trace (…) a histogram, the screen shows information about the traced bar. Trace cursor Range of the traced bar # of data points in the traced bar Using the Y= Editor with Stat Plots The previous sections described how to define and select stat plots from the Data/Matrix Editor. You can also define and select stat plots from the Y= Editor.
Showing the List of Stat Plots Press 8 # to display the Y= Editor. Initially, the nine stat plots are located “off the top” of the screen, above the y(x) functions. However, the PLOTS indicator provides some information. For example, PLOTS 23 means that Plots 2 & 3 are selected. To see the list of stat plots, use C to scroll above the y(x) functions. If a Plot is highlighted, this shows the data variable that will be used for the plots.
Note: Plots defined with column numbers always use the last data variable in the Data/Matrix Editor, even if that variable was not used to create the definition. To: Do this: Edit a plot definition Highlight the plot and press …. You will see the same definition screen that is displayed in the Data/Matrix Editor. Select or deselect a plot Highlight the plot and press †. Turn all plots and/or functions off Press ‡ and select the applicable item. You can also use this menu to turn all functions on.
Defining the Viewing Window Stat plots are displayed on the current graph, and they use the Window variables that are defined in the Window Editor. Use 8 $ to display the Window Editor. You can either: • Enter appropriate values. — or — • Select 9:ZoomData from the „ Zoom toolbar menu. (Although you can use any zoom, ZoomData is optimized for st plots.) ZoomData sets the viewing window to display all statistical data points. For histograms and box plots, only xmin and xmax are adjusted.
Changing the Graph Format Press: ,9 — or — @ 8Í from the Y= Editor, Window Editor, or Graph screen. Then change the settings as necessary. Tracing a Stat Plot From the Graph screen, press … to trace a plot. The movement of the trace cursor depends on the Plot Type. Plot Type Description Scatter or xyline Tracing begins at the first data point. Box plot Tracing begins at the median. Press A to trace to Q1 and minX. Press B to trace to Q3 and maxX.
When you press C or D to move to another plot or y(x) function, tracing moves to the current or beginning point on that plot (not to the nearest pixel). Using Frequencies and Categories To manipulate the way in which data points are analyzed, you can use frequency values and/or category values. Frequency values let you “weight” particular data points. Category values let you analyze a subset of the data points.
• In the Data/Matrix Editor, you can enter the test scores and frequency values in two columns. Test scores Frequency values c1 c2 85 1 97 1 97 92 2 92 Ê 89 1 92 Ê 91 1 89 95 3 91 These weighted scores are equivalent to the single column of scores listed to the right. c1 85 95 Ë 95 Ë 95 Ë Ê Frequency of 2 Ë Frequency of 3 Note: A frequency value of 0 effectively removes the data point from analysis.
Set this to YES. Type the column number (or list name) that contains the frequency values. Note: You can also use frequency values from a list variable instead of a column. Example of a Category Column In a data variable, you can use any column to specify a category (or subset) value for the data points on each row. A category value can be any number. Suppose you enter the test scores from a class that has 10th and 11th grade students.
In the Data/Matrix Editor, you can enter the scores and the category values in two columns. Test scores Category values c1 c2 85 1 97 3 92 2 88 3 90 2 95 1 79 4 68 2 92 4 84 3 82 1 To use category values, specify the category column and the category values to include in the analysis when you perform a statistical calculation or define a stat plot.
Set this to YES. Type the column number (or list name) that contains the category values. Within braces { }, type the category values to use, separated by commas. (Do not type a column number or list name.) Note: You can also use category values from a list variable instead of a column.
If You Have a CBL 2™ or CBR™ The Calculator-Based Laboratory™ System (CBL 2) and Calculator-Based Ranger™ System (CBR) are optional accessories, available separately, that let you collect data from a variety of real-world experiments. TI-89 Titanium, CBL 2 and CBR programs are available from the TI web site at education.ti.com. How CBL 2™ Data Is Stored When you collect data with the CBL 2, that data is initially stored in the CBL 2 unit itself.
Note: For specifics about using the CBL 2 and retrieving data to the TI-89 Titanium, refer to the guidebook that comes with the CBL 2 unit. Referring to the CBL 2™ Lists When you perform a statistical calculation or define a plot, you can refer explicitly to the CBL 2 list variables. For example: Type the CBL 2 list variable name instead of a column number Creating a Data Variable with the CBL 2™ Lists You can create a new data variable that consists of the necessary CBL 2 list variables.
• From the Home screen or a program, use the NewData command. NewData dataVar, list1 [,list2 ] [,list3 ] ... CBL 2 list variable names. In the new data variable, list1 will be copied to column 1, list 2 to column 2, etc. Name of the new data variable that you want to create. For example: NewData temp1, time, temp creates a data variable called temp1 in which time is in column 1 and temp is in column 2. • From the Data/Matrix Editor, create a new, empty data variable with the applicable name.
CBR™ You can also use the Calculator-Based Ranger™ (CBR) to explore the mathematical and scientific relationships between distance, velocity, acceleration, and time using data collected from activities you perform.
Programming Running an Existing Program After a program is created (as described in the remaining sections of this module), you can run it from the Home screen. The program’s output, if any, is displayed on the Program I/O screen, in a dialog box, or on the Graph screen. Running a Program On the Home screen: 1. Type the name of the program. 2. You must always type a set of parentheses after the name. Some programs require you to pass an argument to the program. Note: Use 2 ° to list existing PRGM variables.
Note: Arguments specify initial values for a program. When you run a program, the TI-89 Titanium automatically checks for errors. For example, the following message is displayed if you: • Do not enter ( ) after the program name. This error message appears if you: • Do not enter enough arguments, if required. To cancel program execution if an error occurs, press N. You can then correct any problems and run the program again.
Press ´ to stop program execution. A message is then displayed. • To display the program in the Program Editor, press ¸. The cursor appears at the command where the break occurred. • To cancel program execution, press N. Where Is the Output Displayed? Depending on the commands in the program, the TI-89 Titanium automatically displays information on the applicable screen. • Most output and input commands use the Program I/O screen. (Input commands prompt the user to enter information.
Last output On the Program I/O screen: ‡ toolbar is available; all others are dimmed. There is no entry line. Note: To clear any previous output, enter the Clr[O command in your program. You can also execute Clr[O from the Home screen. When a program stops on the Program I/O screen, you need to recognize that it is not the Home screen (although the two screens are similar). The Program I/O screen is used only to display output or to prompt the user for input.
Starting a Program Editor Session Each time you start the Program Editor, you can resume the current program or function (that was displayed the last time you used the Program Editor), open an existing program or function, or start a new program or function. Starting a New Program or Function 1. Press O and then select Program Editor. 2. Select 3:New. 3. Specify the applicable information for the new program or function. Item Lets you: Type Select whether to create a new program or function.
Item Lets you: Variable Type a variable name for the program or function. If you specify a variable that already exists, an error message will be displayed when you press ¸. When you press N or ¸ to acknowledge the error, the NEW dialog box is redisplayed. 4. Press ¸ (after typing in an input box such as Variable, you must press ¸ twice) to display an empty “template.” This is the template for a program. Functions have a similar template.
Starting a New Program from the Program Editor To leave the current program or function and start a new one: 1. Press ƒ and select 3:New. 2. Specify the type, folder, and variable for the new program or function. 3. Press ¸ twice. Opening a Previous Program You can open a previously created program or function at any time. 1. From within the Program Editor, press ƒ and select 1:Open. – or – From another application, launch Program Editor again and select 2:Open. 2.
Copying a Program In some cases, you may want to copy a program or function so that you can edit the copy while retaining the original. 1. Display the program or function you want to copy. 2. Press ƒ and select 2:Save Copy As. 3. Specify the folder and variable for the copy. 4. Press ¸ twice. Note about Deleting a Program Because all Program Editor sessions are saved automatically, you can accumulate quite a few previous programs and functions, which take up memory storage space.
Entering and Editing Program Lines On a blank template, you can begin entering commands for your new program. Program name, which you specify when you create a new program. Enter your program commands between Prgm and EndPrgm. All program lines begin with a colon. Note: Use the cursor pad to scroll through the program for entering or editing commands. Use 8 C or 8 D to go to the top or bottom of a program, respectively.
Entering Comments A comment symbol (¦) lets you enter a remark in a program. When you run the program, all characters to the right of ¦ are ignored. :prog1() :Prgm Ê :¦Displays sum of 1 thru n :Request "Enter an integer",n Ë :expr(n)!n:¦Convert to numeric expression :-----Ê Description of the program . Ë Description of expr. Note: Use comments to enter information that is useful to someone reading the program code.
• Control structures such as If...EndIf commands use a conditional test to decide which part of a program to execute. • Loops commands such as For...EndFor repeat a group of commands. Using Indentation For more complex programs that use If...EndIf and loop structures such as For...EndFor, you can make the programs easier to read and understand by using indentation.
Displaying a calculation result does not store that result. If you need to refer to a result later, store it to a variable. :cos(p/4)!maximum :Disp maximum Note: A list of output commands is available. Getting Values into a Program To input values into a program, you can: • Require the users to store a value (with §) to the necessary variables before running the program. The program can then refer to these variables. • Enter the values directly into the program itself.
Example of Passing Values to a Program The following program draws a circle on the Graph screen and then draws a horizontal line across the top of the circle. Three values must be passed to the program: x and y coordinates for the circle’s center and the radius r. • When you write the program in the Program Editor: In the ( ) beside the program name, specify the variables that will be used to store the passed values. Notice that the program also contains commands that set up the Graph screen.
• To run the program from the Home screen: The user must specify the applicable values as arguments within the ( ). circ(0,0,5) Passed to r Passed to y Passed to x The arguments, in order, are passed to the program. Note: This example assumes that the user enters values that can be displayed by the viewing window set up by ZoomStd and ZoomSqr.
• You can create functions that expand on the TI-89 Titanium’s built-in functions. You can then use the new functions the same as any other function. • Functions return values that can be graphed or entered in a table; programs cannot. • You can use a function (but not a program) within an expression. For example: 3ùfunc1(3) is valid, but not 3ùprog1(3). • Because you pass arguments to a function, you can write generic functions that are not tied to specific variable names.
• Can use all built-in TI-89 Titanium / Voyage™ 200 functions except: setFold setTable • setGraph switch setMode Can refer to any variable; however, it can store a value to a local variable only. - The arguments used to pass values to a function are treated as local variables automatically. If you store to any other variables, you must declare them as local from within the function. • Cannot call a program as a subroutine, but it can call another user-defined function. • Cannot define a program.
Function name, which you specify when you create a new function. Enter your commands between Func and EndFunc. All function lines begin with a colon. Be sure to edit this line to include any necessary arguments. Remember to use argument names in the definition that will never be used when calling the function. If the function requires input, one or more values must be passed to the function.
• Use Return. This is useful for exiting a function and returning a value at some point other than the end of the function. :cube(x) :Func :If x<0 : Return 0 :x^3 :EndFunc Note: This example calculates the cube if x|0; otherwise, it returns a 0. The argument x is automatically treated as a local variable. However, if the example needed another variable, the function would need to declare it as local by using the Local command. There is an implied Return at the end of the function.
Note: Because x and y in the function are local, they are not affected by any existing x or y variable. Function as called from the Home Screen Function as defined in the Program Editor 3!x:125!y 4ùxroot(3,125) 20 5 :xroot(x,y) :Func :y^(1/x) :EndFunc Calling One Program from Another One program can call another program as a subroutine. The subroutine can be external (a separate program) or internal (included in the main program).
Calling a Separate Program To call a separate program, use the same syntax used to run the program from the Home screen. :subtest1() :Prgm :For i,1,4,1 : subtest2(i,iù1000) :EndFor :EndPrgm :subtest2(x,y) :Prgm : Disp x,y :EndPrgm Calling an Internal Subroutine To define an internal subroutine, use the Define command with Prgm...EndPrgm. Because a subroutine must be defined before it can be called, it is a good practice to define subroutines at the beginning of the main program.
An internal subroutine is called and executed in the same way as a separate program. Ê Ë © Ë Ì :subtest1() :Prgm :local subtest2 :Define subtest2(x,y)=Prgm : Disp x,y :EndPrgm :¦Beginning of main program :For i,1,4,1 : subtest2(i,I*1000) :EndFor :EndPrgm Ê Declares the subroutine as a local variable. Ë Defines the subroutine. Ì Calls the subroutine. Note: Use the Program Editor’s † Var toolbar menu to enter the Define and Prgm...EndPrgm commands.
Lbl commands are local to the programs in which they are located. Therefore, a Goto command in the calling program cannot branch to a label in a subroutine or vice versa. Using Variables in a Program Programs use variables in the same general way that you use them from the Home screen. However, the “scope” of the variables affects how they are stored and accessed.
Scope Description Folder Variables Variables that are stored in a particular folder. • If you store to a variable name only, it is stored in the current folder. For example: 5!start • If you refer to a variable name only, that variable must be in the current folder. Otherwise, it cannot be found (even if the variable exists in a different folder). • To store or refer to a variable in another folder, you must specify a path name.
Note: If a program has local variables, a graphed function cannot access them. For example: Local a 5!a Graph aùcos(x) may display an error or an unexpected result (if a is an existing variable in the current folder). Circular Definition Errors When evaluating a user-defined function or running a program, you can specify an argument that includes the same variable that was used to define the function or create the program.
Variable-Related Commands and Functions Command Description § key Stores a value to a variable. As on the Home screen, pressing § enters a ! symbol. Archive Moves specified variables from RAM to user data archive memory. BldData Lets you create a data variable based on the graph information entered in the Y= Editor, Window Editor, etc. CopyVar Copies the contents of a variable. Define Defines a program (subroutine) or function variable within a program. DelFold Deletes a folder.
Command Description Lock Locks a variable so that it cannot be accidentally changed or deleted without first being unlocked. MoveVar Moves a variable from one folder to another. NewData Creates a data variable whose columns consist of a series of specified lists. NewFold Creates a new folder. NewPic Creates a picture variable based on a matrix. Rename Renames a variable. Unarchiv Moves specified variables from user data archive memory to RAM. Unlock Unlocks a locked variable.
Example of a Local Variable The following program segment shows a For...EndFor loop (which is discussed later in this module). The variable i is the loop counter. In most cases, the variable i is used only while the program is running. Ê :Local I :For i,0,5,1 : Disp I :EndFor :Disp i Ê Declares variable i as local. Note: As often as possible, use local variables for any variable that is used only within a program and does not need to be stored after the program stops.
For example: Define fact(n)=Func: Ê Local m: While n>1: n†m!m: n–1!n: EndWhile: Return m: EndFunc Ê Local variable m is not assigned an initial value. In the example above, the local variable m exists independently of any variable m that exists outside of the function. You Must Initialize Local Variables All local variables must be assigned an initial value before they are referenced.
To Perform Symbolic Calculations If you want a function or program to perform symbolic calculations, you must use a global variable instead of a local. However, you must be certain that the global variable does not already exist outside of the program. The following methods can help. • Refer to a global variable name, typically with two or more characters, that is not likely to exist outside of the function or program.
How Strings Are Used A string is a sequence of characters enclosed in "quotes." In programming, strings allow the program to display information or prompt the user to perform some action. For example: Disp "The result is",answer – or – Input "Enter the angle in degrees",ang1 – or – "Enter the angle in degrees”!str1 Input str1,ang1 Some input commands (such as InputStr) automatically store user input as a string and do not require the user to enter quotation marks.
String Commands Note: See the Technical Reference module for syntax for all commands and functions. Command Description # Converts a string into a variable name. This is called indirection. & Appends (concatenates) two strings into one string. char Returns the character that corresponds to a specified character code. This is the opposite of the ord command. dim Returns the number of characters in a string. expr Converts a string into an expression and executes that expression.
Command Description right Returns a specified number of characters from the right side (end) of a string. rotate Rotates the characters in a string. The default is L1 (rotate right one character). shift Shifts the characters in a string and replaces them with spaces. The default is L1 (shift right one character and replace with one space). Examples: shift("abcde",2)⇒"cde " and shift("abcde")⇒" abcd" string Converts a numeric expression into a string. This is the opposite of the expr command.
Entering a Test Operator • Type the operator directly from the keyboard. – or – • Press 2 I and select 8:Test. Then select the operator from the menu. – or – • Display the built-in functions. Press: ½The test operators are listed near the bottom of the „ Built-in menu. Relational Tests Relational operators let you define a conditional test that compares two values. The values can be numbers, expressions, lists, or matrices (but they must match in type and dimension).
Note: From the keyboard, you can type: >= for | <= for { /= for ƒ (To get the / character, press e.) Boolean Tests Boolean operators let you combine the results of two separate tests. Operator True if: Example and Both tests are true a>0 and a{10 or At least one test is true a{0 or b+c>10 xor One test is true and the other is false a+6
Using If, Lbl, and Goto to Control Program Flow An If...EndIf structure uses a conditional test to decide whether or not to execute one or more commands. Lbl (label) and Goto commands can also be used to branch (or jump) from one place to another in a program. F2 Control Toolbar Menu To enter If...EndIf structures, use the Program Editor’s „ Control toolbar menu. The If command is available directly from the „ menu. To see a submenu that lists other If structures, select 2:If...Then.
If Command To execute only one command if a conditional test is true, use the general form: :If x>5 Ê : Disp "x is greater than 5" Ë :Disp x Ê Executed only if x>5; otherwise, skipped. Ë Always displays the value of x. In this example, you must store a value to x before executing the If command. Note: Use indentation to make your programs easier to read and understand. If...Then...
Note: EndIf marks the end of the Then block that is executed if the condition is true. If...Then...Else... EndIf Structures To execute one group of commands if a conditional test is true and a different group if the condition is false, use this structure: :If x>5 Then Ê : Disp "x is greater than 5" Ê : 2†x!x :Else Ë : Disp "x is less than or equal to 5" Ë : 5†x!x :EndIf Ì :Disp x Ê Executed only if x>5. Ë Executed only if x{5. Ì Displays value of: • 2x if x>5 • 5x if x{5 If...Then...ElseIf...
Refer to the Technical Reference module for more information and an example. Lbl and Goto Commands You can also control the flow of your program by using Lbl (label) and Goto commands. Use the Lbl command to label (assign a name to) a particular location in the program. Lbl labelName name to assign to this location (use the same naming convention as a variable name) You can then use the Goto command at any point in the program to branch to the location that corresponds to the specified label.
Because a Goto command is unconditional (it always branches to the specified label), it is often used with an If command so that you can specify a conditional test. For example: :If x>5 Ê : Goto GT5 Ë :Disp x :-------:-------:Lbl GT5 :Disp "The number was > 5” Ê If x>5, branches directly to label GT5. Ë For this example, the program must include commands (such as Stop) that prevent Lbl GT5 from being executed if x{5.
When you select a loop, the loop command and its corresponding End command are inserted at the cursor location. :For | Ê :EndFor Ê If the loop requires arguments, the cursor is positioned after the command. You can then begin entering the commands that will be executed in the loop. Note: A loop command marks the start of the loop. The corresponding End command marks the end of the loop. For...EndFor Loops A For...EndFor loop uses a counter to control the number of times the loop is repeated.
When For is executed, the variable value is compared to the end value. If variable does not exceed end, the loop is executed; otherwise, program control jumps to the command following EndFor. i>5 i{5 :For i,0,5,1 : -------: -------:EndFor :-------- Note: The For command automatically increments the counter variable so that the program can exit the loop after a certain number of repetitions.
While...EndWhile Loops A While...EndWhile loop repeats a block of commands as long as a specified condition is true. The syntax of the While command is: While condition When While is executed, the condition is evaluated. If condition is true, the loop is executed; otherwise, program control jumps to the command following EndWhile. x|5 x<5 :While x<5 : -------: -------:EndWhile :-------- Note: The While command does not automatically change the condition.
For example: Ê :0!x :While x<5 Ë : Disp x Ì : x+1!x :EndWhile Í :Disp x Ê Initially sets x. Ë Displays 0, 1, 2, 3, and 4. Ì Increments x. Í Displays 5. When x increments to 5, the loop is not executed. Loop...EndLoop Loops A Loop...EndLoop creates an infinite loop, which is repeated endlessly. The Loop command does not have any arguments.
Typically, the loop contains commands that let the program exit from the loop. Commonly used commands are: If, Exit, Goto, and Lbl (label). For example: :0!x :Loop : Disp x : x+1!x Ê : If x>5 : Exit :EndLoop Ë :Disp x Ê An If command checks the condition. Ë Exits the loop and jumps to here when x increments to 6. Note: The Exit command exits from the current loop. In this example, the If command can be anywhere in the loop.
Repeating a Loop Immediately The Cycle command immediately transfers program control to the next iteration of a loop (before the current iteration is complete). This command works with For...EndFor, While...EndWhile, and Loop...EndLoop. Lbl and Goto Loops Although the Lbl (label) and Goto commands are not strictly loop commands, they can be used to create an infinite loop. For example: :Lbl START : -------: -------:Goto START :-------As with Loop...
Configuration Commands Command Description getConfg Returns a list of calculator characteristics. getFold Returns the name of the current folder. getMode Returns the current setting for a specified mode. getUnits Returns a list of default units. setFold Sets the current folder. setGraph Sets a specified graph format (Coordinates, Graph Order, etc.). setMode Sets any mode except Current Folder. setTable Sets a specified table setup parameter (tblStart, @tbl, etc.
1. Position the cursor where you want to insert the setMode command. 2. Press: 2 ˆ to display a list of modes. Note: The Mode menu does not let you set the Current Folder mode. To set this mode, use the setFold command. 3. Select a mode to display a menu of its valid settings. 4. Select a setting. The correct syntax is inserted into your program.
To see a submenu that lists additional commands, select 1:Dialog. Input Commands Command Description getKey Returns the key code of the next key pressed. See the Technical Reference module for a listing of key codes. Input Prompts the user to enter an expression. The expression is treated according to how it is entered. For example: • A numeric expression is treated as an expression. • An expression enclosed in "quotes" is treated as a string.
Command Description Request Displays a dialog box that prompts the user to enter an expression. Request always treats the entered expression as a string. Note: String input cannot be used in a calculation. To convert a string to a numeric expression, use the expr command. Output Commands Command Description Clr[O Clears the Program I/O screen. Disp Displays an expression or string on the Program I/O screen.
Command Description Text Displays a dialog box that contains a specified character string. Notes: • In a program, simply performing a calculation does not display the result. You must use an output command. • After Disp and Output, the program immediately continues. You may want to add a Pause command. Graphical User Interface Commands Command Description Dialog... EndDlog Defines a program block (consisting of Title, Request, etc., commands) that displays a dialog box. Toolbar...
Command Description DropDown Displays a drop-down menu within a dialog box. Item Displays a menu item for a redefined toolbar. Request Creates an input box within a dialog box. Text Displays a character string within a dialog box. Title Displays the title of a dialog box or a menu title within a toolbar. Notes: • When you run a program that sets up a custom toolbar, that toolbar is still available even after the program has stopped.
Turning the Custom Menu On and Off When you create a custom menu, you can let the user turn it on and off manually, or you can let a program turn it on and off automatically. To: Do this: Turn on the custom menu From the Home screen or any other application: • Press 2 ½. From the Home screen or a program: • Turn off the custom menu Execute the CustmOn command. From any application: • Press 2 ½ again. – or – • Go to a different application. Using the default custom menu on the Home screen: 1.
Defining a Custom Menu To create a custom menu, use the following general structure. Custom : Title title of F1 menu: : Item item 1 : Item item 2 : … : Title title of F2 menu :: … : Title title of F3 menu : … Note: When the user selects a menu item, the text defined by that Item command is pasted to the current cursor location.
Ë Ë Ë :Title "Units" :Item "_m/_s^2":Item "_ft/_s^2":Item "_m":Item "_ft":Item "_l" :Item "_gal":Item "_\o\C":Item "_\o\F":Item "_kph":Item "_mph" :Title "Symbols" :Item "#":Item "\beta\":Item "?":Item "~":Item "&" :Title "Internat'l" :Item "\e`\":Item "\e'\":Item "\e^\":Item "\a`\" :Item "\u`\":Item "\u^\":Item "\o^\":Item "\c,\":Item "\u..
Editor to create a new program, and paste them into the blank program. Then modify the commands as necessary. Note: This inserts all the commands on a single line. You do not need to split them into separate lines. You can create and use only one custom menu at a time. If you need more, write a separate program for each custom menu. Then run the program for the menu you need. Restoring the Default Custom Menu To restore the default: 1.
Creating a Table or Graph To create a table or a graph based on one or more functions or equations, use the commands listed in this section. Table Commands Command Description DispTbl Displays the current contents of the Table screen. setTable Sets the Graph <–> Table or Independent table parameters. (To set the other two table parameters, you can store the applicable values to the tblStart and @tbl system variables.) Table Builds and displays a table based on one or more expressions or functions.
Command Description Graph Graphs one or more specified expressions, using the current graphing mode. Input Displays the Graph screen and lets the user update the variables xc and yc (rc and qc in polar mode) by positioning the graph cursor. NewPlot Creates a new stat plot definition. PlotsOff Deselects all (or only specified) stat data plots. PlotsOn Selects all (or only specified) stat data plots. setGraph Changes settings for the various graph formats (Coordinates, Graph Order, etc.).
Command Description CyclePic Animates a series of stored graph pictures. NewPic Creates a graph picture variable based on a matrix. RclGDB Restores all settings stored in a graph database. RclPic Displays the Graph screen and superimposes a stored graph picture by using OR logic. RplcPic Clears the Graph screen and displays a stored graph picture. StoGDB Stores the current graph settings to a graph database variable.
• Pixel coordinates — Refer to the pixels that physically make up the screen. These are independent of the viewing window because the screen is always: 159 (0 to 158) pixels wide and 77 (0 to 76) pixels tall. • Point coordinates — Refer to the coordinates in effect for the current viewing window (as defined in the Window Editor).
Drawing a Point or Pixel Command Description PtChg or PxlChg Toggles (inverts) a pixel at the specified coordinates. PtChg, which uses point coordinates, affects the pixel closest to the specified point. If the pixel is off, it is turned on. If the pixel is on, it is turned off. PtOff or PxlOff Turns off (erases) a pixel at the specified coordinates. PtOff, which uses point coordinates, affects the pixel closest to the specified point.
Command Description LineHorz or PxlHorz Draws, erases, or inverts a horizontal line at a specified row coordinate. LineTan Draws a tangent line for a specified expression at a specified point. (This draws the tangent line only, not the expression.) LineVert or PxlVert Draws, erases, or inverts a vertical line at a specified column coordinate. Drawing Expressions Command Description DrawFunc Draws a specified expression. DrawInv Draws the inverse of a specified expression.
Accessing Another TI-89 Titanium Titanium,, a CBL 2, or a CBR If you link two graphing calculators (described in the Connectivity module), programs on both units can transmit variables between them. If you link a TI-89 Titanium to a Calculator-Based Laboratory™ (CBL 2™) or a Calculator-Based Ranger™ (CBR™), a program on the TI-89 Titanium can access the CBL 2 or CBR. F3 I/O Toolbar Menu Use the Program Editor’s … I/O toolbar menu to enter the commands in this section. 1. Press … and select 8:Link. 2.
Accessing Another TI-89 Titanium When two calculators are linked, one acts as a receiving unit and the other as a sending unit. Command Description GetCalc Executed on the receiving unit. Sets up the unit to receive a variable via the I/O port. SendCalc • After the receiving unit executes GetCalc, the sending unit must execute SendCalc. • After the sending unit executes SendCalc, the sent variable is stored on the receiving unit (in the variable name specified by GetCalc).
Command Description Send Sends a list variable from the graphing calculator to the CBL 2 or CBR. Debugging Programs and Handling Errors After you write a program, you can use several techniques to find and correct errors. You can also build an error-handling command into the program itself. Run-Time Errors The first step in debugging your program is to run it. The graphing calculator automatically checks each executed command for syntax errors.
Debugging Techniques Run-time error messages can locate syntax errors but not errors in program logic. The following techniques may be useful. • During testing, do not use local variables so that you can check the variable values after the program stops. When the program is debugged, declare the applicable variables as local. • Within a program, temporarily insert Disp and Pause commands to display the values of critical variables. - Disp and Pause cannot be used in a user-defined function.
Example: Using Alternative Approaches The example in the Previews module shows a program that prompts the user to enter an integer, sums all integers from 1 to the entered integer, and displays the result. This section gives several approaches that you can use to achieve the same goal. Example 1 This example uses InputStr for input, a While...EndWhile loop to calculate the result, and Text to display the result.
Note: For {, type 8 µ (zero). For &, press: 8 p (times) Example 2 This example uses Prompt for input, Lbl, and Goto to create a loop, and Disp to display the result. Ê Ë © © © Ë Ì :prog2() :Prgm :Prompt n :0!temp:1!I :Lbl top : temp+i!temp : i+1!I : If i{n : Goto top :Disp temp :EndPrgm Ê Prompts for input on Program I/O screen. Ë Loop calculation. Ì Displays output on Program I/O screen. Note: Because Prompt returns n as a number, you do not need to use expr to convert n.
Example 3 This example uses Dialog...EndDlog to create dialog boxes for input and output. It uses Loop...EndLoop to calculate the result. Ê © © Ê Ë Ì © © © © Ì Í © © Í ê :prog3() :Prgm :Dialog : Title "Enter an integer" : Request "Integer",n :EndDlog :expr(n)!n :0!temp:0!I :Loop : temp+i!temp : i+1!I : If i>n : Exit :EndLoop :Dialog : Title "The answer is" : Text string(temp) :EndDlog :EndPrgm Ê Defines a dialog box for input. Ë Converts string entered with Request to an expression. Ì Loop calculation.
Example 4 This example uses built-in functions to calculate the result without using a loop. :prog4() :Prgm Ê :Input "Enter an integer",n Ë :sum(seq(i,i,1,n))!temp Ì :Disp temp :EndPrgm Ê Prompts for input on Program I/O. Ë Calculates sum. Ì Displays output on Program I/O screen. Note: Because Input returns n as a number, you do not need to use expr to convert n. Function Used in this example to: seq Generate the sequence of integers from 1 to n.
Assembly-Language Programs You can run programs written for the TI-89 Titanium in assembly language. Typically, assembly-language programs run much faster and provide greater control than the keystroke programs that you write with the built-in Program Editor. Where to Get Assembly-Language Programs Assembly-language programs, as well as keystroke programs, are available on the Texas Instruments web site at education.ti.com.
You can purchase computer-to-calculator and unit-to-unit cables from the TI Online Store at education.ti.com/buy. Running an Assembly-Language Program After a TI-89 Titanium assembly-language program is stored on your unit, you can run the program from the Home screen just as you would any other program. • If the program requires one or more arguments, type them within the ( ). Refer to the program’s documentation to find out about required arguments.
The programs must be stored in the MAIN folder. Also, you cannot use a shortcut to run a program that requires an argument. If you have a program with a different name and you would like to run it with a keyboard shortcut, copy or rename the existing program to kbdprgm1( ), etc. You Cannot Edit an Assembly-Language Program You cannot use your TI-89 Titanium to edit an assembly-language program. The built-in Program Editor will not open assembly-language programs.
For Information about Writing an Assembly-Language Program The information required to teach a novice programmer how to write an assemblylanguage program is beyond the scope of this book. However, if you have a working knowledge of assembly language, please check the Texas Instruments web site (education.ti.com) for specific information about how to access TI-89 Titanium features. The graphing calculator also includes an Exec command that executes a string consisting of a series of Motorola 68000 op-codes.
Text Editor Starting a Text Editor Session Each time you start the Text Editor, you can start a new text session, resume the current session (the session that was displayed the last time you used the Text Editor), or open a previous session. Starting a New Session 1. Press O and then select the Text Editor icon. Press ¸. 2. Select 3:New. The NEW dialog box is displayed. 3. Specify a folder and text variable that you want to use to store the new session.
Item Description Variable Type a variable name. If you specify a variable that already exists, an error message will be displayed when you press ¸. When you press N or ¸ to acknowledge the error, the NEW dialog box is redisplayed. 4. Press ¸ (after typing in an input box such as Variable, you must press ¸ twice) to display an empty Text Editor screen. A colon marks the beginning of a paragraph. The blinking cursor shows where typed text will appear.
Starting a New Session from the Text Editor To leave the current Text Editor session and start a new one: 1. Press ƒ and select 3:New. 2. Specify a folder and text variable for the new session. 3. Press ¸ twice. Opening a Previous Session You can open a previous Text Editor session at any time. 1. From within the Text Editor, press ƒ and select 1:Open. — or — From any application, launch Text Editor again and select 2:Open. 2. Select the applicable folder and text variable. 3. Press ¸.
Copying a Session In some cases, you may want to copy a session so that you can edit the copy while retaining the original. 1. Display the session you want to copy. 2. Press ƒ and select 2:Save Copy As. 3. Specify the folder and text variable for the copied session. 4. Press ¸ twice. Note about Deleting a Session Because all Text Editor sessions are saved automatically, you can accumulate quite a few previous sessions, which take up memory storage space.
Typing Text When you create a new Text Editor session, you see an empty screen. When you open a previous session or return to the current session, you see the existing text for that session. All text paragraphs begin with a space and a colon. The beginning space is used in command scripts and lab reports. Blinking text cursor You do not need to press ¸ at the end of each line. At the end of a line, the next character you type wraps to the next line. Press ¸ only when you want to start a new paragraph.
• Press 2 C or 2 D to scroll up or down one screen at a time, and ¹ C or ¹ D to go to the top or bottom of the text session. Typing Alphabetic Characters To: Press: Type a single lowercase alpha character. @ j and then the letter key (status line shows Type a single uppercase alpha character. @ ¤ and then the letter key (status line shows +) Type a space. @ j (alpha function of the ?·key) Turn on lowercase alphalock. @ 2 ™ (status line shows Turn on uppercase ALPHA-lock.
On the TI-89 Titanium, while either type of alpha-lock is on: • To type a period, comma, or other character that is the primary function of a key, you must turn alpha-lock off. • To type a second function character such as 2 [, you do not need to turn alphalock off. After you type the character, alpha-lock remains on.
Highlighting Text To: Do this: Highlight text Move the cursor to the beginning or end of the text. Hold ¤ and press: • A or B to highlight characters to the left or right of the cursor, respectively. • D or C to highlight all characters up to the cursor position on the next or previous line, respectively. Note: To remove highlighting without replacing or deleting, move the cursor. Replacing or Deleting Highlighted Text To: Do this: Replace highlighted text Type the new text.
Cutting, Copying, and Pasting Text Cutting and copying both place highlighted text into the clipboard of the TI-89 Titanium. Cutting deletes the text from its current location (used to move text) and copying leaves the text. 1. Highlight the text you want to move or copy. 2. Press ƒ. 3. Select the applicable menu item. • To move the text, select 4:Cut. — or — • To copy the text, select 5:Copy. Note: You can press: @ ¹ 5, ¹ 6, ¹ 7 to cut, copy, and paste without having to use the ƒ toolbar menu. 4.
Finding Text From the Text Editor: 1. Place the text cursor at any location preceding the text you want to search for. All searches start at the current cursor location. 2. Press ‡. 3. Type the search text. The search is not case sensitive. For example: CASE, case, and Case have the same effect. Note: The FIND dialog box retains the last search text you entered. You can type over it or edit it. 4. Press ¸ twice. If the search text is: The cursor: Found Moves to beginning of the search text.
Inserting or Overtyping a Character By default, the TI-89 Titanium is in insert mode. To toggle between insert and overtype mode, press 2 /. If the TI-89 Titanium is in: The next character you type: Will be inserted at the cursor. Thin cursor between characters Will replace the highlighted character. Cursor highlights a character Note: Look at the shape of the cursor to see if you’re in insert or overtype mode.
Selecting Characters from the CHAR Menu 1. Press 2 G. 2. Select the applicable category. A menu lists the characters in that category. 3. Select a character. You may need to scroll through the menu. $ indicates that you can scroll. Note: For accented characters, select International. Commonly used international characters are also available from the default custom menu (2 ¾).
• Press N to exit the map. TI-89 Titanium Keyboard map To access the TI-89 Titanium shortcuts, first press the ¹ key. TI-89 Titanium keyboard map feature shortcuts: • GREEK (¹ c) — Accesses the Greek character set (described later in this section). • SYSDATA (¹ b) — Copies the current graph coordinates to the system variable sysdata. • FMT (¹ Í) — Displays the FORMATS dialog box.
• HOMEDATA (¹ ?) — Copies the current graph coordinates to the Home screen’s history area. Typing Special Symbols from the Keyboard Note: To help you find the applicable keys, these maps show only the special symbols. On the TI-89 Titanium: f Press ¹ and then the key for the symbol. For example: ¹ p (times) displays &. These special symbols are not affected by whether Alpha-Lock is on or off.
On the TI-89 Titanium: f Press ¹ c to access the Greek character set. ξ ψ ζ X Y Z α β A B φ F K T ∆ δ ε C D E H I J Γ γ G λ µ L M Π π P τ Q N Σ σ O ρ R S U Ω ω V W Note: If you press a key combination that does not access a Greek letter, you get the normal letter for that key. Your calculator does not display a map of Greek letters; the map shown here is for reference only. Several keys let you access lowercase and uppercase Greek letters.
• Press ¹ c 7 + letter to access uppercase Greek letters. Example: ¹ c 7 [W] displays Ω The exact keys that you press on the TI-89 Titanium depend on whether alpha-lock is on or off. For example: On the TI-89 Titanium, if: Then: Alpha-lock is off. ¹ c X or ¹ c j X displays ξ. (j is not required for X, Y, Z, or T.) ¹ c j W displays ω. ¹ c 7 W displays Ω. (7 is used for uppercase letters.) Lowercase alpha-lock (2 ™) is on. ¹ c X displays ξ. ¹ c W displays ω. ¹ c 7 W displays Ω.
Entering and Executing a Command Script By using a command script, you can use the Text Editor to type a series of command lines that can be executed at any time on the Home screen. This lets you create interactive example scripts in which you predefine a series of commands and then execute them individually. Inserting a Command Mark In the Text Editor: 1. Place the cursor on the line for the command. 2. Press „ to display the Command toolbar menu. 3. Select 1:Command.
4. Type a command just as you would on the Home screen. The line can contain only the command, with no additional text. Note: You can mark a line as a command either before or after typing the command on that line. You can type multiple commands on the same line if you type a colon to separate the commands. Deleting a Command Mark This deletes only the C mark; it does not delete the command text itself. 1. Place the cursor anywhere on the marked line. 2. Press „ and select 4:Clear command.
The command is copied to the entry line on the Home screen and executed. The Home screen is displayed temporarily during execution, and then the Text Editor is redisplayed. After execution, the cursor moves to the next line in the script so that you can continue to execute a series of commands.
Creating a Script from Your Home Screen Entries From the Home screen, you can save all the entries in the history area to a text variable. The entries are automatically saved in a script format so that you can open the text variable in the Text Editor and execute the entries as commands. For information, refer to “Saving the Home Screen Entries as a Text Editor Script” in the Calculator Home Screen module.
Example 1. Type your script. Press „ and select 1:Command to mark the command lines. 2. Press … and select 1:Script view. 3. Move the cursor to the first command line. Then press † to execute the command. Note: Some commands take longer to execute. Wait until the Busy indicator disappears before pressing † again. 4. Continue using † to execute each command, but stop just before executing the Graph command. 5. Execute the Graph command.
Numeric Solver Displaying the Solver and Entering an Equation After you display the Numeric Solver, start by entering the equation that you want to solve. Displaying the Numeric Solver To display the Numeric Solver, press O and then select the Numeric Solver icon. Press ¸. The Numeric Solver screen shows the last entered equation, if any. Entering an Equation On the eqn: line, type in your equation. You can: For example: Type an equation directly.
You can: For example: Refer to a function or equation defined elsewhere. Notes: Suppose you defined y1(x) on either the: • • • Y= Editor: Do not use system function y1(x)=1.25x†cos(x) names (such as y1(x) or r1(q)) – or – as simple variables (y1 or r1). • Home screen: Be careful with implied Define y1(x)=1.25x†cos(x) multiplication. For example, In the Numeric Solver, you then would a(m2+m1) is treated as a enter: function reference, not as y1(x)=0 or y1(t)=0, etc. a†(m2+m1).
Recalling Previously Entered Equations Your most recently entered equations (up to 11 with the default setting) are retained in memory. To recall one of these equations: 1. From the Numeric Solver screen, press à ‡. A dialog box displays the most recently entered equation. 2. Select an equation. • To select the displayed equation, press ¸. • To select a different equation, press B to display a list. Then select the one you want. Note: You can specify how many equations are retained.
Saving Equations for Future Use Because the number of equations that you can recall with ‡ Eqns is limited, a particular equation may not be retained indefinitely. To store the current equation for future use, save it to a variable. 1. From the Numeric Solver screen, press , and select 2:Save Copy As. 2. Specify a folder and a variable name for the equation. 3. Press ¸ twice. Note: An equation variable has an EXPR data type, as shown on the MEMORY and VAR-LINK screens.
2. Select the applicable folder and equation variable. 3. Press ¸. Variable eqn contains the current equation; it always appears alphabetically in the list. Defining the Known Variables After you type an equation in the Numeric Solver, enter the applicable values for all variables except the unknown variable. Defining the List of Variables After typing your equation on the eqn: line, press ¸ or D. The screen lists the variables in the order they appear in the equation.
Enter a number or expression for all variables except the one you want to solve for. Notes and Common Errors • If you define a variable: - - • In terms of another variable in the equation, that variable must be defined first. In terms of another variable that is not in the equation, that variable must already have a value; it cannot be undefined. As an expression, it is evaluated when you move the cursor off the line.
• • If you refer to a previously defined function, any variables used as arguments in the function call are listed, not the variables used to define the function. If the equation contains a system variable (xmin, xmax, etc.), that variable is not listed. The solver uses the system variable’s existing value. Note: You cannot solve for a system variable other than exp. Also, if the equation contains a system variable, you cannot use … to graph.
• If you see the error shown to the right, delete the entered variable value. Then edit the equation to use a different variable. Note: This error occurs if you use a reserved name incorrectly or refer to an undefined system function as a simple variable without parentheses. For example, y1(x) is undefined and you use y1. Editing the Equation In the Numeric Solver, press C until the cursor is on the equation. The screen automatically changes to show only the eqn: line.
For the bounds, you can also enter variables or expressions that evaluate to appropriate values (bound={lower,upper}) or a valid list variable that contains a two-element list (bound=list). The bounds must be two floating point elements with the first one less than or equal to the second one. Note: You can also select an initial guess graphically.
Note: To stop (break) a calculation, press ´. The unknown variable shows the value being tested when the break occurred. Using the solution and your entered values, the left and right sides of the equation are evaluated separately. leftNrt shows the difference, which indicates the solution’s accuracy. The smaller the value, the more accurate the solution. If the solution is precise, leftNrt=0. If you: Do this: Want to solve for other values Edit the equation or variable values.
see how many solutions exist and use the cursor to select an accurate initial guess and bounds. Displaying the Graph In the Numeric Solver, leave the cursor on the unknown variable. Press … and select: 1:Graph View – or – 3:ZoomStd – or – 4:ZoomFit Graph View uses the current Window variable values. For information about ZoomStd and ZoomFit, refer to Basic Function Graphing. The graph is shown in a split screen, where: • The unknown variable is plotted on the x axis.
You can explore the graph by using the free-moving cursor, tracing, zooming, etc., as described in Basic Function Graphing. How the Graph Affects Various Settings When you use the Numeric Solver to display a graph: • The following modes are changed automatically to these settings: Mode Setting Graph FUNCTION Any functions selected in the Y= Editor will not be graphed.
Selecting a New Initial Guess from the Graph To use the graph cursor to select an initial guess: 1. Move the cursor (either free-moving or trace) to the point that you want to use as the new guess. 2. Use 2 a to make the Numeric Solver screen active. 3. Make sure the cursor is on the unknown variable, and press †. Note: Cursor coordinate xc is the unknown variable value, and yc is the leftNrt value. 4. Press „ to re-solve the equation.
Clearing Variables Before Leaving the Numeric Solver When you solve an equation, its variables still exist after you leave the Numeric Solver. If the equation contains single-character variables, their values may inadvertently affect later symbolic calculations. Before leaving the Numeric Solver, you may want to: 1. Press: @ 2ˆ to clear all single-character variables in the current folder. 2. Press ¸ to confirm the action. The screen returns to the solver’s eqn: line.
Number Bases Entering and Converting Number Bases Regardless of the Base mode, you must always use the appropriate prefix when entering a binary or hexadecimal number.
Converting between Number Bases Use the 4 conversion operator integerExpression 4 Bin integerExpression 4 Dec integerExpression 4 Hex For 4, press 2 4. Also, you can select base conversions from the MATH/Base menu. For example, to convert 256 from decimal to binary: For a binary or hex entry, you must use the 0b or 0h prefix. 256 4 Bin Note: If your entry is not an integer, a Domain error is displayed. To convert 101110 from binary to hexadecimal: Results use the 0b or 0h prefix to identify.
2. From the Home screen, type the number that you want to convert (using the correct prefix) and press ¸. If Base mode = HEX: Performing Math Operations with Hex or Bin Numbers For any operation that uses an integer number, you can enter a hexadecimal or binary number. Results are displayed according to the Base mode. However, results are restricted to certain size limits when Base = HEX or BIN. Setting the Base Mode for Displayed Results 1. Press 3 „ to display Page 2 of the MODE screen. 2.
The Base mode controls the displayed format of integer results only. If Base mode = HEX: Note: The Base mode affects output only. You must always use the 0h or 0b prefix to enter a hex or binary number. Fractional and floating-point results are always shown in decimal form. 0h prefix in result identifies the base. Dividing When Base = HEX or BIN When Base=HEX or BIN, a division result is displayed in hexadecimal or binary form only if the result is an integer.
Size Limitations When Base = HEX or BIN When Base=HEX or BIN, an integer result is stored internally as a signed, 32-bit binary number, which uses the range (shown in hexadecimal and decimal): 0hFFFFFFFF L1 0h80000000 ‘L2,147,483,648 0h1 1 0h0 0 0h7FFFFFFF 2,147,483,647 If a result’s magnitude is too large to be stored in a signed, 32-bit binary form, a symmetric modulo operation brings the result into the range. Any number greater than 0h7FFFFFFF is affected.
Operator with syntax Description integer1 and integer2 In a bit-by-bit and comparison, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results. integer1 or integer2 In a bit-by-bit or comparison, the result is 1 if either bit is 1; the result is 0 only if both bits are 0. The returned value represents the bit results.
0h7AC36 = 0b00000000000001111010110000110110 and 0h3D5F and 0b00000000000000000011110101011111 0b00000000000000000010110000010110 = 0h2C16 Leading zeros are not shown in the result. Note: If you enter an integer that is too large to be stored in a signed, 32-bit binary form, a symmetric modulo operation brings the value into the range. The result is displayed according to the Base mode.
Function with syntax Description shift(integer) – or – shift(integer,#ofShifts) If #ofShifts is: • omitted — bits shift once to the right (default is L1). • negative — bits shift the specified number of times to the right. • positive — bits shift the specified number of times to the left. In a right shift, the rightmost bit is dropped and 0 or 1 is inserted to match the leftmost bit. In a left shift, the leftmost bit is dropped and 0 is inserted as the rightmost bit.
Each bit shifts to the right. 7AC36 = 0b00000000000001111010110000110110 Inserts 0 if leftmost bit is 0, or 1 if leftmost bit is 1 Dropped b00000000000000111101011000011011 = 0h3D61B Leading zeros are not shown in the result. The result is displayed according to the Base mode. Note: If you enter an integer that is too large to be stored in a signed, 32-bit binary form, a symmetric modulo operation brings the value into the range.
Memory and Variable Management Checking and Resetting Memory The MEMORY screen shows the amount of memory (in bytes) used by all variables in each data type, regardless of whether the variables are stored in RAM or the user data archive. You can also use this screen to reset the memory. Displaying the MEMORY Screen Press 2 ;. (The numbers on your MEMORY screen may vary from those shown.) Prgm/Asn: Includes programs written for the TI-89 Titanium as well as any assembly-language programs you have loaded.
Resetting the Memory From the MEMORY screen: 1. Press ƒ. 2. Select the applicable item. Item Description RAM 1:All RAM: Resetting RAM erases all data and programs from RAM. 2:Default: Resets all system variables and modes to their original factory settings. This does not affect any user-defined variables, functions, or folders. Flash ROM 1:Archive: Resetting Archive erases all data and programs from Flash ROM. 2:Flash Apps: Resetting Flash Apps erases all Flash applications from Flash ROM.
Displaying the VAR-LINK Screen The VAR-LINK screen lists the variables and folders that are currently defined. After displaying the screen, you can manipulate the variables and/or folders. Displaying the VAR-LINK Screen Press 2 °. By default, the VAR-LINK screen lists all user-defined variables in all folders and with all data types. Ë Ê Ì Î Í Ê Folder names (alphabetically listed) Ë Shows installed Flash applications Ì Size in bytes Í Data type Î Variable names (alphabetically listed) This...
This... Indicates this... 6 Expanded folder view (to right of folder name). 6 You can scroll for more variables and/or folders (in bottom left corner of screen). Ÿ If selected with †. Œ Locked û Archived To scroll through the list: • Press D or C. (Use 2 D or 2 C to scroll one page at a time.) – or – • Type a letter. If there are any variable names that start with that letter, the cursor moves to highlight the first of those variable names.
Variable Types as Listed on VAR-LINK Type Description ASM Assembly-language program DATA Data EXPR Expression (includes numeric values) FUNC Function GDB Graph database LIST List MAT Matrix PIC Picture of a graph PRGM Program STR String TEXT Text Editor session Types not listed above are miscellaneous data types used by software applications. Closing the VAR-LINK Screen To close the VAR-LINK screen and return to the current application, use ¸ or N as described below.
Press: To: N Return to the current application without pasting the highlighted name. Displaying Information about Variables on the Home Screen From the Home screen, you can display information about variables without opening the VAR-LINK screen. • To determine if a variable with a given name exists in the system table, Enter the IsVar() function on the Home screen. IsVar (var_name) IsVar is a function, which requires you to enclose the variable name in parentheses.
Showing the Contents of a Variable You can show all variable types except ASM, DATA, GDB, and variables created by Flash Apps. For example, you must open a DATA variable in the Data/Matrix Editor. 1. On VAR-LINK, move the cursor to highlight the variable. 2. Press: 2ˆ If you highlight a folder, the screen shows the number of variables in that folder. 3. To return to VAR-LINK, press any key. Note: You cannot edit the contents from this screen.
To select: Do this: All folders and all variables Press B to expand the folder, then press ‡ All and select 1:Select All. Choosing 3:Select Current selects the last set of items transmitted to your unit during the current VAR-LINK session. Choosing 4:Expand All or 5:Collapse All expands or collapses your folders or Flash applications. Note: Press either A or B to toggle between expanded or collapsed view when you have a folder highlighted.
By creating additional folders, you can store independent sets of user-defined variables (including user-defined functions). For example, you can create separate folders for different TI-89 Titanium applications (Math, Text Editor, etc.) or classes. You can store a user-defined variable in any existing folder. The user-defined variables in one folder are independent of the variables in any other folder. Therefore, folders can store separate sets of variables with the same names but different values.
The system variables in the MAIN folder are always directly accessible, regardless of the current folder. Note: User-defined variables are stored in the “current folder” unless you specify otherwise. Creating a Folder from the VAR-LINK Screen 1. Press 2 °. 2. Press ƒ Manage and select 5:Create Folder. 3. Type a unique folder name up to eight characters, and press ¸ twice. After you create a new folder from VAR-LINK, that folder is not automatically set as the current folder.
Setting the Current Folder from the Home Screen Enter the setFold function on the Home screen. setFold (folderName) setFold is a function, which requires you to enclose the folder name in parentheses. When you execute setFold, it returns the name of the folder that was previously set as the current folder. Setting the Current Folder from the MODE Dialog Box 1. Press 3. 2. Highlight the Current Folder setting. 3. Press B to display a menu of existing folders.
Renaming Variables or Folders Remember, if you use † to select a folder, the variables in that folder are selected automatically. As necessary, use † to deselect individual variables. 1. On VAR-LINK, select the variables and/or folders. 2. Press ƒ Manage and select 3:Rename. 3. Type a unique name, and press ¸ twice. If you selected multiple items, you are prompted to enter a new name for each one.
For example: If Current Folder = MAIN Folders and Variables MAIN a=1 f(x)=x³+x²+x MATH a=42 f(x)=3x²+4x+25 To see a list of existing folders and variables, press 2 °. On the VAR-LINK screen, you can highlight a variable and press ¸ to paste that variable name to the open application's entry line. If you paste a variable name that is not in the current folder, the pathname (folderName\variableName) is pasted.
From the VAR-LINK screen: 1. Press „ View. 2. Highlight the setting you want to change, and press B. This displays a menu of valid choices. (To cancel a menu, press N.) View — Allows you to choose variables, Flash applications, or system variables to view. Note: To list system variables (window variables, etc.), select 3:System. Folder — Always lists 1:All and 2:main, but lists other folders only if you have created them. Var Type — Lists the valid variable types.
Copying or Moving Variables from One Folder to Another You must have at least one folder other than MAIN. You cannot use VAR-LINK to copy variables within the same folder. 1. On VAR-LINK, select the variables. 2. Press ƒ Manage and select 2:Copy or 4:Move. 3. Select the destination folder. 4. Press ¸. The copied or moved variables retain their original names. Note: To copy a variable to a different name in the same folder, use 9 (such as a1!a2) or the CopyVar command from the Home screen.
2. Press ƒ Manage and select 6:Lock or 7:UnLock. Œ indicates a locked variable or folder in RAM. û indicates an archived variable, which is locked automatically. Deleting a Folder from the VAR-LINK Screen When you delete a folder from the VAR-LINK screen, all of the variables in that folder are also deleted. You cannot delete the MAIN folder. 1. Press 2 °. 2. Press † to select the folder(s) to delete. (The folder's variables become selected automatically.) 3. Press ƒ 1:Delete or 0. 4.
Deleting a Variable or a Folder from the Home Screen Before deleting a folder from the Home screen, you must first delete all the variables stored in that folder. • To delete a variable, enter the DelVar command on the calculator Home screen. DelVar var1 [, var2] [, var3] ... • To delete all variables of a specific type, enter the DelType command on the calculator Home screen. DelType var_type where var_type is the variable type.
• Home screen, Y= Editor, Table Editor, or Data/Matrix Editor — The cursor must be on the entry line. • Text Editor, Window Editor, Numeric Solver, or Program Editor — The cursor can be anywhere on the screen. You can also paste a variable name to the current cursor location in many Flash applications. Procedure Starting from an application listed above: 1. Position the cursor where you want to insert the variable name. sin(| 2. Press 2 °. 3. Highlight the applicable variable.
If you paste a variable name that is not in the current folder, the variable’s pathname is pasted. sin(class\a2 Assuming that CLASS is not the current folder, this is pasted if you highlight the a2 variable in CLASS. Archiving and Unarchiving a Variable To archive or unarchive one or more variables interactively, use the VAR-LINK screen. You can also perform these operations from the Home screen or a program.
Additional free RAM can improve performance times for certain types of calculations. From the VAR-LINK Screen To archive or unarchive: 1. Press 2 ° to display the VAR-LINK screen. 2. Select one or more variables, which can be in different folders. (You can select an entire folder by selecting the folder name.) Note: To select a single variable, highlight it. To select multiple variables, highlight each variable and press † Ÿ. 3.
From the Home Screen or a Program Use the Archive and Unarchiv commands: Archive variable1, variable2, … Unarchiv variable1, variable2, … If a Garbage Collection Message Is Displayed If you use the user data archive extensively, you may see a Garbage Collection message. This occurs if you try to archive a variable when there is not enough free archive memory. However, the TI-89 Titanium will attempt to rearrange the archived variables to make additional room.
Why not Perform Garbage Collection Automatically, without a Message? The message: • Lets you know why an archive will take longer than usual. It also alerts you that the archive may fail if there is not enough memory. • Can alert you when a program is caught in a loop that repetitively fills the user data archive. Cancel the archive and investigate the reason. Why Is Garbage Collection Necessary? The user data archive is divided into sectors.
variable D variable A Sector 1 variable B Empty block variable C Sector 2 Depending on its size, variable D is stored in one of these locations. Sector 3 This process continues to the end of the last sector. Depending on the size of individual variables, the empty blocks may account for a significant amount of space. Note: Garbage collection occurs when the variable you are archiving is larger than any empty block.
v a r ia b le A After you unarchive variables B and C, they continue to take up space. Sector 1 Sector 2 v a r ia b le D Sector 3 Unarchived variables are “marked for deletion,” meaning they will be deleted during the next garbage collection. If the MEMORY Screen Shows Enough Free Space Even if the MEMORY screen shows enough free space to archive a variable, you may still get a Garbage Collection message.
The Garbage Collection Process The garbage collection process: • Deletes unarchived variables from the user data archive. • Rearranges the remaining variables into consecutive blocks. v a r ia b le A Sector 1 v a r ia b le D Sector 2 Memory Error When Accessing an Archived Variable An archived variable is treated the same as a locked variable. You can access the variable, but you cannot edit or delete it. In some cases, however, you may get a Memory Error when you try to access an archived variable.
• Opening a text variable in the Text Editor. • Opening a data variable, list, or matrix in the Data/Matrix Editor. • Opening a program or function in the Program Editor. • Running a program or referring to a function. Note: A temporary copy lets you open or execute an archived variable. However, you cannot save any changes to the variable. So that you do not have to unarchive variables unnecessarily, the TI-89 Titanium performs a “behind-the scenes” copy.
3. Free up the needed amount of memory by: • Deleting unnecessary variables from RAM. • Archiving large variables or programs (moving them from RAM to the user data archive). Note: Typically, the RAM free size must be larger than the archived variable.
Connectivity Connecting Two Units The TI-89 Titanium comes with a cable that lets you connect two units. Once connected, you can transmit information between two units. A USB unit-to-unit cable is included with the TI-89 Titanium; use the calculator’s USB port with this cable. Note: The TI-89 Titanium features both a USB port and an I/O port, so you can connect TI graphing calculators with either type of link port.
USB Port USB unit-to-unit cable USB Port Two TI-89 Titanium calculators linked together USB unit-to-unit cable Position so that the USB symbols face each other; then insert the connector.
I/O Port I/O unit-to-unit cable I/O Port A TI-89 Titanium and a Voyage™ 200 linked together Connectivity 718
I/O Port I/O unit-to-unit cable TI-89 I/O Port A TI-89 Titanium and a TI-89 linked together Transmitting Variables, Flash Applications, and Folders Transmitting variables is a convenient way to share any variable listed on the VAR-LINK screen — functions, programs, etc. You can also transmit Flash applications (Apps) and folders.
Setting Up the Units Flash applications will transfer only between certain units. For example, you can transfer an App from a TI-89 Titanium to another TI-89 Titanium, or from a TI-89 Titanium to a TI89. 1. Connect two graphing calculators using the appropriate cable. 2. On the sending unit, press 2 ° to display the VAR-LINK screen. 3. On the sending unit, select the variables, folders, or Flash applications you want to send.
- If selecting a Flash App (from the F7 tab), this selects the App folder and its contents. A checkmark appears beside the folder, but not beside the contents. Collapsed Flash App folders do not automatically become expanded. • To select multiple variables, Flash applications, or folders, highlight each one and press † to place a checkmark (Ÿ) beside it. Use † again to deselect any that you do not want to transmit. • To select all variables, Flash applications, or folders use ‡ All 1:Select All. 4.
5. On both the receiving and the sending unit, press … Link to display the menu options. 6. On the receiving unit, select 2:Receive. The message VAR-LINK: WAITING TO RECEIVE and the BUSY indicator are displayed in the status line of the receiving unit. 7. On the sending unit, select 1:Send This starts the transmission. During transmission, a progress bar is displayed in the status line of the receiving unit. When transmission is complete, the VAR-LINK screen is updated on the receiving unit.
Locked variables that have the same name on both the sending and receiving units must be unlocked on the receiving unit before they can be overwritten from the sending unit. If archived variables have the same names on both the sending and receiving units, a message asks you to confirm that you will allow the variables to be overwritten. If you select: What happens: Unlocked variable The variable is transmitted to the current folder and it remains unlocked on the receiving unit.
Canceling a Transmission From either the sending or receiving unit: 1. Press ´. An error message is displayed. 2. Press N or ¸. Common Error and Notification Messages Shown on: Message and Description: Sending unit This is displayed after several seconds if: • A cable is not attached to the sending unit’s link port. – or – • A receiving unit is not attached to the other end of the cable. – or – • The receiving unit is not set up to receive. Press N or ¸ to cancel the transmission.
Shown on: Message and Description: Sending unit The receiving unit does not have the correct certification for the operating system (OS) or Flash application being sent. Receiving unit New Name is active only if you change Overwrite to NO. The receiving unit has a variable with the same name as the specified variable being sent. Connectivity • To overwrite the existing variable, press ¸. (By default, Overwrite = YES.) • To store the variable to a different name, set Overwrite = NO.
Shown on: Message and Description: Receiving unit The receiving unit does not have enough memory for what is being sent. Press N or ¸ to cancel the transmission. Deleting Variables, Flash Applications, or Folders 1. Press 2 ° to display the VAR-LINK screen. 2. Select the variables, folders, or Flash applications to delete. • To select a single variable, Flash application, or folder, move the cursor to highlight it and press † to place a checkmark (Ÿ) beside it.
3. Press ƒ and choose 1:Delete. – or – Press 0. A confirmation message appears. 4. Press ¸ to confirm the deletion. Where to Get Flash Applications (Apps) For up-to-date information about available Flash applications, check the Texas Instruments Web site at education.ti.com. Many Apps no longer require a certificate. If you try to transfer an App from one unit to another and receive an Unlicensed OS or Flash application message, try downloading the App again from the Texas Instruments Web site at education.
You can use optional parameters with the SendCalc or GetCalc command to specify either the USB port or I/O port. (See Appendix A for details.) If you do not include these parameters, the TI-89 Titanium communicates through the USB port. The “Chat” Program The following program uses GetCalc and SendCalc. The program sets up two loops that let the linked devices take turns sending and receiving/displaying a variable named msg. InputStr lets each user enter a message in the msg variable.
Ê Ë Í Î :Chat() :Prgm :ClrIO :Disp "On first unit to send,"," enter 1;","On first to receive," :InputStr " enter 0",msg :If msg="0" Then : While true : GetCalc msg : Disp msg Ì : InputStr msg : SendCalc msg : EndWhile :Else : While true : InputStr msg : SendCalc msg Ï : GetCalc msg : Disp msg : EndWhile :EndIf :EndPrgm Notes: Ê Sets up this unit to receive and display the variable msg. Ë Then lets this user enter a message in msg and send it. Ì Loop executed by the unit that receives the first message.
To synchronize GetCalc and SendCalc, the loops are arranged so that the receiving unit executes GetCalc while the sending unit is waiting for the user to enter a message. Running the Program This procedure assumes that: • The two devices are linked with the connecting cable. • The Chat program is loaded on both devices. - Use each device’s Program Editor to enter the program. – or – Enter the program on one device and then use VAR-LINK to transmit the program variable to the other device.
Stopping the Program Because the Chat program sets up an infinite loop on both devices, press ´ (on both devices) to break the program. If you press N to acknowledge the error message, the program stops on the Program I/O screen. Press ‡ or N to return to the Home screen. Upgrading the Operating System (OS) You can upgrade the OS on your TI-89 Titanium using your computer.
messages and status information related to new functionality in the OS may not display correctly. When in OS download mode, the Automatic Power Down™ (APD™) feature does not function. If you leave your device in download mode for an extended time before you actually start the downloading process, your batteries may become depleted. You will then need to replace the depleted batteries with new batteries before downloading.
• Use a USB cable or TI Connectivity Cable USB and TI Connect™ software (education.ti.com/downloadticonnect) to send the variables and/or Flash applications to a computer. Where to Get Operating System Upgrades For up-to-date information about available OS upgrades, check the Texas Instruments Web site at education.ti.com/downloadticonnect.
4. On the receiving unit, select 5:Receive OS. A warning message displays. Press N to halt the process, or press ¸ to proceed. Pressing ¸, displays VAR-LINK: WAITING TO RECEIVE and BUSY in the status line of the receiving unit. 5. On the sending unit, select 4:Send OS. A warning message displays. Press N to halt the process, or press ¸ to start the transmission. Important: • For each receiving unit, remember to back up information as necessary and install new batteries.
If You are Upgrading the Operating System on Multiple Units To perform an OS upgrade on multiple units, download and install the OS into one unit and then transfer the OS upgrade from one unit to another. This method is faster than installing it on each unit via a computer. OS upgrades are released free of charge and you do not need to obtain a certificate before you download or install them. Error Messages Most error messages are displayed on the sending unit.
Error Message Description Replace the batteries on the unit displaying this message. Collecting and Transmitting ID Lists The VAR-LINK screen … 6:Send ID List menu option allows collection of electronic ID numbers from individual TI-89 Titanium, TI-89, Voyage™ 200, or TI-92 Plus devices. ID Lists and Group Certificates The ID list feature provides a convenient way to collect device IDs for group purchase of commercial applications.
To send an ID number from one device to another, first connect two units by using a USB unit-to-unit cable or I/O unit-to-unit cable. Step: On the: Do this: 1. Collecting unit (Receiving unit) Display the Home screen. Press:" 2. Sending unit a. Press 2 ° to display the VAR-LINK screen. b. Press … Link and select 6:Send ID List. The sending unit adds a copy of its unique ID number to the collection unit’s ID list.
• Each time an ID list is successfully sent from one device to another, the ID list is automatically deleted from the sending unit. • If an ID is collected from a device twice, the duplicate ID is automatically deleted from the list. Clearing the ID List The ID list remains on the collection device after it is uploaded to the computer. You can then use the collection device to upload the list to other computers. To clear the ID list from the collection unit: 1. Press 2 ° to display the VAR-LINK screen.
Most functions of the TI-89 Titanium are compatible with the TI-89, Voyage™ 200, and TI-92 Plus. The TI-89 Titanium and the TI-89 are similar, except that the TI-89 Titanium has more memory (more room for Apps and user archive) and the TI-89 Titanium has a USB port. The Voyage™ 200 is the same as the TI-92 Plus except it has more memory, and thus more room for applications (Apps).
Link Transmission Table To & From ( TI-89 Titanium TI-89 Titanium OS Apps Variables Apps Variables Variables Variables TI-89 Apps Variables OS Apps Variables Variables Variables Voyage™ 2 Variables 00 Variables OS Apps Variables Apps Variables TI-92 Plus Variables Apps Variables OS Apps Variables Connectivity Variables TI-89 Voyage™ 2 00 TI-92 Plus 740
Activities Analyzing the Pole-Corner Problem A ten-foot-wide hallway meets a five-foot-wide hallway in the corner of a building. Find the maximum length pole that can be moved around the corner without tilting the pole. Maximum Length of Pole in Hallway The maximum length of a pole c is the shortest line segment touching the interior corner and opposite sides of the two hallways as shown in the diagram below. Use proportional sides and the Pythagorean theorem to find the length c with respect to w.
10 a = w+5 b = 10a w w a c 5 b 1. Define the expression for side a in terms of w and store it in a(w). Note: When you want to define a function, use multiple character names as you build the definition. 2. Define the expression for side b in terms of w and store it in b(w). 3. Define the expression for side c in terms of w and store it in c(w).
4. Use the zeros( ) function to compute the zeros of the first derivative of c(w) to find the minimum value of c(w). Note: The maximum length of the pole is the minimum value of c(w). 5. Compute the exact maximum length of the pole. Enter: c (2 ±) 6. Compute the approximate maximum length of the pole. Result: Approximately 20.8097 feet. Note: Use the auto-paste feature to copy the result from step 4 to the entry line inside the parentheses of c( ) and press 8 ¸.
Detailed information about using the functions in this example can be found in Symbolic Manipulation. Performing Computations to Derive the Quadratic Formula Perform the following steps to derive the quadratic formula by completing the square of the generalized quadratic equation. 1. Clear all one-character variables in the current folder. 2ˆ Choose 1:Clear a-z and press ¸ to confirm. 2. On the Home screen, enter the generalized quadratic equation: ax2+bx+c=0. 3. Subtract c from both sides of the equation.
4. Divide both sides of the equation by the leading coefficient a. Note: Continue to use the last answer (2 ±) as in step 3 in steps 4 through 9. 5. Use the expand( ) function to expand the result of the last answer. 6. Complete the square by adding ((b/a)/2)2 to both sides of the equation. 7. Factor the result using the factor( ) function. 8. Multiply both sides of the equation by 4a2.
9. Take the square root of both sides of the equation with the constraint that a>0 and b>0 and x>0. 10. Solve for x by subtracting b from both sides and then dividing by 2a. Note: This is only one of the two general quadratic solutions due to the constraint in step 9. Exploring a Matrix This activity shows you how to perform several matrix operations.
Exploring a 3x3 Matrix Perform these steps to generate a random matrix, augment and find the identity matrix, and then solve to find an invalid value of the inverse. 1. On the Home screen, use RandSeed to set the random number generator seed to the factory default, and then use randMat( ) to create a random 3x3 matrix and store it in a. 2. Replace the [2,3] element of the matrix with the variable x, and then use the augment( ) function, to augment the 3x3 identity to a and store the result in b. 3.
4. Solve for the value of x that will cause the inverse of the matrix to be invalid. Enter: solve(getDenom( 2 ± [1,4] )=0,x) Result: x= L70/17 Note: Use the cursor in the history area to scroll the result. Exploring cos(x) = sin(x) This activity uses two methods to find where cos(x) = sin(x) for the values of x between 0 and 3p. Method 1: Graph Plot Perform the following steps to observe where the graphs of the functions y1(x)=cos(x) and y2(x)=sin(x) intersect. 1.
4. Find the intersection point of the two functions. Note: Press ‡ and select 5:Intersection. Respond to the screen prompts to select the two curves, and the lower and upper bounds for intersection A. 5. Note the x and y coordinates. (Repeat steps 4 and 5 to find the other intersections.) Method 2: Symbolic Manipulation Perform the following steps to solve the equation sin(x)=cos(x) with respect to x. 1. On the Home screen, enter solve(sin(x)= cos(x),x). The solution for x is where @n1 is any integer. 2.
3. Enter the general solution for x and apply the constraint for @n1 as shown. Compare the result with Method 1. Note: To get the with operator, press: Í Finding Minimum Surface Area of a Parallelepiped This activity shows you how to find the minimum surface area of a parallelepiped having a constant volume V. Detailed information about the steps used in this example can be found in Symbolic Manipulation and 3D Graphing.
2. Select the 3D Graph mode. Then enter the function for z1(x,y) as shown in this example with volume v=300. 3. Set the Window variables to: eye= [60,90,0] x= [0,15,15] y= [0,15,15] z= [260,300] ncontour= [5] 4. Graph the function and use Trace to go to the point close to the minimum value of the surface area function. Finding the Minimum Surface Area Analytically Perform the following steps to solve the problem analytically on the Home screen. 1. Solve for x and y in terms of v.
2. Find the minimum surface area when the value of v equals 300. Enter: 300!v Enter: sa(v^(1/3), v^(1/3),v) Note: Press ¸ to obtain the exact result in symbolic form. Press 8 ¸ to obtain the approximate result in decimal form. Running a Tutorial Script Using the Text Editor This activity shows you how to use the Text Editor to run a tutorial script.
2. Type the following lines into the Text Editor. C C C C C C : Compute the maximum value of f on the closed interval [a,b] : assume that f is differentiable on [a,b] : define f(x)=x^3N2x^2+xN7 : 1!a:3.22!b : d(f(x),x)!df(x) : zeros(df(x),x) : f(ans(1)) : f({a,b}) : The largest number from the previous two commands is the maximum value of the function. The smallest number is the minimum value. 3. Press … and select 1:Script view to show the Text Editor and the Home screen on a split-screen.
4. Press † repeatedly to execute each line in the script one at a time. Note: Press † and select 2:Clear split to go back to a full-sized Text Editor screen. 5. To see the results of the script on a fullsized screen, go to the Home screen. Note: Press 2 K twice to display the Home screen. Decomposing a Rational Function This activity examines what happens when a rational function is decomposed into a quotient and remainder.
Decomposing a Rational Function To examine the decomposition of the rational function f(x)=(x3N10x2Nx+50)/(xN2) on a graph: 1. On the Home screen, enter the rational function as shown below and store it in a function f(x). Enter: (x^3N10x^2Nx+50)/(xN2)!f(x) Note: Actual entries are displayed in reverse type in the example screens. 2. Use the proper fraction function (propFrac) to split the function into a quotient and remainder. 3. Copy the last answer to the entry line.
5. In the Y= Editor, select the thick graphing style for y2(x). 6. Add the original function f(x) to y3(x) and select the square graphing style. 7. In the Window Editor, set the window variables to: x= [L10,15,10] y= [L100,100,10] 8. Draw the graph. Note: Be sure the Graph mode is set to Function.
Observe that the global behavior of the f(x) function is basically represented by the quadratic quotient y2(x). The rational expression is basically a quadratic function as x gets very large in both the positive and negative directions. The lower graph is y3(x)=f(x) graphed separately using the line style. Studying Statistics: Filtering Data by Categories This activity provides a statistical study of the weights of high school students using categories to filter the data.
Filtering Data by Categories Each student is placed into one of eight categories depending on the student’s sex and academic year (freshman, sophomore, junior, or senior). The data (weight in pounds) and respective categories are entered in the Data/Matrix Editor. Table 1: Category vs.
Perform the following steps to compare the weight of high school students to their year in school. 1. Start the Data/Matrix Editor, and create a new Data variable named students. 2. Enter the data and categories from Table 2 into columns c1 and c2, respectively. 3. Open the „ Plot Setup toolbar menu. Note: Set up several box plots to compare different subsets of the entire data set. 4. Define the plot and filter parameters for Plot 1 as shown in this screen.
5. Copy Plot 1 to Plot 2. 6. Repeat step 5 and copy Plot 1 to Plot 3, Plot 4, and Plot 5. 7. Press ƒ, and modify the Include Categories item for Plot 2 through Plot 5 to the following: Plot 2: {1,2} (freshman boys, girls) Plot 3: {7,8} (senior boys, girls) Plot 4: {1,3,5,7} (all boys) Plot 5: {2,4,6,8} (all girls) 8. In the Y= Editor, deselect any functions that may be selected from a previous activity. Note: Only Plot 1 through Plot 5 should be selected.
9. Display the plots by pressing „ and selecting 9:Zoomdata. 10. Use the Trace tool to compare the median student weights for different subsets. Ê median, all students Ë all students Ì all freshmen Í all seniors Î all boys Ï all girls Ì Ë Ï Î Ê Í CBL 2™ Program for the TI-89 Titanium This activity provides a program that can be used when the TI-89 Titanium is connected to a Calculator-Based Laboratory™ (CBL 2™) unit. This program works with the “Newton’s Law of Cooling” experiment.
Program Instruction Description :setMode("Graph","FUNCTION") Set up the TI-89 Titanium for function graphing. :PlotsOff Turn off any previous plots. :FnOff Turn off any previous functions. :ClrDraw Clear any items previously drawn on graph screens. :ClrGraph Clear any previous graphs. :ClrIO Clear the TI-89 Titanium Program IO (input/output) screen. :L10!xmin:99!xmax:10!xscl Set up the Window variables. :L20!ymin:100!ymax:10!yscl :{0}!data Create and/or clear a list named data.
Program Instruction Description :Send{3,1,L1,0} Send the Trigger command to the CBL 2™; collect data in real-time. :For i,1,99 Repeat next two instructions for 99 temperature readings. :Get data[i] Get a temperature from the CBL 2™ and store it in a list. :PtOn i,data[i] Plot the temperature data on a graph. :EndFor :seq(i,i,1,99,1)!time Create a list to represent time or data sample number. :NewPlot 1,1,time,data,,,,4 Plot time and data using NewPlot and the Trace tool.
Setting Up a Parametric Graph and Table Perform the following steps to study the flight of a hit baseball that has an initial velocity of 95 feet per second and an initial angle of 32 degrees. 1. Set the modes for Page 1 as shown in this screen. 2. Set the modes for Page 2 as shown in this screen. 3. In the Y= Editor on the left side, enter the equation for the distance of the ball at time t for xt1(t). xt1(t)=95†t†cos(32¡) Note: Press 2 “ to obtain the degree symbol. 4.
5. Set the Window variables to: t values= [0,4,.1] x values= [0,300,50] y values= [0,100,10] 6. Switch to the right side and display the graph. Note: Press 2 a. 7. Display the TABLE SETUP dialog box, and change tblStart to 0 and @tbl to 0.1. Note: Press 8 &. 8. Display the table in the left side and press D to highlight t=2. Note: Press 8 '. 9. Switch to the right side. Press …, and trace the graph to show the values of xc and yc when tc=2. Note: As you move the trace cursor from tc=0.0 to tc=3.
Optional Exercise Assuming the same initial velocity of 95 feet per second, find the angle that the ball should be hit to achieve the greatest distance. Visualizing Complex Zeros of a Cubic Polynomial This activity describes graphing the complex zeros of a cubic polynomial. Visualizing Complex Roots Perform the following steps to expand the cubic polynomial (xN1)(xNi)(x+i), find the absolute value of the function, graph the modulus surface, and use the Trace tool to explore the modulus surface. 1.
3. Use the abs( ) function to find the absolute value of f(x+yi). (This calculation may take about 2 minutes.) Note: The absolute value of a function forces any roots to visually just touch rather than cross the x axis. Likewise, the absolute value of a function of two variables will force any roots to visually just touch the xy plane. 4. Copy and paste the last answer to the entry line and store it in the function z1(x,y). Note: The graph of z1(x,y) will be the modulus surface. 5.
6. In the Y=Editor, press: 8Í and set the Graph Format variables to: Axes= ON Labels= ON Style= HIDDEN SURFACE Note: Calculating and drawing the graph takes about three minutes. 7. Graph the modulus surface. The 3D graph is used to visually display a picture of the roots where the surface touches the xy plane. 8. Use the Trace tool to explore the function values at x=1 and y=0. 9. Use the Trace tool to explore the function values at x=0 and y=1.
10. Use the Trace tool to explore the function values at x=0 and y=L1. Summary Note that zc is zero for each of the function values in steps 7–9. Thus, the complex zeros 1,Li, i of the polynomial x3Nx2+xN1 can be visualized with the three points where the graph of the modulus surface touches the xy plane. Solving a Standard Annuity Problem This activity can be used to find the interest rate, starting principal, number of compounding periods, and future value of an annuity.
Finding the Interest Rate of an Annuity Perform the following steps to find the interest rate (i) of an annuity where the starting principal (p) is 1,000, number of compounding periods (n) is 6, and the future value (s) is 2,000. 1. On the Home screen, enter the equation to solve for p. 2. Enter the equation to solve for n. 3. Enter the equation to solve for i using the with operator. solve(s=p†(1+i)^n,i) | s=2000 and p=1000 and n=6 Result: The interest rate is 12.246%.
Finding the Future Value of an Annuity Find the future value of an annuity using the values from the previous example where the interest rate is 14%. Enter the equation to solve for s. solve(s=p†(1+i)^n,s) | i=.14 and p=1000 and n=6 Result: The future value at 14% interest is 2,194.97. Computing the Time-Value-of-Money This activity creates a function that can be used to find the cost of financing an item.
period (1 = beginning of month, 0 = end of month).
Finding the Monthly Payment Find the monthly payment on 10,000 if you make 48 payments at 10% interest per year. On the Home screen, enter the tvm values to find pmt. Result: The monthly payment is 251.53. Finding the Number of Payments Find the number of payments it will take to pay off the loan if you could make a 300 payment each month. On the Home screen, enter the tvm values to find n. Result: The number of payments is 38.8308.
Finding Factors Enter the expressions shown below on the Home screen. 1. factor(x^3N5x) ¸ displays a rational result. 2. factor(x^3+5x) ¸ displays a rational result. 3. factor(x^3N5x,x) ¸ displays a real result. 4. cfactor(x^3+5x,x) ¸ displays a complex result.
Simulation of Sampling without Replacement This activity simulates drawing different colored balls from an urn without replacing them. Detailed information about the steps used in this example can be found in the electronic chapter Programming. Sampling-without- Replacement Function In the Program Editor, define drawball( ) as a function that can be called with two parameters. The first parameter is a list where each element is the number of balls of a certain color.
Sampling without Replacement Suppose an urn contains n1 balls of a color, n2 balls of a second color, n3 balls of a third color, etc. Simulate drawing balls without replacing them. 1. Enter a random seed using the RandSeed command. 2. Assuming the urn contains 10 red balls and 25 white balls, simulate picking 5 balls at random from the urn without replacement. Enter drawball({10,25},5). Result: 2 red balls and 3 white balls.
a mph Eastward Traveling Current Boat Intended Path Actual Path river bank 1. Set the modes for Page 1 as shown in this screen. (Show angles in degrees and display all digits with a floating decimal point.) Press: 3 D D D. On the Angle option, select 2:DEGREE. On the Display Digits option, select E:FLOAT. 2. Set the modes for Page 2 as shown in this screen. (Display answers in decimal form.) Press: 3 „ D D. On the Exact/Approx option, select 3:APPROXIMATE.
3. Enter vectors describing the initial path of the boat, water current, and resultant path of the boat. Store these vectors as i, c, and r. Use the value a for the unknown speed of the current. Use the value b for the speed of the boat. Enter: [20,80¡]!i [a,0¡]!c [b,60°]!r Vectors are commonly written in either polar or rectangular form, so it is useful to convert polar vectors into rectangular form. 4. Define function p2r.
When converted to rectangular form, the sum of vectors i and c equals the resultant vector r. 5. Using function p2r, convert vectors i, c, and r to rectangular form. Enter: p2r(i)!i p2r(c)!c p2r(r)!r Because the vectors are equal, the xcoordinate of i+c must equal the x-coordinate of the resultant vector r. Likewise, the ycoordinate of i+c must equal the y-coordinate of resultant vector r. 6. Set up two equations involving vectors i+c and r. • Equation 1 sets the x-coordinates equal to each other.
7. Solve eq2 for b to calculate the actual speed of the boat. solve(eq2,b) 8. Substitute the known value of b into eq1, and solve eq1 for a to determine a, the speed of the eastward traveling current. solve(eq1,a) | b The boat travels at a speed of 22.7 knots, and the water current is approximately 7.9 knots.
A Appendix A: Functions and Instructions Categorical Listing of Operations ................................................................... 782 Alphabetical Listing of Operations.................................................................. 786 This section describes the syntax and action of each TI-89 Titanium function and instruction that is included in the operating system (OS). See modules relating to calculator software applications (Apps) for functions and instructions specific to those Apps.
Categorical Listing of Operations This section lists the TI-89 Titanium functions and instructions in functional groups along with the page numbers where they are described.
Math + (add) à (divide) ! (factorial) G (gradian) ¡, ', " 10^() 4Cylind 4DMS 4Polar abs() approx() cos coshê() coth() cscê() E 4ln fPart() impDif() iPart() ln() min() nPr() r (radian) real() round() secê() shift() sinê() tan() tanhê() xê 900 902 906 909 910 911 803 812 853 786 788 795 797 798 799 814 837 823 831 832 837 844 848 909 862 866 868 874 877 886 888 911 ì (subtract) ë (negate) ‡ () (sqr.
Programming = ≤ # (indirection) and checkTmr() ClrErr ClrIO CustmOff Cycle DelFold Dialog DispHome Else EndDlog EndIf EndTBar entry() For Get getDate() getFold() getTime() getTmZn() Goto InputStr Lbl isVar() Lock NewFold or PassErr Prgm Request Send setDate() setGraph() setTime() startTmr() Style Text Title Unarchiv While 784 905 906 908 786 791 792 793 802 803 807 810 811 815 815 815 816 816 822 824 824 825 826 827 828 831 833 833 838 846 850 853 855 864 868 869 870 872 881 884 889 889 892 894 ≠ > !
Statistics ! (factorial) cumSum() LnReg median() NewData OneVar PowerReg rand() ShowStat SortD TwoVar 906 802 838 842 845 849 855 861 875 881 892 BldData ExpReg Logistic MedMed NewPlot PlotsOff QuadReg randNorm() SinReg stdDev() variance() 790 819 840 843 847 853 859 862 878 882 893 CubicReg LinReg mean() nCr() nPr() PlotsOn QuartReg RandSeed SortA stdDevPop() 801 836 842 845 848 853 860 862 881 882 Strings & (append) dim() inString() ord() shift() 907 810 832 850 874 # (indirection) expr() left()
Alphabetical Listing of Operations Operations whose names are not alphabetic (such as +, !, and >) are listed at the end of this appendix, starting on page 900. Unless otherwise specified, all examples in this section were performed in the default reset mode, and all variables are assumed to be undefined. Additionally, due to formatting restraints, approximate results are truncated at three decimal places (3.14159265359 is shown as 3.141...).
AndPic CATALOG AndPic picVar[, row, column] Displays the Graph screen and logically “ANDS” the picture stored in picVar and the current graph screen at pixel coordinates (row, column). picVar must be a picture type. Default coordinates are (0,0), which is the upper left corner of the screen. In function graphing mode and Y= Editor: y1(x) = cos(x) C @ 2 ˆ Style = 3:Square „ Zoom = 7:ZoomTrig ƒ = 2:Save Copy As...
ans() 2 ± key ans() ⇒ value ans(integer) ⇒ value To use ans() to generate the Fibonacci sequence on the Home screen, press: Returns a previous answer from the Home screen history area. integer, if included, specifies which previous answer to recall. Valid range for integer is from 1 to 99 and cannot be an expression. Default is 1, the most recent answer. approx() 1¸ 1¸ 2±«2±A02¸ ¸ ¸ 1 1 2 3 5 MATH/Algebra menu approx(expression) ⇒ value approx(p) ¸ 3.141...
augment() MATH/Matrix menu augment(list1, list2) ⇒ list Returns a new list that is list2 appended to the end of list1. augment(matrix1, matrix2) augment(matrix1; matrix2) ⇒ matrix ⇒ matrix Returns a new matrix that is matrix2 appended to matrix1. When the “,” character is used, the matrices must have equal row dimensions, and matrix2 is appended to matrix1 as new columns. When the “;” character is used, the matrices must have equal column dimensions, and matrix2 is appended to matrix1 as new rows.
BldData CATALOG In function graphing mode and Radian angle mode: BldData [dataVar] Creates data variable dataVar based on the information used to plot the current graph. BldData is valid in all graphing modes. 8ùsin(x)!y1(x) ¸ 2ùsin(x)!y2(x) ¸ ZoomStd ¸ If dataVar is omitted, the data is stored in the system variable sysData.
cFactor() MATH/Algebra/Complex menu cFactor(expression1[, var]) ⇒ expression cFactor(list1[,var]) ⇒ list cFactor(matrix1[,var]) ⇒ matrix cFactor(expression1) returns expression1 factored with respect to all of its variables over a common denominator. expression1 is factored as much as possible toward linear rational factors even if this introduces new non-real numbers. This alternative is appropriate if you want factorization with respect to more than one variable.
Circle CATALOG In a ZoomSqr viewing window: Circle x, y, r [, drawMode] ZoomSqr:Circle 1,2,3 ¸ Draws a circle with its center at window coordinates (x, y) and with a radius of r. x, y, and r must be real values. If drawMode = 1, draws the circle (default). If drawMode = 0, turns off the circle. If drawMode = -1, inverts pixels along the circle. Note: Regraphing erases all drawn items. See also PxlCrcl. ClockOff CATALOG ClockOff Turns the clock OFF. ClockOn CATALOG ClockOn Turns the clock ON.
ClrGraph CATALOG ClrGraph Clears any functions or expressions that were graphed with the Graph command or were created with the Table command. (See Graph or Table.) Any previously selected Y= functions will be graphed the next time that the graph is displayed. ClrHome CATALOG ClrHome Clears all items stored in the entry() and ans() Home screen history area. Does not clear the current entry line. While viewing the Home screen, you can clear the history area by pressing ƒ and selecting 8:Clear Home.
comDenom(expression1,var) returns a reduced ratio of numerator and denominator expanded with respect to var. The terms and their factors are sorted with var as the main variable. Similar powers of var are collected. There might be some incidental factoring of the collected coefficients. Compared to omitting var, this often saves time, memory, and screen space, while making the expression more comprehensible. It also makes subsequent operations on the result faster and less likely to exhaust memory.
cos() 2 X key cos(expression1) ⇒ expression cos(list1) ⇒ list In Degree angle mode: cos(expression1) returns the cosine of the cos((p/4)ô ) ¸ ‡2 2 cos(45) ¸ ‡2 2 argument as an expression. cos(list1) returns a list of the cosines of all elements in list1. Note: The argument is interpreted as a degree, gradian or radian angle, according to the current G angle mode setting. You can use ó , o r ô to override the angle mode temporarily.
cosê () ¥ R key cosê (expression1) ⇒ expression cosê (list1) ⇒ list In Degree angle mode: cosê (expression1) returns the angle whose cosine 0 is expression1 as an expression. In Gradian angle mode: cosê (list1) returns a list of the inverse cosines of cosê (0) ¸ each element of list1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. cosê(squareMatrix1) ⇒ squareMatrix Returns the matrix inverse cosine of squareMatrix1.
cot() MATH/Trig menu cot(expression1) ⇒ expression cot(list1) ⇒ list Returns the cotangent of expression1 or returns a list of the cotangents of all elements in list1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. In Degree angle mode: cot(45) ¸ 1 In Gradian angle mode: cot(50) ¸ 1 In Radian angle mode: cot({1,2.1,3}) ¸ 1 1 L.
csc() MATH/Trig menu csc(expression1) ⇒ expression csc(list1) ⇒ list In Degree angle mode: Returns the cosecant of expression1 or returns a list containing the cosecants of all elements in list1.
cSolve() temporarily sets the domain to complex during the solution even if the current domain is real. In the complex domain, fractional powers having odd denominators use the principal rather than the real branch. Consequently, solutions from solve() to equations involving such fractional powers are not necessarily a subset of those from cSolve(). cSolve(x^(1/3)=ë 1,x) ¸ false solve(x^(1/3)=ë 1,x) ¸ x = ë1 Display Digits mode in Fix 2: cSolve() starts with exact symbolic methods.
Simultaneous polynomial equations can have extra variables that have no values, but represent given numeric values that could be substituted later. cSolve(u_ùv_ìu_=c_ùv_ and v_^2=ëu_,{u_,v_}) ¸ u_= or ë( 1ì4øc_+1)2 and v_= 1ì4øc_+1 2 4 ë( 1ì4øc_ì1) 2 or u_=0 and v_=0 u_= You can also include solution variables that do not appear in the equations. These solutions show how families of solutions might contain arbitrary constants of the form @k, where k is an integer suffix from 1 through 255.
CubicReg MATH/Statistics/Regressions menu CubicReg list1, list2[, [list3] [, list4, list5]] Calculates the cubic polynomial regression and updates all the statistics variables. All the lists must have equal dimensions except for list5. In function graphing mode. {0,1,2,3}! L1 ¸ {0,2,3,4}! L2 ¸ CubicReg L1,L2 ¸ ShowStat ¸ {0 1 2 3} {0 2 3 4} Done list1 represents xlist. list2 represents ylist. list3 represents frequency. list4 represents category codes. list5 represents category include list.
cumSum() MATH/List menu cumSum(list1) ⇒ list cumSum({1,2,3,4}) ¸ Returns a list of the cumulative sums of the elements in list1, starting at element 1. cumSum(matrix1) ⇒ matrix Returns a matrix of the cumulative sums of the elements in matrix1. Each element is the cumulative sum of the column from top to bottom. CustmOff {1 3 6 10} 1 3 5 1 4 9 [1,2;3,4;5,6]! m1 ¸ cumSum(m1) ¸ 2 4 6 2 6 12 CATALOG See Custom program listing example. CustmOff Removes a custom toolbar.
Cycle CATALOG Program listing: Cycle Transfers program control immediately to the next iteration of the current loop (For, While, or Loop). Cycle is not allowed outside the three looping structures (For, While, or Loop). :¦ Sum the integers from 1 to 100 skipping 50. :0! temp :For i,1,100,1 :If i=50 :Cycle :temp+i! temp :EndFor :Disp temp Contents of temp after execution:5000 CyclePic CATALOG CyclePic picNameString, n [, [wait] , [cycles], [direction]] 1. Save three pics named pic1, pic2, and pic3.
Optionally, you can specify an initial guess for a variable. Each varOrGuess must have the form: variable – or – variable = real or non-real number For example, x is valid and so is x=3+i. If all of the expressions are polynomials and you do NOT specify any initial guesses, cZeros() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all complex zeros. Note: The following examples use an underscore _ ( ¥ ) so that the variables will be treated as complex.
A non-real guess is often necessary to determine a non-real zero. For convergence, a guess might have to be rather close to a zero. d() cZeros({e^(z_)ìw_,w_ìz_^2}, {w_,z_=1+ i}) ¸ [.149…+4.89…øi 1.588…+1.540…øi] 2 = key or MATH/Calculus menu d (expression1, var [,order]) ⇒ expression d (list1,var [,order]) ⇒ list d (matrix1,var [,order]) ⇒ matrix Returns the first derivative of expression1 with respect to variable var. expression1 can be a list or a matrix. order, if included, must be an integer.
prior to 1583 (pre-Gregorian calendar). 3 = Tuesday Enter the year as a four-digit integer. The month and day can be either one- or two-digit integers. 4 = Wednesday 5 = Thursday 6 = Friday 7 = Saturday 4DD MATH/Angle menu number 4DD ⇒ value list1 4DD ⇒ list matrix1 4DD ⇒ matrix In Degree angle mode: 1.5ó 4DD ¸ Returns the decimal equivalent of the argument expressed in degrees. The argument is a number, list, or matrix that is interpreted by the Mode setting in gradians, radians or degrees.
Define CATALOG Define funcName(arg1Name, arg2Name, ...) = expression Creates funcName as a user-defined function. You then can use funcName(), just as you use built-in functions. The function evaluates expression using the supplied arguments and returns the result. funcName cannot be the name of a system variable or built-in function. The argument names are placeholders; you should not use those same names as arguments when you use the function.
DelType Deltype “LIST” ¸ DelType var_type Done Deletes all unlocked variables of the type specified by var_type. Note: Possible values for var_type are: ASM, DATA, EXPR, FUNC, GDB, LIST, MAT, PIC, PRGM, STR, TEXT, AppVar_type_name, All. DelVar CATALOG 2! a ¸ (a+2)^2 ¸ DelVar a ¸ (a+2)^2 ¸ DelVar var1[, var2] [, var3] ... Deletes the specified variables from memory. deSolve() 2 16 Done (a + 2)ñ MATH/Calculus menu Note: To type a prime symbol ( ' ), press 2 È.
the general solution. soln|x=0 and y=0 ¸ initialCondition is an equation of the form: d(right(eq)ìleft(eq),x)/ (d(left(eq)ìright(eq),y)) dependentVar (initialIndependentValue) = initialDependentValue true !impdif(eq,x,y) ¸ Done The initialIndependentValue and initialDependentValue can be variables such as x0 and y0 that have no ode|y'=impdif(soln,x,y) ¸ stored values. Implicit differentiation can help verify implicit solutions.
diag() MATH/Matrix menu diag(list) ⇒ matrix diag(rowMatrix) ⇒ matrix diag(columnMatrix) ⇒ matrix diag({2,4,6}) ¸ 2 0 0 0 0 4 0 0 6 [4,6,8;1,2,3;5,7,9] ¸ 4 1 5 6 8 2 3 7 9 diag(ans(1)) ¸ [4 2 9] Returns a matrix with the values in the argument list or matrix in its main diagonal. diag(squareMatrix) ⇒ rowMatrix Returns a row matrix containing the elements from the main diagonal of squareMatrix. squareMatrix must be square.
Disp CATALOG Disp [exprOrString1] [, exprOrString2] ... Displays the current contents of the Program I/O screen. If one or more exprOrString is specified, each expression or character string is displayed on a separate line of the Program I/O screen. Disp "Hello" ¸ Hello Disp cos(2.3) ¸ {1,2,3,4}!L1 ¸ Disp L1 ¸ An expression can include conversion operations such as 4DD and 4Rect. You can also use the 4 operator to perform unit and number base conversions.
4DMS MATH/Angle menu In Degree angle mode: expression 4DMS list 4DMS matrix 4DMS 45.371 4DMS ¸ Interprets the argument as an angle and displays the equivalent DMS (DDDDDD¡MM¢SS.ss£) number. See ¡, ', " on page 910 for DMS (degree, minutes, seconds) format. 45ó 22'15.6" {45.371,60} 4DMS ¸ {45ó 22'15.6" 60ó } Note: 4DMS will convert from radians to degrees when used in radian mode. If the input is followed by a degree symbol ( ¡ ), no conversion will occur.
DrawParm CATALOG DrawParm expression1, expression2 [, tmin] [, tmax] [, tstep] Draws the parametric equations expression1 and expression2, using t as the independent variable. In function graphing mode and ZoomStd window: DrawParm tù cos(t),tù sin(t),0,10,.1 ¸ Defaults for tmin, tmax, and tstep are the current settings for the Window variables tmin, tmax, and tstep. Specifying values does not alter the window settings. If the current graphing mode is not parametric, these three arguments are required.
DrwCtour CATALOG In 3D graphing mode: DrwCtour expression DrwCtour list Draws contours on the current 3D graph at the z values specified by expression or list. The 3D graphing mode must already be set. DrwCtour automatically sets the graph format style to CONTOUR LEVELS. By default, the graph automatically contains the number of equally spaced contours specified by the ncontour Window variable. DrwCtour draws contours in addition to the defaults.
eigVc() MATH/Matrix menu eigVc(squareMatrix) ⇒ matrix In Rectangular complex format mode: Returns a matrix containing the eigenvectors for a [L1,2,5;3,L6,9;2,L5,7]!m1 ¸ real or complex squareMatrix, where each column ë 1 2 5 in the result corresponds to an eigenvalue. Note 3 ë 6 9 that an eigenvector is not unique; it may be 2 ë 5 7 scaled by any constant factor. The eigenvectors are normalized, meaning that if V = [x 1, x 2, … , eigVc(m1) ¸ x n], then: ë.800… .767… .
EndLoop See Loop, page 840. EndPrgm See Prgm, page 855. EndTBar See ToolBar, page 891. EndTry See Try, page 891. EndWhile See While, page 894. entry() CATALOG entry() ⇒ expression entry(integer) ⇒ expression On the Home screen: 1 + 1 x Returns a previous entry-line entry from the Home screen history area. 1+1/x ¸ integer, if included, specifies which entry 1+1/entry(1) ¸ expression in the history area. The default is 1, the most recently evaluated entry.
Exec CATALOG Exec string [, expression1] [, expression2] ... Executes a string consisting of a series of Motorola 68000 op-codes. These codes act as a form of an assembly-language program. If needed, the optional expressions let you pass one or more arguments to the program. For more information, check the TI Web site: http://www.ti.com/calc Warning: Exec gives you access to the full power of the microprocessor.
expand(expression1,var) returns expression expanded with respect to var. Similar powers of var are collected. The terms and their factors are sorted with var as the main variable. There might be some incidental factoring or expansion of the collected coefficients. Compared to omitting var, this often saves time, memory, and screen space, while making the expression more comprehensible.
ExpReg MATH/Statistics/Regressions menu ExpReg list1, list2 [, [list3] [, list4, list5]] Calculates the exponential regression and updates all the system statistics variables. All the lists must have equal dimensions except for list5. list1 represents xlist. list2 represents ylist. list3 represents frequency. list4 represents category codes. list5 represents category include list.
For the AUTO setting of the Exact/Approx mode, factor(x^5+4x^4+5x^3ì 6xì 3) ¸ including var permits approximation with floatingx 5 + 4ø x4 + 5ø x3ì 6ø x ì 3 point coefficients where irrational coefficients cannot be explicitly expressed concisely in terms factor(ans(1),x) ¸ of the built-in functions. Even when there is only (xì.964…)ø (x +.611…)ø one variable, including var might yield more (x + 2.125…)ø (xñ + 2.227…ø complete factorization. x + 2.
fMax() MATH/Calculus menu fMax(expression, var) ⇒ Boolean expression fMax(1ì (xì a)^2ì (xì b)^2,x) ¸ Returns a Boolean expression specifying candidate values of var that maximize expression or locate its least upper bound. x = a+b 2 x=ˆ fMax(.5x^3ì xì 2,x) ¸ Use the “|” operator to restrict the solution interval and/or specify the sign of other undefined variables. fMax(.
FnOn CATALOG FnOn Selects all Y= functions that are defined for the current graphing mode. In split-screen, two-graph mode, FnOn only applies to the active graph. FnOn [1] [, 2] ... [,99] Selects the specified Y= functions for the current graphing mode. Note: In 3D graphing mode, only one function at a time can be selected. FnOn 2 selects z2(x,y) and deselects any previously selected function. In the other graph modes, previously selected functions are not affected.
G[n][c]: Same as fixed format but also separates digits to the left of the radix into groups of three. c specifies the group separator character and defaults to a comma. If c is a period, the radix will be shown as a comma. [Rc]: Any of the above specifiers may be suffixed with the Rc radix flag, where c is a single character that specifies what to substitute for the radix point.
Get CATALOG Program segment: Get var Retrieves a CBL 2é (Calculator-Based Laboratoryé) or CBRé (Calculator-Based Rangeré) value from the link port and stores it in variable var. GetCalc © :Send {3,1,ë 1,0} :For i,1,99 : Get data[i] : PtOn i,data[i] :EndFor © CATALOG Program segment: GetCalc var Retrieves a value from the link port and stores it in variable var. This is for unit-to-unit linking.
getDenom() MATH/Algebra/Extract menu getDenom(expression1) ⇒ expression Transforms expression1 into one having a reduced common denominator, and then returns its denominator. getDtFmt() getDenom((x+2)/(yì 3)) ¸ getDenom(2/7) ¸ getDenom(1/x+(y^2+y)/y^2) ¸ y ì3 7 xø y CATALOG getDtFmt() ⇒ integer Returns an integer representing the date format that is currently set on the device. Integer values: 1 = MM/DD/YY 2 = DD/MM/YY 3 = MM.DD.YY 4 = DD.MM.YY 5 = YY.MM.
getMode() CATALOG getMode(modeNameString) ⇒ string getMode("ALL") ⇒ ListStringPairs If the argument is a specific mode name, returns a string containing the current setting for that mode. If the argument is "ALL", returns a list of string pairs containing the settings of all the modes. If you want to restore the mode settings later, you must store the getMode("ALL") result in a variable, and then use setMode() to restore the modes. For a listing of mode names and possible settings, see setMode().
getTmZn() CATALOG getTmZn() ⇒ integer If Greenwich Mean Time is 14:07:07, it is: Returns an integer representing the time zone that is currently set on the device. The returned integer represents the number of minutes the time zone is offset from Greenwich Mean Time (GMT), as established in Greenwich, England. For example, if the time zone is offset from GMT by two hours, the device would return 120 (minutes). 8:07:07 a.m. in Denver, Colorado (Mountain Daylight Time) (–360 minutes from GMT) 16:07:07 p.
getUnits() CATALOG getUnits() ⇒ list getUnits() ¸ Returns a list of strings that contain the current default units for all categories except constants, temperature, amount of substance, luminous intensity, and acceleration. list has the form: {"system" "cat1" "unit1" "cat2" "unit2" …} The first string gives the system (SI, ENG/US, or CUSTOM). Subsequent pairs of strings give a {"SI" "Area" "NONE" "Capacitance" "_F" "Charge" "_coul" … } Note: Your screen may display different default units.
Graph CATALOG Graph expression1[, expression2] [, var1] [, var2] The Smart Graph feature graphs the requested expressions/ functions using the current graphing mode. Expressions entered using the Graph or Table commands are assigned increasing function numbers starting with 1. They can be modified or individually deleted using the edit functions available when the table is displayed by pressing † Header. The currently selected Y= functions are ignored.
identity() MATH/Matrix menu ⇒ matrix identity(expression) identity(4) ¸ 1 0 0 0 Returns the identity matrix with a dimension of expression. expression must evaluate to a positive integer. If 0 1 0 0 0 0 1 0 0 0 0 1 CATALOG If Boolean expression If Boolean expression Then statement block EndIf If Boolean expression evaluates to true, executes the single statement statement or the block of statements block before continuing execution.
imag(matrix1) ⇒ matrix 0 0 [c d] imag([a,b;ic,id]) ¸ Returns a matrix of the imaginary parts of the elements. ImpDif() MATH/Calculus Menu, CATALOG ImpDif(equation, independentVar, dependentVar[,order ]) ⇒ expression impDif(x^2+y^2=100,x,y)¸ -x/y where the order defaults to 1. Computes the implicit derivative for equations in which one variable is defined implicitly in terms of another. Indirection Input See #(), page 908.
inString() MATH/String menu inString(srcString, subString[, start]) ⇒ integer Returns the character position in string srcString at which the first occurrence of string subString begins. start, if included, specifies the character position within srcString where the search begins. Default = 1 (the first character of srcString). inString("Hello there","the") ¸ 7 "ABCEFG"! s1:If inString(s1, "D")=0:Disp "D not found." ¸ D not found.
isLocked() CATALOG isLocked(var_name) ⇒ true,false isLocked(PROG1) ¸ False Determines if var_name is locked or not. Returns true if var_name is locked or archived. Returns false if var_name is not locked or archived. isPrime() MATH/Test menu isPrime(number) ⇒ Boolean constant expression Returns true or false to indicate if number is a whole number ‚ 2 that is evenly divisible only by itself and 1.
lcm() MATH/Number menu lcm(number1, number2) ⇒ expression lcm(list1, list2) ⇒ list lcm(matrix1, matrix2) ⇒ matrix lcm(6,9) ¸ Returns the least common multiple of the two arguments. The lcm of two fractions is the lcm of their numerators divided by the gcd of their denominators. The lcm of fractional floatingpoint numbers is their product. 18 lcm({1/3,ë 14,16},{2/15,7,5}) ¸ {2/3 14 80} For two lists or matrices, returns the least common multiples of the corresponding elements.
limit() uses methods such as L’Hopital’s rule, so there are unique limits that it cannot determine. If expression1 contains undefined variables other than var, you might have to constrain them to obtain a more concise result. limit(a^x,x,ˆ) ¸ undef limit(a^x,x,ˆ)|a>1 ¸ ˆ limit(a^x,x,ˆ)|a>0 and a<1 ¸ 0 Limits can be very sensitive to rounding error. When possible, avoid the APPROX setting of the Exact/Approx mode and approximate numbers when computing limits.
LineTan CATALOG In function graphing mode and a ZoomTrig window: LineTan expression1, expression2 Displays the Graph screen and draws a line tangent to expression1 at the point specified. Graph cos(x) expression1 is an expression or the name of a @ " H ¥" function, where x is assumed to be the independent variable, and expression2 is the x value of the point that is tangent. LineTan cos(x),p/4 ¸ Note: In the example shown, expression1 is graphed separately. LineTan does not graph expression1.
@list() MATH/List menu list ( list1 ) ⇒ list @list({20,30,45,70}) ¸ Returns a list containing the differences between consecutive elements in list1. Each element of list1 is subtracted from the next element of list1. The resulting list is always one element shorter than the original list1. list44mat() {10,15,25} MATH/List menu list44mat( list [, elementsPerRow]) ⇒ matrix Returns a matrix filled row-by-row with the elements from list.
LnReg MATH/Statistics/Regressions menu LnReg list1, list2[, [list3] [, list4, list5]] In function graphing mode: Calculates the logarithmic regression and updates {1,2,3,4,5,6,7,8}! L1 ¸ all the system statistics variables. {1 2 3 ...} All the lists must have equal dimensions except for list5. list1 represents xlist. list2 represents ylist. list3 represents frequency. list4 represents category codes. list5 represents category include list.
log() CATALOG/ ¥ 7 key log(expression1[,expression2]) ⇒ log(list1[,expression2]) ⇒ list expression log(2.0) ¸ .301... If complex format mode is REAL: Returns the base-expression2 logarithm of the argument. log({ë 3,1.2,5}) ¸ Error: Non-real result For a list, returns the base-expression2 logarithm of the elements. If complex format mode is RECTANGULAR: If expression 2 is omitted, 10 is used as base. log(squareMatrix1) ⇒ squareMatrix Returns the matrix base-expression2 logarithm of squareMatrix1.
Logistic MATH/Statistics/Regressions menu Logistic list1, list2 [ , [iterations] , [list3] [, list4, list5] ] In function graphing mode: Calculates the logistic regression and updates all the system statistics variables. All the lists must have equal dimensions except for list5. list1 represents xlist. list2 represents ylist. list3 represents frequency. list4 represents category codes. list5 represents category include list. iterations specifies the maximum number of times a solution will be attempted.
LU MATH/Matrix menu LU matrix, lMatName, uMatName, pMatName[, tol] Calculates the Doolittle LU (lower-upper) decomposition of a real or complex matrix. The lower triangular matrix is stored in lMatName, the upper triangular matrix in uMatName, and the permutation matrix (which describes the row swaps done during the calculation) in pMatName.
mat44list() MATH/List menu ⇒ list mat44list(matrix) mat4list([1,2,3]) ¸ Returns a list filled with the elements in matrix. The elements are copied from matrix row by row. max() {1 2 3} [1,2,3;4,5,6]! M1 ¸ 1 2 3 [4 5 6] mat4list(M1) ¸ {1 2 3 4 5 6} max(2.3,1.4) ¸ 2.3 MATH/List menu max(expression1, expression2) ⇒ expression max(list1, list2) ⇒ list max(matrix1, matrix2) ⇒ matrix max({1,2},{ë 4,3}) ¸ {1 3} Returns the maximum of the two arguments.
MedMed MATH/Statistics/Regressions menu In function graphing mode: MedMed list1, list2[, [list3] [, list4, list5]] Calculates the median-median line and updates all the system statistics variables. All the lists must have equal dimensions except for list5. {0,1,2,3,4,5,6}! L1 ¸ {0,2,3,4,3,4,6}! L2 ¸ MedMed L1,L2 ¸ ShowStat ¸ {0 1 2 ...} {0 2 3 ...} Done list1 represents xlist. list2 represents ylist. list3 represents frequency. list4 represents category codes. list5 represents category include list.
min() MATH/List menu min(expression1, expression2) ⇒ expression min(list1, list2) ⇒ list min(matrix1, matrix2) ⇒ matrix min(2.3,1.4) ¸ 1.4 min({1,2},{ë 4,3}) ¸ {ë 4 2} Returns the minimum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the minimum value of each pair of corresponding elements. min(list) ⇒ expression min({0,1,ë 7,1.3,.5}) ¸ ë7 Returns the minimum element of list.
nCr() MATH/Probability menu nCr(expression1, expression2) ⇒ expression For integer expression1 and expression2 with expression1 ‚ expression2 ‚ 0, nCr() is the number of combinations of expression1 things taken expression2 at a time. (This is also known as a binomial coefficient.) Both arguments can be integers or symbolic expressions.
NewData sysData, matrix Loads the contents of matrix into the system data variable sysData. NewFold CATALOG NewFold games ¸ NewFold folderName Done Creates a user-defined folder with the name folderName, and then sets the current folder to that folder. After you execute this instruction, you are in the new folder. newList() CATALOG newList(numElements) ⇒ list newList(4) ¸ {0 0 0 0} Returns a list with a dimension of numElements. Each element is zero.
NewPlot CATALOG NewPlot n, type, xList [,[yList], [frqList], [catList], [includeCatList], [mark] [, bucketSize]] Creates a new plot definition for plot number n. type specifies the type of the graph plot. 1 = scatter plot 2 = xyline plot 3 = box plot 4 = histogram 5 = modified box plot FnOff ¸ Done PlotsOff ¸ Done {1,2,3,4}!L1 ¸ {1 2 3 4} {2,3,4,5}!L2 ¸ {2 3 4 5} NewPlot 1,1,L1,L2,,,,4 ¸ Done Press ¥ % to display: mark specifies the display type of the mark.
Nest nInt() to do multiple numeric integration. Integration limits can depend on integration variables outside them. nInt(nInt(e^(ë xù y)/‡(x^2ì y^2), y,ë x,x),x,0,1) ¸ 3.304... Note: See also ‰(). norm() MATH/Matrix/Norms menu norm(matrix) ⇒ expression norm([a,b;c,d]) ¸ Returns the Frobenius norm. añ +bñ +cñ +dñ norm([1,2;3,4]) ¸ not 30 MATH/Test menu not Boolean expression1 ⇒ Boolean expression Returns true, false, or a simplified Boolean expression1.
nPr(matrix1, matrix2) ⇒ matrix nPr([6,5;4,3],[2,2;2,2]) ¸ nSolve() 30 20 6] [12 Returns a matrix of permutations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix. MATH/Algebra menu nSolve(equation, varOrGuess) ⇒ number or error_string Iteratively searches for one approximate real numeric solution to equation for its one variable. Specify varOrGuess as: variable – or – variable = real number nSolve(x^2+5xì 25=9,x) ¸ 3.844...
or MATH/Test menu Boolean expression1 or Boolean expression2 ⇒ expression Boolean Returns true or false or a simplified form of the original entry. Returns true if either or both expressions simplify to true. Returns false only if both expressions evaluate to false. Note: See xor. integer1 or integer2 ⇒ integer x‚3 or x‚4 ¸ x‚3 Program segment: © If x<0 or x‚5 Goto END © If choice=1 or choice=2 Disp "Wrong choice" © In Hex base mode: Compares two real integers bit-by-bit using an or operation.
P44Rx() MATH/Angle menu P44Rx(rExpression, qExpression) ⇒ expression P44Rx(rList, qList) ⇒ list P44Rx(rMatrix, qMatrix) ⇒ matrix Returns the equivalent x-coordinate of the (r, q) pair. In Radian angle mode: P4Rx(r,q) ¸ cos(q)ø r P4Rx(4,60¡) ¸ Note: The q argument is interpreted as either a degree, gradian or radian angle, according to the current angle mode. If the argument is an G expression, you can use ó , o r ô to override the angle mode setting temporarily. P44Ry() {ë 3/2 } 5ø ‡2 1.
part(expression1, n) ⇒ expression part(cos(pùx+3),1) ¸ Note: Simplification changed the order of the argument. By combining the variations of part(), you can extract all of the sub-expressions in the simplified result of expression1. As shown in the example to the right, you can store an argument or operand and then use part() to extract further subexpressions.
PassErr CATALOG PassErr See ClrErr program listing example. Passes an error to the next level. If “errornum” is zero, PassErr does not do anything. The Else clause in the program should use ClrErr or PassErr. If the error is to be processed or ignored, use ClrErr. If what to do with the error is not known, use PassErr to send it to the next error handler. (See also ClrErr.) Pause CATALOG Pause [expression] Suspends program execution.
In Radian angle mode: complexValue 4Polar 3+4i 4Polar ¸ Displays complexVector in polar form. • Degree angle mode returns (rq). • Radian angle mode returns e iø(p2 ì tanê(3/4))ø5 i øp (4p/3)4Polar ¸ e 3 ø4 re iq. complexValue can have any complex form. In Gradian angle mode: However, an re iq entry causes an error in Degree angle mode. 4i 4Polar ¸ Note: You must use the parentheses for an (rq) polar entry.
PowerReg MATH/Statistics/Regressions menu PowerReg list1, list2[, [list3] [, list4, list5]] Calculates the power regression and updates all the system statistics variables. All the lists must have equal dimensions except for list5. list1 represents xlist. list2 represents ylist. list3 represents frequency. list4 represents category codes. list5 represents category include list.
propFrac() MATH/Algebra menu propFrac(expression1[, var]) ⇒ expression propFrac(rational_number) returns rational_number as the sum of an integer and a fraction having the same sign and a greater denominator magnitude than numerator magnitude. propFrac(4/3) ¸ 1 + 1/3 propFrac(ë 4/3) ¸ ë 1ì 1/3 propFrac(rational_expression,var) returns the sum of proper ratios and a polynomial with respect to var. The degree of var in the denominator exceeds the degree of var in the numerator in each proper ratio.
PtText CATALOG PtText string, x, y PtText "sample",3,5 ¸ Displays the Graph screen and places the character string string on the screen at the pixel nearest the specified (x, y) window coordinates. string is positioned with the upper-left corner of its first character at the coordinates. PxlChg CATALOG PxlChg row, col PxlChg rowList, colList PxlChg 2,4 ¸ Displays the Graph screen and reverses the pixel at pixel coordinates (row, col). Note: Regraphing erases all drawn items.
PxlOff CATALOG PxlHorz 25,1 ¸ PxlOff 25,50 ¸ PxlOff row, col PxlOff rowList, colList Displays the Graph screen and turns off the pixel at pixel coordinates (row, col). Note: Regraphing erases all drawn items. 25,50 PxlOn CATALOG PxlOn 25,50 ¸ PxlOn row, col PxlOn rowList, colList Displays the Graph screen and turns on the pixel at pixel coordinates (row, col). Note: Regraphing erases all drawn items.
QR MATH/Matrix menu QR matrix, qMatName, rMatName[ , tol] Calculates the Householder QR factorization of a real or complex matrix. The resulting Q and R matrices are stored to the specified MatNames. The Q matrix is unitary. The R matrix is upper triangular. Optionally, any matrix element is treated as zero if its absolute value is less than tol. This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value.
Note: list1 through list4 must be a variable name or c1–c99. (columns in the last data variable shown in the Data/Matrix Editor). list5 does not have to be a variable name and cannot be c1–c99 . QuartReg ¸ Regeq(x)"y1(x) ¸ NewPlot 1,1,L1,L2 ¸ Done Done ¥% MATH/Statistics/Regressions menu QuartReg list1, list2[, [list3] [, list4, list5]] In function graphing mode: Calculates the quartic polynomial regression and updates the system statistics variables.
R44Pq q() MATH/Angle menu R44Pq q (xExpression, yExpression) ⇒ expression R44Pq q (xList, yList) ⇒ list R44Pq q (xMatrix, yMatrix) ⇒ matrix In Degree angle mode: R8Pq(x,y) ¸ Returns the equivalent q-coordinate of the (x,y) pair arguments. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting. In Gradian angle mode: R8Pq(x,y) ¸ In Radian angle mode: R4Pq(3,2) ¸ R4Pq([3,-4,2],[0,pà4,1.
randMat() MATH/Probability menu randMat(numRows, numColumns) ⇒ matrix RandSeed 1147 ¸ Returns a matrix of integers between -9 and 9 of the specified dimension. Both arguments must simplify to integers. randNorm() Note: The values in this matrix will change each time you press ¸. MATH/Probability menu randNorm(mean, sd) ⇒ expression Returns a decimal number from the specific normal distribution. It could be any real number but will be heavily concentrated in the interval [mean-3ù sd, mean+3ù sd].
⇒ list real( list1) real({a+iù b,3,i}) ¸ {a 3 0} Returns the real parts of all elements. real( matrix1) ⇒ matrix a 3 [c 0] real([a+iù b,3;c,i]) ¸ Returns the real parts of all elements. 4Rect MATH/Matrix/Vector ops menu vector 4Rect Displays vector in rectangular form [x, y, z]. The vector must be of dimension 2 or 3 and can be a row or a column. Note: 4Rect is a display-format instruction, not a conversion function. You can use it only at the end of an entry line, and it does not update ans.
remain() MATH/Number menu remain( expression1, expression2) ⇒ expression remain( list1, list2) ⇒ list remain( matrix1, matrix2) ⇒ matrix Returns the remainder of the first argument with respect to the second argument as defined by the identities: remain(7,0) ¸ 7 remain(7,3) ¸ 1 remain(ë 7,3) ¸ ë1 remain(7,ë 3) ¸ 1 remain(ë 7,ë 3) ¸ remain(x,0) x remain(x,y) xì yùiPart(x/y) ë1 remain({12,ë 14,16},{9,7,ë 5}) ¸ {3 0 1} As a consequence, note that remain(ì x,y) ì remain(x,y).
right() MATH/List menu right(list1[, num]) ⇒ list right({1,3,ë 2,4},3) ¸ {3 ë 2 4} Returns the rightmost num elements contained in list1. If you omit num, returns all of list1. ⇒ right(sourceString[, num]) string right("Hello",2) ¸ "lo" Returns the rightmost num characters contained in character string sourceString. If you omit num, returns all of sourceString. right(comparison) ⇒ expression right(x<3) ¸ 3 Returns the right side of an equation or inequality.
⇒ string rotate(string1[,#ofRotations]) Returns a copy of string1 rotated right or left by #of Rotations characters. Does not alter string1. If #of Rotations is positive, the rotation is to the left. If #of Rotations is negative, the rotation is to the right. The default is ë 1 (rotate right one character). round() rotate("abcd") ¸ "dabc" rotate("abcd",ë2) ¸ "cdab" rotate("abcd",1) ¸ "bcda" round(1.234567,3) ¸ 1.
rowSwap() MATH/Matrix/Row ops menu rowSwap( matrix1, rIndex1, rIndex2) ⇒ matrix [1,2;3,4;5,6]! Mat ¸ 1 2 3 4 5 6 Returns matrix1 with rows rIndex1 and rIndex2 exchanged. rowSwap(Mat,1,3) ¸ 5 6 3 4 1 2 RplcPic CATALOG RplcPic picVar[, row][, column] Clears the Graph screen and places picture picVar at pixel coordinates (row, column). If you do not want to clear the screen, use RclPic. picVar must be a picture data type variable.
sec L1() MATH/Trig menu sec L1(expression1) ⇒ expression sec L1(list1) ⇒ list In Degree angle mode: Returns the angle whose secant is expression1 or returns a list containing the inverse secants of each element of list1. Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.
@ SendCalc var[,port] Sends contents of var from a TI-89 Titanium to another TI-89 Titanium. If the port is not specified, or port = 0 is specified, the TI-89 Titanium sends data using the USB port if connected, if not, it will send using the I/O port. If port = 1, the TI-89 Titanium sends data using the USB port only. If port = 2, the TI-89 Titanium sends data using the I/O port only.
setFold() CATALOG setFold( newfolderName) ⇒ oldfolderString Returns the name of the current folder as a string and sets newfolderName as the current folder. The folder newfolderName must exist. newFold chris ¸ Done setFold(main) ¸ "chris" setFold(chris)! oldfoldr ¸ "main" 1! a ¸ setFold(#oldfoldr) ¸ setGraph() 1 "chris" a¸ a chris\a ¸ 1 CATALOG ⇒ string Sets the Graph mode modeNameString to settingString, and returns the previous setting of the mode.
3 Applies only to 3D graph mode. Applies only to Sequence graph mode. 5 Applies only to Diff Equations graph mode. 6 Applies only to Function graphing mode, when “Graph Order” is set to “Seq.” 4 setMode() CATALOG setMode(modeNameString, settingString) setMode(list) ⇒ stringList ⇒ string Sets mode modeNameString to the new setting settingString, and returns the current setting of setMode("Angle","Degree") ¸ "RADIAN" ‡2 2 sin(45) ¸ that mode.
"Split Screen" "Full", "Top-Bottom", "Left-Right" "Split 1 App" "Home", "Y= Editor", "Window Editor", "Graph", "Table", "Data/Matrix Editor", "Program Editor", "Text Editor", "Numeric Solver", "Flash App" "Split 2 App" "Home", "Y= Editor", "Window Editor", "Graph", "Table", "Data/Matrix Editor", "Program Editor", "Text Editor", "Numeric Solver", "Flash App" "Number of Graphs" "1", "2" "Graph2" "Function", "Parametric", "Polar", "Sequence", "3D", "Diff Equations" "Split Screen Ratio" "1:1", "1:2",
setTmZn() CATALOG setTmZn(integer) ⇒ integerold Sets the time zone according to the argument and returns the previous time zone value. The time zone is defined by an integer that gives the minutes offset from Greenwich Mean Time (GMT), as established in Greenwich, England. For example, if the time zone is offset from GMT by two hours, the device would return 120 (minutes). If Greenwich Mean Time is 14:07:07, it is: 7:07:07 a.m.
Shade CATALOG In the ZoomTrig viewing window: Shade expr1, expr2, [xlow], [xhigh], [pattern], [patRes] Displays the Graph screen, graphs expr1 and expr2, and shades areas in which expr1 is less than expr2. (expr1 and expr2 must be expressions that use x as the independent variable.) Shade cos(x),sin(x) ¸ xlow and xhigh, if included, specify left and right boundaries for the shading. Valid inputs are between xmin and xmax. Defaults are xmin and xmax.
Each bit shifts right. 0b00000000000001111010110000110101 Inserts 0 if leftmost bit is 0, or 1 if leftmost bit is 1. Dropped produces: 0b00000000000000111101011000011010 The result is displayed according to the Base mode. Leading zeros are not shown. shift(list1 [,#ofShifts]) ⇒ list In Dec base mode: Returns a copy of list1 shifted right or left by #ofShifts elements. Does not alter list1. shift({1,2,3,4}) ¸ If #ofShifts is positive, the shift is to the left.
simult() MATH/Matrix menu simult(coeffMatrix, constVector[, tol]) ⇒ matrix Solve for x and y: Returns a column vector that contains the solutions to a system of linear equations. x + 2y = 1 3x + 4y = ë 1 simult([1,2;3,4],[1;ë1]) ¸ coeffMatrix must be a square matrix that contains constVector must have the same number of rows (same dimension) as coeffMatrix and contain the constants. Optionally, any matrix element is treated as zero if its absolute value is less than tol.
sin(squareMatrix1) ⇒ squareMatrix Returns the matrix sine of squareMatrix1. This is not the same as calculating the sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result In Radian angle mode: sin([1,5,3;4,2,1;6,ë2,1]) ¸ .942… ë.045… ë.048… ë.045… ë.031… .949… ë.020… ë.005… .961… always contains floating-point numbers.
sinhê(squareMatrix1) ⇒ squareMatrix In Radian angle mode: Returns the matrix inverse hyperbolic sine of squareMatrix1. This is not the same as calculating the inverse hyperbolic sine of each element. For information about the calculation method, refer to cos(). sinhê([1,5,3;4,2,1;6,ë2,1]) ¸ .041… 1.463… 2.750… 2.155… 1.158… .926… .112… ë 1.528… .572… squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.
Due to default cancellation of the greatest common divisor from the numerator and denominator of ratios, solutions might be solutions only in the limit from one or both sides. (x+1)(xì 1)/(xì 1)+xì 3 ¸ solve(entry(1)=0,x) ¸ entry(2)|ans(1) ¸ limit(entry(3),x,1) ¸ 2ø xì 2 x=1 undef 0 For inequalities of types ‚, , <, or >, explicit solutions are unlikely unless the inequality is linear and contains only var.
If all of the equations are polynomials and if you do NOT specify any initial guesses, solve() uses the lexical Gröbner/Buchberger elimination method to attempt to determine all real solutions. For example, suppose you have a circle of radius r at the origin and another circle of radius r centered where the first circle crosses the positive x-axis. Use solve() to find the intersections.
Each solution variable starts at its guessed value if there is one; otherwise, it starts at 0.0. Use guesses to seek additional solutions one by one. For convergence, a guess may have to be rather close to a solution. SortA solve(e^(z)ùy=1 and ëy=sin(z),{y,z=2p}) ¸ y=.001… and z=6.281… MATH/List menu SortA listName1[, listName2] [, listName3] ... SortA vectorName1[, vectorName2] [, vectorName3] ... Sorts the elements of the first argument in ascending order.
stdDev() MATH/Statistics menu stdDev(list[, freqlist]) ⇒ expression Returns the standard deviation of the elements in list. stdDev({a,b,c}) ¸ stdDev({1,2,5,ë 6,3,ë 2}) ¸ Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Note: list must have at least two elements. stdDev({1.3,2.5,L6.4},{3,2,5}) ¸ stdDev(matrix1[, freqmatrix]) ⇒ matrix Returns a row vector of the standard deviations of the columns in matrix1.
StoGDB CATALOG StoGDB GDBvar Creates a Graph database (GDB) variable that contains the current: * Graphing mode * Y= functions * Window variables * Graph format settings 1- or 2-Graph setting (split screen and ratio settings if 2-Graph mode) Angle mode Real/complex mode * Initial conditions if Sequence or Diff Equations mode * Table flags * tblStart, @tbl, tblInput You can use RclGDB GDBvar to restore the graph environment. *Note: These items are saved for both graphs in 2-Graph mode.
Style CATALOG Style equanum, stylePropertyString Sets the system graphing function equanum in the current graph mode to use the graphing property stylePropertyString. equanum must be an integer from 1–99 and the function must already exist. Style 1,"thick" ¸ Done Style 10,"path" ¸ Done Note: In function graphing mode, these examples set the style of y1(x) to "Thick" and y10(x) to "Path". stylePropertyString must be one of: "Line", "Dot", "Square", "Thick", "Animate", "Path", "Above", or "Below".
switch() CATALOG switch([integer1]) ⇒ integer Returns the number of the active window. Also can set the active window. Note: Window 1 is left or top; Window 2 is right or bottom. If integer1 = 0, returns the active window number. If integer1 = 1, activates window 1 and returns the previously active window number. switch() ¸ If integer1 = 2, activates window 2 and returns the previously active window number. If integer1 is omitted, switches windows and returns the previously active window number.
Table CATALOG In function graphing mode. Table expression1[, expression2] [, var1] Table 1.25xù cos(x) ¸ Builds a table of the specified expressions or functions. The expressions in the table can also be graphed. Expressions entered using the Table or Graph commands are assigned increasing function numbers starting with 1. The expressions can be modified or individually deleted using the edit functions available when the table is displayed by pressing † Header.
tan(squareMatrix1) ⇒ squareMatrix Returns the matrix tangent of squareMatrix1. This is not the same as calculating the tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result In Radian angle mode: tan([1,5,3;4,2,1;6,ë2,1]) ¸ ë 28.291… 12.117… 36.818… 26.088… 11.114… ë 7.835… ë 5.481… ë 32.806… ë 10.459… always contains floating-point numbers.
tanhê () MATH/Hyperbolic menu tanhê (expression1) ⇒ expression tanhê (list1) ⇒ list In rectangular complex format mode: tanhê (expression1) returns the inverse hyperbolic tangent of the argument as an expression. tanhê (0) ¸ tanhê ({1,2.1,3}) ¸ {ˆ tanhê (list1) returns a list of the inverse 0 .518... ì 1.570...ø i hyperbolic tangents of each element of list1. tanhê(squareMatrix1) ⇒ squareMatrix Returns the matrix inverse hyperbolic tangent of squareMatrix1.
tExpand() MATH\Algebra\Trig menu tExpand(expression1) ⇒ expression Returns an expression in which sines and cosines of integer-multiple angles, angle sums, and angle differences are expanded. Because of the identity (sin(x)) 2+(cos(x))2=1, there are many possible equivalent results. Consequently, a result might differ from a result shown in other publications.
tmpCnv() CATALOG tmpCnv(100_¡c,_¡f) ¸ tmpCnv(expression1_¡tempUnit1, _¡tempUnit2) ⇒ expression _¡tempUnit2 Converts a temperature value specified by expression1 from one unit to another. Valid temperature units are: _¡C _¡F _¡K _¡R 212.ø_¡F tmpCnv(32_¡f,_¡c) ¸ Celsius Fahrenheit Kelvin Rankine 0.ø_¡C tmpCnv(0_¡c,_¡k) ¸ 273.15ø_¡K tmpCnv(0_¡f,_¡r) ¸ 459.67ø_¡R Note: To select temperature units from a menu, press 2 9 For ¡, press 2 “. For _ , press ¥ .
Toolbar CATALOG Toolbar block EndTBar Creates a toolbar menu. block can be either a single statement or a sequence of statements separated with the “:” character. The statements can be either Title or Item. Items must have labels. A Title must also have a label if it does not have an item.
TwoVar MATH/Statistics menu {0,1,2,3,4,5,6}! L1 ¸ TwoVar list1, list2[, [list3] [, list4, list5]] {0 1 2 ...} Calculates the TwoVar statistics and updates all the system statistics variables. {0,2,3,4,3,4,6}! L2 ¸ All the lists must have equal dimensions except for list5. TwoVar L1,L2 ¸ ShowStat ¸ {0 2 3 ...} Done list1 represents xlist. list2 represents ylist. list3 represents frequency. list4 represents category codes. list5 represents category include list.
variance() MATH/Statistics menu variance(list[, freqlist]) ⇒ expression Returns the variance of list. variance({a,b,c}) ¸ añ -aø (b+c)+bñ -bø c+cñ 3 Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. variance({1,2,5,ë 6,3,ë 2}) ¸ Note: list must contain at least two elements. variance({1,3,5},{4,6,2}) ¸ variance(matrix1[, freqmatrix]) ⇒ matrix Returns a row vector containing the variance of each column in matrix1.
when() is helpful for defining recursive functions. While when(n>0,nù factoral(nì 1),1) ! factoral(n) ¸ factoral(3) ¸ 3! ¸ Done 6 6 CATALOG Program segment: While condition block EndWhile Executes the statements in block as long as condition is true. block can be either a single statement or a sequence of statements separated with the “:” character. “With” See |, page 912.
XorPic CATALOG XorPic picVar[, row] [, column] Displays the picture stored in picVar on the current Graph screen. Uses xor logic for each pixel. Only those pixel positions that are exclusive to either the screen or the picture are turned on. This instruction turns off pixels that are turned on in both images. picVar must contain a pic data type. row and column, if included, specify the pixel coordinates for the upper left corner of the picture. Defaults are (0, 0).
r 2 ans(1)[2] ¸ You can also (or instead) include unknowns that do not appear in the expressions. For example, you can include z as an unknown to extend the previous example to two parallel intersecting cylinders of radius r. The cylinder zeros illustrate how families of zeros might contain arbitrary constants in the form ck, where k is an integer suffix from 1 through 255. The suffix resets to 1 when you use ClrHome or ƒ 8:Clear Home.
ZoomData CATALOG ZoomData Adjusts the window settings based on the currently defined plots (and data) so that all statistical data points will be sampled, and displays the Graph screen. In function graphing mode: {1,2,3,4}! L1 ¸ {2,3,4,5}! L2 ¸ newPlot 1,1,L1,L2 ¸ ZoomStd ¸ {1 2 3 4} {2 3 4 5} Done Note: Does not adjust ymin and ymax for histograms. " ZoomData ¸ ZoomDec CATALOG ZoomDec Adjusts the viewing window so that @x and @y = 0.
ZoomFit CATALOG In function graphing mode: ZoomFit Displays the Graph screen, and calculates the necessary window dimensions for the dependent variables to view all the picture for the current independent variable settings. 1.25xù cos(x)! y1(x) ¸ ZoomStd ¸ Done " ZoomFit ¸ ZoomIn CATALOG In function graphing mode: ZoomIn Displays the Graph screen, lets you set a center point for a zoom in, and updates the viewing window. 1.
ZoomOut CATALOG ZoomOut Displays the Graph screen, lets you set a center point for a zoom out, and updates the viewing window. In function graphing mode: 1.25xù cos(x)! y1(x) ¸ ZoomStd:ZoomOut ¸ Done The magnitude of the zoom is dependent on the Zoom factors xFact and yFact. In 3D Graph mode, the magnitude is dependent on xFact, yFact, and zFact. ¸ ZoomPrev CATALOG ZoomPrev Displays the Graph screen, and updates the viewing window with the settings in use before the last zoom.
ZoomStd CATALOG In function graphing mode: ZoomStd Sets the window variables to the following standard values, and then updates the viewing window. 1.
list1 + list2 ⇒ list matrix1 + matrix2 ⇒ matrix Returns a list (or matrix) containing the sums of corresponding elements in list1 and list2 (or matrix1 and matrix2). Dimensions of the arguments must be equal.
ù (multiply) p key expression1 ù expression2 ⇒ expression Returns the product of expression1 and expression2. list1ù list2 ⇒ list Returns a list containing the products of the corresponding elements in list1 and list2. 2ù 3.45 ¸ 6.9 xù yù x ¸ x2ø y {1.0,2,3}ù {4,5,6} ¸ {4. 10 18} {2àa,3à2}ù {añ,bà3} ¸ b {2ø a 2} Dimensions of the lists must be equal. matrix1 ù matrix2 ⇒ [1,2,3;4,5,6]ù [a,d;b,e;c,f] ¸ matrix Returns the matrix product of matrix1 and matrix2.
^ (power) Z key expression1 ^ expression2 ⇒ expression list1 ^ list2 ⇒ list Returns the first argument raised to the power of the second argument. 4^2 ¸ 16 {a,2,c}^{1,b,3} ¸ {a 2 b cò } For a list, returns the elements in list1 raised to the power of the corresponding elements in list2. In the real domain, fractional powers that have reduced exponents with odd denominators use the real branch versus the principal branch for complex mode.
.ù (dot mult.) ¶ p keys matrix1 .ù matrix2 ⇒ matrix expression .ù matrix1 ⇒ matrix [a,2;b,3].ù [c,4;5,d] ¸ x.ù [a,b;c,d] ¸ matrix1 . ù matrix2 returns a matrix that is the product of each pair of corresponding elements in matrix1 and matrix2. expression . ù matrix1 returns a matrix containing the products of expression and each element in matrix1. . / (dot divide) ¶ e keys matrix1 . / matrix2 ⇒ matrix expression . / matrix1 ⇒ matrix [a,2;b,3]./[c,4;5,d] ¸ x./[c,4;5,d] ¸ matrix1 .
= (equal) Á key expression1 = expression2 ⇒ Boolean expression list1 = list2 ⇒ Boolean list matrix1 = matrix2 ⇒ Boolean matrix Returns true if expression1 is determined to be equal to expression2. Returns false if expression1 is determined to not be equal to expression2. Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element.
≤ ¹ µ key expression1 ≤ expression2 ⇒ Boolean expression list1 ≤ list2 ⇒ Boolean list matrix1 ≤ matrix2 ⇒ Boolean matrix See "=" (equal) example. Returns true if expression1 is determined to be less than or equal to expression2. Returns false if expression1 is determined to be greater than expression2. Anything else returns a simplified form of the equation. For lists and matrices, returns comparisons element by element.
& (append) ¥ p key string1 & string2 ⇒ string "Hello " & "Nick" ¸ Returns a text string that is string2 appended to string1. "Hello Nick" ‰ () (integrate) 2 < key ‰ (expression1, var[, lower] [,upper]) ‰ (list1,var [,order]) ⇒ list ‰ (matrix1,var [,order]) ⇒ matrix ⇒ expression Returns the integral of expression1 with respect to the variable var from lower to upper. ‰(x^2,x,a,b) ¸ Returns an anti-derivative if lower and upper are omitted. A symbolic constant of integration such as C is omitted.
‡() (square root) 2 ] key ‡ (expression1) ⇒ expression ‡ (list1) ⇒ list ‡(4) ¸ 2 ‡({9,a,4}) ¸ Returns the square root of the argument. {3 ‡a 2} For a list, returns the square roots of all the elements in list1. Π() (product) MATH/Calculus menu Π (expression1, var, low, high) ⇒ expression Evaluates expression1 for each value of var from low to high, and returns the product of the results.
G (gradian) MATH/Angle menu expression1 G ¡ ⇒ expression list1 G ¡ ⇒ list matrix1 G ¡ ⇒ matrix This function gives you a way to use a gradian angle while in the Degree or Radian modes. In Degree, Gradian or Radian mode: ‡2 cos(50G) ¸ 2 cos({0,100G,200G}) ¸ {1,0.-1} In Radian angle mode, multiplies expression by p/200. In Degree angle mode, multiplies expression 1 by g/100. In Gradian mode, returns expression1 unchanged.
(magnitude angle) ⇒ complexValue (polar input) Enters a complex value in (rq) polar form. The angle is interpreted according to the current Angle mode setting. ¡, ', " In Radian angle mode and Rectangular complex format mode: 5+3iì (10p/4) ¸ 5ì 5ø 2+(3ì 5ø 2)øi ¥¸ ë 2.071…ì 4.071…øi 2 “ key (¡), 2 È key ('), 2 É key (") dd ¡ mm ' ss.ss " ⇒ expression dd mm ss.ss In Degree angle mode: 25°13'17.5" ¸ A positive or negative number A non-negative number A non-negative number 25°30' ¸ 25.221...
4 (convert) 2 key expression_unit1 4 _unit2 ⇒ expression_unit2 3_m 4 _ft ¸ 9.842…ø_ft 10^(1.5) ¸ 31.622... Converts an expression from one unit to another. The units must be in the same category. The _ underscore character designates the units. For a list of valid pre-defined units, refer to the module about constants and measurement units. You can press 2 9 to select units from a menu, or you can type the unit names directly.
| (“with”) Í key x+1| x=3 ¸ expression | Boolean expression1 [and Boolean expression2]...[and Boolean expressionN] x+y| x=sin(y) ¸ The “with” (|) symbol serves as a binary operator. x+y| sin(y)=x ¸ The operand to the left of | is an expression. The operand to the right of | specifies one or more relations that are intended to affect the simplification of the expression. Multiple relations after | must be joined by a logical “and”.
0b, 0h µ j [B] keys µ j [H] keys 0b binaryNumber 0h hexadecimalNumber In Dec base mode: 0b10+0hF+10 ¸ 27 In Bin base mode: Denotes a binary or hexadecimal number, respectively. To enter a binary or hex number, you must enter the 0b or 0h prefix regardless of the Base mode. Without a prefix, a number is treated as decimal (base 10). 0b10+0hF+10 ¸ 0b11011 In Hex base mode: 0b10+0hF+10 ¸ 0h1B Results are displayed according to the Base mode.
Appendix B: Technical Reference This section contains a comprehensive list of TI-89 Titanium / Voyage™ 200 error messages and character codes. It also includes information about how certain TI-89 Titanium / Voyage™ 200 operations are calculated. TI-89 Titanium / Voyage™ 200 Error Messages This section lists error messages that may be displayed when input or internal errors are encountered. The number to the left of each error message represents an internal error number that is not displayed.
Error Number Description 163 Attribute (8-digit number) of object (8-digit number) not found 165 Batteries too low for sending or receiving Install new batteries before sending or receiving. 170 Bound For the interactive graph math functions like 2:Zero, the lower bound must be less than the upper bound to define the search interval. 180 Break The ´ key was pressed during a long calculation or during program execution.
Error Number Description 280 Else and ElseIf invalid outside of If..EndIf block 290 EndTry is missing the matching Else statement 295 Excessive iteration 300 Expected 2 or 3-element list or matrix 307 Flash application extension (function or program) not found 308 Flash application not found 310 First argument of nSolve must be a univariate equation The first argument must be an equation, and the equation cannot contain a non-valued variable other than the variable of interest.
Error Number Description 460 Invalid in Custom..EndCustm block 470 Invalid in Dialog..EndDlog block 480 Invalid in Toolbar..EndTBar block 490 Invalid in Try..EndTry block 500 Invalid label Label names must follow the same rules used for naming variables. 510 Invalid list or matrix For example, a list inside a list such as {2,{3,4}} is not valid. 520 Invalid outside Custom..EndCustm or ToolBar..EndTbar blocks For example, an Item command is attempted outside a Custom or ToolBar structure.
Error Number Description 610 Invalid variable name in a Local statement 620 Invalid variable or function name 630 Invalid variable reference 640 Invalid vector syntax 650 Link transmission A transmission between two units was not completed. Verify that the connecting cable is connected firmly to both units.
Error Number Description 850 Program not found A program reference inside another program could not be found in the provided path during execution.
Error Number Description Warning: Expected finite real integrand Warning: May not be fully simplified Warning: More solutions may exist Warning: May introduce false solutions Warning: Operation may lose solutions Warning: Requires & returns 32 bit value Warning: Overflow replaced by % or -% Warning: Questionable accuracy Warning: Questionable solution Warning: Solve may specify more zeros Warning: Trig argument too big to reduce Warning: Non-real intermediate result Note: Domain of result may be larger Not
Note: For detailed information about using folders, see Calculator Home Screen. 1:main Default folder included with the TI-89 Titanium / Voyage™ 200. 2: — Other folders are available only if they have (custom folders) been created by a user. Display Digits Selects the number of digits. These decimal settings affect only how results are displayed—you can enter a number in any format. Internally, the TI-89 Titanium / Voyage™ 200 retains decimal numbers with 14 significant digits.
3:ENGINEERING Similar to scientific notation. However: • The number may have one, two, or three digits before the decimal. • The power-of-10 exponent is a multiple of three. For example, 12.34567E3 means 12.34567×10 3 Note: If you select NORMAL, but the answer cannot be displayed in the number of digits selected by Display Digits, the TI-89 Titanium / Voyage™ 200 displays the answer in SCIENTIFIC notation.
Split Screen Lets you split the screen into two parts. For example, you can display a graph and see the Y= Editor at the same time. 1:FULL The screen is not split. 2:TOPBOTTOM The applications are shown in two screens that are above and below each other. 3:LEFT-RIGHT The applications are shown in two screens that are to the left and right of each other.
Exact/Approx Specifies how fractional and symbolic expressions are calculated and displayed. By retaining rational and symbolic forms in the EXACT setting, the TI-89 Titanium / Voyage™ 200 increases precision by eliminating most numeric rounding errors. 1:AUTO Uses EXACT setting in most cases. However, uses APPROXIMATE if the entry contains a decimal point. 2:EXACT Displays non-whole-number results in their rational or symbolic form. 3:APPROXIMATE Displays numeric results in floating-point form.
Unit System Lets you enter a unit for values in an expression, such as 6_m * 4_m or 23_m/_s * 10_s, convert values from one unit to another within the same category, and create your own user-defined units. 1:SI Select SI for the metric system of measurements 2:ENG/US Select ENG/US for the non-metric system of measurements 3:CUSTOM Allows you to select custom defaults. Custom Units Lets you select custom defaults. This mode is dimmed until you select Unit System, 3:CUSTOM.
TI-89 Titanium / Voyage™ 200 Character Codes The char() function lets you refer to any character by its numeric character code. For example, to display 2 on the Program I/O screen, use Disp char(127). char(127) You can use ord() to find the numeric code of a character. For example, ord("A") returns 65. 1. SOH 2. STX 3. ETX 4. EOT 5. ENQ 6. ACK 7. BELL 8. BS 9. TAB 10. LF 11. ÷ 12. FF 13. CR 14. 15. 16. 17. 18. 19. 20. 51. 3 é 7 8 9 : 21. ← 22. → 23. 24. ↑ ↓ 26. 3 4 27. ' 25. ∪ 29. ∩ 30. ⊂ 31.
TI-89 Titanium Key Codes The getKey() function returns a value that corresponds to the last key pressed, according to the tables shown in this section. For example, if your program contains a getKey() function, pressing 2 ˆ will return a value of 273. Table 1: Key Codes for Primary Keys Key Modifier Û¤ None Assoc. Value Assoc. 2 Value Assoc. ¥ Value Assoc.
Table 1: Key Codes for Primary Keys Key Modifier Û¤ None Assoc. ¸ Value Assoc. 2 Value Assoc. ¥ Value Assoc. j Value Assoc Value 8205 CR 13 CR 13 CR 13 ENTRY 4109 STO4 258 P 80 RCL 4354 @ 64 p 112 Á = 61 A 65 ‘ 39 "# 157 a 97 ^ EE 149 K 75 , 159 SYMB 8341 k 107 · - 173 SPACE 32 ANS 4372 8365 SPACE 32 ¶ .
Table 2: Arrow Keys (including diagonal movement) Key Normal ¤ 2 ¥ j C 338 16722 4434 8530 33106 B 340 16724 4436 8532 33108 D 344 16728 4440 8536 33112 A 337 16721 4433 8529 33105 C and A 339 16723 4435 8531 33107 C and B 342 16726 4438 8534 33110 D and A 345 16729 4441 8537 33113 D and B 348 16732 4444 8540 33116 Table 3: Greek Letters (prefixed by ¥ c) Keys Second modifier j ¤ Assoc.
Table 1: Key Codes for Primary Keys Key Modifier ¤ None Assoc. Value Assoc. 2 Value Assoc. 8 Value Assoc.
Key Modifier ¤ None Assoc. Value Assoc. 2 Value Assoc. Ï θ 136 θ 136 : · - 173 - 173 ANS ¶ . 46 . 46 µ 0 48 0 ¨ 1 49 © 2 ª 8 Value Assoc.
Key Modifier ¤ None Assoc. Value Assoc. 2 Value Assoc. 8 Value Assoc.
Table 2: Arrow Keys (including diagonal movement) Key Normal ¤ 2 ¥ ‚ C 338 16722 4434 8530 33106 B 340 16724 4436 8532 33108 D 344 16728 4440 8536 33112 A 337 16721 4433 8529 33105 C and A 339 16723 4435 8531 33107 C and B 342 16726 4438 8534 33110 D and A 345 16729 4441 8537 33113 D and B 348 16732 4444 8540 33116 Note: The Grab (‚) modifier only affects the arrow keys. Table 3: Grave Accent Letters (prefixed by 2 A) Key Assoc.
Table 5: Acute Accent Letters (prefixed by 2 E) Key Assoc. Normal Û¤ A á 225 193 E é 233 201 I í 237 205 O ó 243 211 U ú 250 218 Y ý 253 221 Û¤ Table 6: Greek Letters (prefixed by 2 G) Key Assoc.
Table 7: Tilde Letters (prefixed by 2 N) Key Assoc. Normal Û¤ N ñ 241 209 O õ 245 Table 8: Caret Letters (prefixed by 2 O) Key Assoc. Normal ¤ A â 226 194 E ê 234 202 I î 238 206 O ô 244 212 U û 251 219 Table 9: Umlaut Letters (prefixed by 2 U) Key Assoc.
Entering Complex Numbers You can enter complex numbers in the polar form (rù, q), where r is the magnitude and q is the angle, or polar form r e i q. You can also enter complex numbers in rectangular form a+bi . Overview of Complex Numbers A complex number has real and imaginary components that identify a point in the complex plane. These components are measured along the real and imaginary axes, which are similar to the x and y axes in the real plane.
Polar form rei q or (r,ùq) Parentheses are required for the (r∠ùq) form. Substitute the applicable values or variable names for r and q, where q is interpreted according to the Angle mode setting. TI-89 Titanium: j [R] ¥ s 2 ) ¥ Ï d Ð or – c j [R] 2 ’ ¥ Ï d Important: Do not use the r e i q polar form in Degree angle mode. It will cause a Domain error. Note: To get the e symbol, press: TI89 Titanium: ¥ s. Voyage™ 200: 2 s Do not simply type an alphabetic e. Tip: To get the ,ù symbol, press 2 Õ’.
REAL Will not display complex results unless you: • Enter a complex number. – or – • Use a complex function such as cFactor(), cSolve(), or cZeros(). If complex results are displayed, they will be shown in either a+bi or r e i q form. Note: You can enter complex numbers in any form (or a mixture of all forms) depending on the Angle mode. RECTANGULAR Displays complex results as a+bi.
Accuracy Information To maximize accuracy, the TI-89 Titanium / Voyage™ 200 carries more digits internally than it displays. Computational Accuracy Floating-point (decimal) values in memory are stored using up to 14 digits with a 3-digit exponent. • For min and max Window variables (xmin, xmax, ymin, ymax, etc.), you can store values using up to 12 digits. Other Window variables use 14 digits.
Graph y1(x)–y99(x)* y1'(t)–y99'(t)* yi1–yi99* r1(q)–r99(q)* xt1(t)–xt99(t)* yt1(t)– yt99(t)* z1(x,y)–z99(x,y)* u1(n)–u99(n)* ui1–ui99* xc yc zc tc rc qc nc xfact yfact zfact xmin xmax xscl xgrid ymin ymax yscl ygrid xres @x @y zmin zmax zscl eyeq eyef eyeψ ncontour qmin qmax qstep tmin tmax tstep t0 tplot ncurves diftol dtime Estep fldpic fldres nmin nmax plotStrt plotStep sysMath Graph Zoom zxmin zxmax zxscl zxgrid zymin zymax zyscl zygrid zxr
Table @tbl tblStart tblInput Data/Matrix c1–c99 sysData* Miscellaneous main ok errornum Solver eqn* exp* EOS (Equation Operating System) Hierarchy This section describes the Equation Operating System (EOSé) that is used by the TI-89 Titanium / Voyage™ 200. Numbers, variables, and functions are entered in a simple, straightforward sequence. EOS evaluates expressions and equations using parenthetical grouping and according to the priorities described below.
14 Constraint “with” operator (|) 15 Store (!) Parentheses, Brackets, and Braces All calculations inside a pair of parentheses, brackets, or braces are evaluated first. For example, in the expression 4(1+2), EOS first evaluates the portion of the expression inside the parentheses, 1+2, and then multiplies the result, 3, by 4. The number of opening and closing parentheses, brackets, and braces must be the same within an expression or equation.
Regression Formulas This section describes how the statistical regressions are calculated.
LnReg Uses the least-squares algorithm and transformed values ln(x) and y to fit the model equation: y=a+b ln(x) Logistic Uses the least-squares algorithm to fit the model equation: y=a/(1+b*e^(c*x))+d MedMed Uses the median-median line (resistant line) technique to calculate summary points x1, y1, x2, y2, x3, and y3, and fits the model equation: y=ax+b where a is the slope and b is the y-intercept.
Contour Levels and Implicit Plot Algorithm Contours are calculated and plotted by the following method. An implicit plot is the same as a contour, except that an implicit plot is for the z=0 contour only. Algorithm Based on your x and y Window variables, the distance between xmin and xmax and between ymin and ymax is divided into a number of grid lines specified by xgrid and ygrid. These grid lines intersect to form a series of rectangles.
Bogacki-Shampine 3(2) Formula The Bogacki-Shampine 3(2) formula provides a result of 3rd-order accuracy and an error estimate based on an embedded 2nd-order formula.
Battery Information The TI-89 Titanium / Voyage™ 200 uses two types of batteries: four alkaline batteries, and a lithium battery as a backup for retaining memory while you change the alkaline batteries. When to Replace the Batteries As the alkaline batteries run down, the display will begin to dim (especially during calculations). To compensate for this, you will need to adjust the contrast to a higher setting.
Replacing the Alkaline Batteries in the TI-89 Titanium 1. If the TI-89 Titanium is on, turn it off (press 2 ®) to avoid loss of information stored in memory. 2. Slide the protective cover over the keyboard and place the device face down. 3. Push down on the battery cover latch, and then pull up to remove the cover. 4. Remove all four discharged AAA batteries. 5. Install four new AAA alkaline batteries, arranged according to the polarity (+ and -) diagram inside the battery compartment. 6.
Replacing the Lithium Battery in the Voyage 200 To replace the lithium backup battery, remove the battery cover. Insert a blunt object into the circular indentation next to the battery. Gently place a finger on the lithium battery and pry the battery out. Slide in a new CR1616 or CR1620 battery, positive (+) side up. Press firmly to snap the new lithium battery into place.
In Case of Difficulty If you have difficulty operating the TI-89 Titanium / Voyage™ 200, the following suggestions may help you correct the problem. If: Suggested action: You cannot see anything on the display. Press ¥ « to darken or ¥ | to lighten the display contrast. The BATT indicator is displayed. Replace the batteries. If BATT is displayed in reverse text ( ), replace the batteries as soon as possible. The BUSY indicator is displayed. A calculation is in progress.
If: Suggested action: The TI-89 Titanium appears to be “locked up” and will not respond to keyboard input. The following action clears RAM. This erases all data, programs, and user-defined variables, functions, or folders. Press and hold A, B, and 2. Then press and release ´. The following action clears RAM and Flash ROM. This erases all data, programs, user-defined variables, functions, folders, Flash applications, and the user data archive. 1. Remove one of the four AAA batteries. 2.
Appendix C: Programmer’s Guide The parameter/mode strings used in the setMode( ), getMode( ), setGraph( ), and setTable( ) functions do not translate into other languages when used in a program. For example, when you write a program in the French Language mode then switch to the Italian Language mode, the program will produce an error. To avoid this error, you must substitute digits for the alpha characters. These digits operate in all languages.
setMode( ) and getMode( ) Parameter/Mode Setting Strings ALL 0 Graph 1 FUNCTION 1 PARAMETRIC 2 POLAR 3 SEQUENCE 4 3D 5 DIFF EQUATIONS 6 DisplayDigits 2 FIX 0 1 FIX 1 2 FIX 2 3 FIX 3 4 FIX 4 5 FIX 5 6 FIX 6 7 FIX 7 8 FIX 8 9 Appendix C: Programmer’s Guide 956
Parameter/Mode Setting Strings FIX 9 10 FIX 10 11 FIX 11 12 FIX 12 13 FLOAT 14 FLOAT 1 15 FLOAT 2 16 FLOAT 3 17 FLOAT 4 18 FLOAT 5 19 FLOAT 6 20 FLOAT 7 21 FLOAT 8 22 FLOAT 9 23 FLOAT 10 24 FLOAT 11 25 FLOAT 12 26 Angle RADIAN Appendix C: Programmer’s Guide 3 1 957
Parameter/Mode Setting Strings DEGREE 2 GRADIAN 3 Exponential Format 4 NORMAL 1 SCIENTIFIC 2 ENGINEERING 3 Complex Format 5 REAL 1 RECTANGULAR 2 POLAR 3 Vector Format 6 RECTANGULAR 1 CYLINDRICAL 2 SPHERICAL 3 Pretty Print 7 OFF 1 ON 2 SplitScreen 8 FULL 1 Appendix C: Programmer’s Guide 958
Parameter/Mode Setting Strings TOP-BOTTOM 2 LEFT-RIGHT 3 Split1App 9 (applications are not numbered) Split2App 10 (applications are not numbered) Number of Graphs 11 1 1 2 2 Parameter/Mode Setting Strings Graph 2 12 FUNCTION 1 PARAMETRIC 2 POLAR 3 SEQUENCE 4 3D 5 DIFF_EQUATIONS 6 Split Screen Ratio 13 1:1 1 1:2 2 Appendix C: Programmer’s Guide 959
Parameter/Mode Setting 2:1 Strings 3 Exact/Approx 14 AUTO 1 EXACT 2 APPROXIMATE 3 Base 15 DEC 1 HEX 2 BIN 3 Appendix C: Programmer’s Guide 960
setGraph( ) Parameter/Mode Setting Strings Coordinates 1 RECT 1 POLAR 2 OFF 3 Graph Order 2 SEQ 1 SIMUL 2 Grid 3 OFF 1 ON 2 Axes 4 In 3D Mode: OFF 1 AXES 2 BOX 3 Not in 3D Mode: OFF Appendix C: Programmer’s Guide 1 961
ON Leading Cursor 2 5 OFF 1 ON 2 Labels 6 OFF 1 ON 1 Seq Axes 7 TIME 1 WEB 2 Custom 3 Solution Method 8 RK 1 EULER 2 Fields 9 SLPFLD 1 DIRFLD 2 FLDOFF 3 DE Axes TIME Appendix C: Programmer’s Guide 10 1 962
Y1-VS-Y2 2 T-VS-Y' 3 Y-VS-Y' 4 Y1-VS-Y2' 5 Y1'-VS-Y2' 6 XR Style 11 WIRE FRAME 1 HIDDEN SRUFACE 2 CONTOUR LEVELS 3 WIRE AND CONTOUR 4 IMPLICIT PLOT 5 Appendix C: Programmer’s Guide 963
setTable( ) Parameter/Mode Setting Strings Graph <->Table 1 OFF 1 ON 2 Independent 2 AUTO 1 ASK 2 Axes 4 964
Appendix D: Service and Warranty Information Texas Instruments Support and Service For general information Home Page: education.ti.com education.ti.com KnowledgeBase and e-mail inquires: education.ti.com/support education.ti.com/support Phone: (800) TI-CARES; (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands only International information: education.ti.com/international education.ti.
For product (hardware) service Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin Islands: Always contact Texas Instruments Customer Support before returning a product for service. All other customers: Refer to the leaflet enclosed with this product (hardware) or contact your local Texas Instruments retailer/distributor. Texas Instruments (TI) Warranty Information Customers in the U.S.
Warranty Performance. During the above one (1) year warranty period, your defective product will be either repaired or replaced with a reconditioned model of an equivalent quality (at TI’s option) when the product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty of the repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer.
Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction.
All Other Customers For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor. Battery Precautions Take these precautions when replacing batteries: • Do not leave batteries within the reach of children. • Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. • Do not mix rechargeable and non-rechargeable batteries.
TI-89 Titanium Shortcut Keys Alpha Rules General j Type one lowercase letter ¤ Type one uppercase letter ¥O List of Flash applications Lowercase alpha lock Toggle between last two chosen applications or split screens 2 ™ 2a ¤j Uppercase alpha lock ¥ |, ¥ « Lighten or darken contrast j Exit alpha lock ¥¸ Calculate approximate answer ¥C, ¥D Move cursor to top or bottom (in editors) ¤ C, ¤ D Scroll tall objects in history C, D, A, B Animate graph ¤ A, ¤ B Highlight left or right fro
Voyage™ 200 Shortcut Keys General ¥O 2a ¥ D List of Flash applications (if desktop is off) Toggle between last two chosen applications or split screens Copy graph coordinates to Editing ¥ C ¥ D 2 A 2 B ‚ C, ‚ D 2 C, 2 D ¥ X ¥ C ¥ V Move cursor to top Move cursor to bottom Move cursor to far left Move cursor to far right Scroll tall objects in history Page up and page down Cut Copy Paste sysdata ¥ F ¥ H ¥ ¥ ¥ ¥ ¥ ¥ N O S |, ¥ «Ç ¸ ´ ¥1–¥6 Display FORMATS dialog box Copy graph coordinates to Home scr
Keystroke Differences There are certain differences in keystrokes using the TI-89 Titanium / Voyage™ 200 for various operations. The following table shows the keystrokes for major commands for the two calculators.
θ (Theta) ¥Ï Ï | (“With”) Í 2Í ' (Prime) 2È 2È ° (Degree) 2v 2v ∠ (Angle) 2’ 2’ Σ (Sigma) ½Σ( 2 [Σ] x (Reciprocal) ½ ^-1 2 [x-1] Space j Space bar Place data in sysdata variable ¥ b ¥ D Greek characters ¥ c j or ¥ c ¤ ¥ G or ¥ G ¤ Keyboard map ¥ ^ ¥ [KEY] Place data in Home screen history ¥· ¥ H Grave (à, è, ì, ò, ù) 2¿5 2 A a, e, i, o, u Cedilla (ç) 2¿5 6 2C c Acute (á, é, í, ó, ú, ý) 2¿5 2 E a, e, i, o, u, y Tilde (ã, ñ, õ) 2¿5 6 2 N a, n, o Caret (â, ê, î
Index Symbols !( , factorial . . . . . . . . . . . . . . . . . . 74, 907 (!, store . . . . . . . . . . . . . . . . . . . 596, 913 (", second notation . . . . . . . . . . . . . . . 911 (#, /=, not equal . . . . . . . . . . . . . 604, 906 (#, indirection . . . . . . . . . . . . . . . 602, 909 ($( ), square root . . . . . . . . . . . . . . . . 909 (%, percent . . . . . . . . . . . . . . . . . . . . 905 (&, append . . . . . . . . . . . . . . . . . 602, 908 (', minute notation . . . . . . . . . . . . . . .
description . . . . . . . . . . . . . . . . . . 13 status . . . . . . . . . . . . . . . . . . . . . . 38 (2 ; (MEMORY) . . . . . . . . . . . . . . 17 (2 ^ (exponent key) . . . . . . . . . . . . 15 (2 4 (measurement conversions) . . 16 (2 6 (recall) . . . . . . . . . . . . . . . . . . 17 (2 E (Catalog) commands . . . . . . . . . . . . . . . . . . 22 description . . . . . . . . . . . . . . . . . . 21 exiting . . . . . . . . . . . . . . . . . . . . . . 24 key command . . . . . . . . . . . . . . . .
(x window variable . . . . . . . . . . . . . . 941 x( /, reciprocal . . . . . . . . . . . . . . . . . . 912 (y window variable . . . . . . . . . . . . . . 941 Numerics 009AppB, page = 574 . . . . . . . . . . . . 949 0b, binary indicator . . . . . . . . . . . . . . 914 0h, hexadecimal indicator . . . . . . . . . 914 10^( ), power of ten . . . . . . . . . . . . . . 912 1Symbols #, indirection . . . . . . . . . . . . . . . . 944 ^, power . . . . . . . . . . . . . . . . . . . 944 |, with . . . . . . . . . . .
shortcuts . . . . . . . . . . . . . . . . . . . . 33 switching . . . . . . . . . . . . . . . . . . . 64 Apps desktop calculator Home screen and . . . . 24 categories . . . . . . . . . . . . . . . . 28, 32 clock . . . . . . . . . . . . . . . . . . . . . . . 41 date and time . . . . . . . . . . . . . . . . 43 initial startup . . . . . . . . . . . . . . . . . . 5 mode . . . . . . . . . . . . . . . . . . . 18, 39 parts of . . . . . . . . . . . . . . . . . . . . . . 7 split-screen status . . . . . . . . . . . .
Box Plot . . . . . . . . . . . . . . . . . . . . . . 556 build data, BldData . . . . . . . 439, 596, 791 table, Table . . . . . . . . . . . . . . . . 887 web, Build Web . . . . . . . . . . . . . 363 Build Web, build web . . . . . . . . 363, 365 build web, Build Web . . . . . . . . . . . . 365 BUSY . . . . . . . . . . . . . . . . . . . . . . . . . 39 BUSY indicator . . . . . . . . . . . . . 204, 573 Busy/Pause status . . . . . . . . . . . . . . . 39 C cables . . . . . . . . . .
get/return, Get . . . . . . . . . . . . . . 825 programs . . . . . . . . . . . . . . . . . . 633 send list variable, Send . . . . . . . 869 statistical data . . . . . . . . . . 568, 569 CBR system connecting . . . . . . . . . . . . . . . . . . 68 programs . . . . . . . . . . . . . . . . . . 761 ceiling( ), ceiling . . . . . . . . . . . . . . . . 791 ceiling, ceiling( ) . . . . . . . . . . . . . . . . 749 certificate 724, 731, 732, 733, 734, 735, 736 Certificate revision (Cert. Rev.) . . . .
colNorm( ), matrix column norm . . . . 794 combinations, nCr( ) . . . . . . . . . . . . . 846 comDenom( ), common denominator 795 command mark . . . . . . . . . . . . . . . . . 661 command scripts . . . . . . . 210, 661, 664 activity . . . . . . . . . . . . . . . . . . . . 752 commands Flash Apps . . . . . . . . . . . . . . . . . . 21 Key . . . . . . . . . . . . . . . . . . . . . 10, 12 comment, | . . . . . . . . . . . . . . . 581, 913 common denominator, comDenom( ) 256, . . . . . . . . . . . . . . . . . .
csch/( ),inverse hyperbolic cosecant 800 cSolve( ), complex solve . . . . . . 240, 800 cSolve(†), complex solve . . . . . . . . . 938 cubic regression, CubicReg . . . 546, 945 CubicReg, cubic regression . . .546, 802, 945 cumSum( ), cumulative sum . . . 534, 803 Current folder mode . . . . . . . . . 187, 922 Current folder status . . . . . . . . . . . . . . 38 Current mode . . . . . . . . . . . . . . . . . . . 18 cursor 3D graph . . . . . . . . . . . . . . . . . . 382 deleting characters . . . . . . . . . .
shift, shift( ) . . . . . . . . . . . . . . . . . 875 sorting columns . . . . . . . . . . . . . 535 statistical plots . . . . . . . . . . . . . . 551 values . . . . . . . . . . . . . . . . . 523, 524 data/matrix editor . . . . . . . . . . . . . . . 469 data4mat( ) . . . . . . . . . . . . . . . . . . . . 806 date reset . . . . . . . . . . . . . . . . . . . . . . . 48 setting . . . . . . . . . . . . . . . . . . . . . . 40 dayOfWk( ), day of week . . . . . . . . . 807 DE (differential equation) mode . . . . .
SLPFLD, slope field . . 415, 423, 448 solution methods . . . . 414, 439, 948 third order . . . . . . . . . . . . . . . . . . 431 troubleshooting . . . . . . . . . . . . . . 447 diftol window variable . . . . . . . . . . . . 418 dim( ), dimension . . . . . . . . . . . . . . . 811 dimension, dim( ) . . . . . . . . . . . . . . . 602 direction field, DIRFLD . . . 415, 423, 450 DIRFLD, direction field . . . 415, 423, 450 discontinuities detecting . . . . . . . . . . . . . . . . . . . .
polar, DrawPol . . . . . . 487, 632, 814 slope, DrawSlp . . . . . . 495, 631, 814 tangent line, LineTan . . . . . 632, 837 vertical line, LineVert . . . . . 632, 837 DrawInv, draw inverse . . . 488, 632, 813 DrawParm, draw parametric . . .487, 632, 814 DrawPol, draw polar . . . . . 487, 632, 814 DrawSlp, draw slope . . . . . 495, 631, 814 drop-down menu, DropDown . . . . . . 622 DropDown, drop-down menu . . 622, 814 DrwCtour, draw contour . . 400, 632, 815 dtime window variable . . . . . . . . . . .
Circular definition . . . . . . . . . . . . 595 clear error, ClrErr . . . . . . . . 636, 793 Memory error . . . . . . . . . . . 713, 714 Out-of-memory . . . . . . . . . . . . . . 273 pass error, PassErr . . . . . . 636, 854 programs . . . . . . . . . . . . . . . . . . 635 transmission . . . . . . . . . . . . 724, 735 warnings . . . . . . . . . . . . . . . . . . . 922 Estep window variable . . . . . . . . . . . 418 Euler method . . . . . . . . . . . . . . 414, 439 evaluate polynomial, polyEval( ) . . . .
parametric graphing . . . . . . . 94, 764 path of a ball . . . . . . . . . . . . . . . . . 94 polar rose . . . . . . . . . . . . . . . . . . . 96 pole-corner problem . . . . . . . . . . 741 population . . . . . . . . . . . . . . . . . . 119 predator-prey model . . . . . . 371, 435 prime factors . . . . . . . . . . . . . . . . 73 programming . . . . . . . 128, 130, 637 Pythagorean theorem . . . . . . . . . 741 quadratic formula . . . . . . . . . . . . 743 rational factors . . . . . . . . . . . . . .
eyeφ z-axis window variable . . .378, 387, 388 eyeθ x-axis window variable . . .378, 387, 388 eyeψ rotation window variable .378, 387, 389 F factor( ), factor . . . . . . 75, 745, 773, 820 factor, factor( ) . 75, 240, 256, 259, 745, 773 factorial, ! . . . . . . . . . . . . . . . . . . 74, 907 factoring . . . . . . . . . . . . . . . . . . . . . . 259 activity . . . . . . . . . . . . . . . . . . . . 773 false message . . . . . . . . . . . . . . . . . 275 family of curves . . . . . . . . . . . . . . . . .
2 K . . . . . . . . . . . . . . . . . . . . 17 Apps desktop . . . . . . . . . . . . . . . . 37 changing from split-screen . . . . . . 64 displaying Apps in . . . . . . . . . . . . 64 FUNC (function) mode . . . . . . . . . . . . 38 Func, program function . . . . . . . 587, 824 function keys (,–-) moving among toolbar menus . . . 55 selecting categories . . . . . . . . 28, 31 selecting menus . . . . . . . . . . . . . . 49 functions . . . . . . . . . . . . . . . . . . . 21, 159 delayed simplification . . . . .
getUnits( ), get/return units . . . . 617, 829 global variables . . . . . . . . . . . . . . . . . 600 go to, Goto . . . . . . . . . . . . 593, 609, 616 Goto, go to . . . . . . . . . . . . . . . . . . . . 829 GRAD (gradian) mode . . . . . . . . . . . . 38 GRAD(gradian) mode . . . . . . . . . . . . . 81 Gradian angle mode . . . . . . . . . . . . . . 81 gradian,G . . . . . . . . . . . . . . . . . . . . . 910 graph mode . . . . . . . . . . . . . . . . . . . 18, 38 number mode . . . . . . . . . . . . . . . .
overview . . 302, 340, 347, 354, 375, 410 panning . . . . . . . . . . . . . . . . . . . 323 parametric . . . . . . . . . . . . . . . . . 347 pausing . . . . . . . . . . . . . . . . . . . . 318 pictures . . . . . . . . . . . . . . . . 497, 499 piecewise functions . . . . . . . . . . 475 pixels . . . . . . . . . . . . . . . . . . . . . 941 polar . . . . . . . . . . . . . . . . . . . . . . 340 programs . . . . . . . . . . . . . . . . . . 627 QuickCenter . . . . . . . . . . . . . . . .
highlighting text . . . . . . . . . . . . . . . . . 652 Histogram . . . . . . . . . . . . . . . . . . . . . 557 History area status . . . . . . . . . . . . . . . . . . . . . . 39 history area . . . . . . . . . . . . 207, 208, 664 History indicator . . . . . . . . . . . . . . . . . 27 Home icon . . . . . . . . . . . . . . . . . . . . . 24 Home screen . . . . . . . . . . . . . . . . . . 205 Home screen. See calculator home screen hyperbolic arccosine cosh/( ) . . . . . . . . . . . 798 arcsine, sinh/( ) . . .
inverse cotangent, cot/( ) . . . . . . . . . inverse hyperbolic cosecant, csch/( ) . . . . . . . . . . . cotangent, coth/( ) . . . . . . . . . . . secant, sech/( ) . . . . . . . . . . . . . inverse, x/ . . . . . . . . . . . . . . . . . . . . iPart( ), integer part . . . . . . . . . . . . . . isArchiv() . . . . . . . . . . . . . . . . . . . . . . isArchiv(), is archived . . . . . . . . . . . . isClkOn( ), is clock on . . . . . . . . . . . . isLocked . . . . . . . . . . . . . . . . . . . . . .
LineVert, draw vertical line . . . . 632, 837 Link transmission table . . . . . . . . . . . 740 linking and transmitting . . . . . . . 869, 870 calculator to calculator 633, 716, 718, . . . 719, 721, 727, 728, 730, 731 cancelling . . . . . . . . . . . . . . . . . . 724 errors . . . . . . . . . . . . . 724, 734, 735 Flash applications . . .719, 720, 721, 726, . . . . . . . . . . . . . . . . . . . 727 folders . . . . 719, 720, 722, 723, 724 get/return CBL/CBR value, Get .
loop, Loop . . . . . . . . . . . . . . . . . . . . . 614 LU, matrix lower-upper decomposition . . 842 M mat4data( ) . . . . . . . . . . . . . . . . . . . . 842 mat4list( ), matrix to list . . . . . . . . . . . 843 math category . . . . . . . . . . . . . . . . . . . 31 MATH menu . . . . . . . . . . . . . . . . . . . 331 MATH menu (2 I) . . . . . . . . . . . 49 math operations . . . . . . . . . . . . . 24, 783 matrices augment/concatenate, augment( ) . . 747, . . . . . . . . . . . . . . . . . . .
conversions (2 4) . . . . . . . . . . 16 median( ), median . . . . . . . . . . . . . . . 843 medium-medium line regression, MedMed . . . . . . . . . . . . . . . . . . 547, 844, 946 MedMed, medium-medium line regression . . . . . . . . . . . . . . . . . . 547, 844, 946 memory archiving, Archive 596, 708, 709, 789 checking . . . . . . . . . . . . . . . 689, 690 insufficient display memory, <<...>> . 229 resetting . . . . . . . . . . . . . . . 689, 690 unarchive, Unarchiv . .
3D (three-dimensional) . . . . . . . . . 38 Angle . . . . . . . 18, 38, 187, 305, 923 APPROX . . . . . . . . . . . . . . . . . . . 38 Approximate . . . . 166, 188, 203, 925 Apps desktop . . . . . . . . . . . . . . . . 18 AUTO . . . . . . . . . . . . . . . . . . . . . . 38 Auto . . . . . . 166, 188, 203, 242, 925 Base . . . . . . . . . . . . . . . 18, 188, 926 Complex Format . . . . . . . . . 188, 923 complex format . . . . . . . . . . . . . . . 18 current . . . . . . . . . . . . . . . . . . . . .
mRowAdd( ), matrix row multiplication and addition . . . . . . . . . . . . . . . . . . . . 845 multiply, * . . . . . . . . . . . . . . . . . . . . . 903 multistatement functions . . . . . . . . . . 477 N natural log base, e . . . . . . . . . . . . . . 277 natural logarithm, ln( ) . . . . . . . . . . . . 838 ncontour window variable . . . . . . . . . 379 nCr( ), combinations . . . . . . . . . . . . . 846 ncurves window variable . . . . . . . . . 417 nDeriv( ), numeric derivative . . . 266, 846 negate, M . .
OneVar, one-variable statistic . . . . . 850 operating system . . . . . . . 733, 734, 735 operating system (OS) downloading . . . . . . . . . . . . . . . . . 69 Operating System (OS) version . . . . 234 operating system, upgrading . .731, 732, 733 operators . . . . . . . . . . . . . . . . . . . . . 159 or (Boolean), or . . . . . . . . . . . . . . . . . 685 or, Boolean or . . . . . . . . . . 605, 685, 851 ord( ), numeric character code . 602, 851 Organizr (organizer) category . . . . . . . 32 OS . . . . . .
off, PlotsOff . . . . . . . . 311, 628, 855 on, PlotsOn . . . . . . . . 311, 628, 855 selecting . . . . . . . . . . . . . . . 553, 560 tracing . . . . . . . . . . . . . . . . . . . . 562 viewing window . . . . . . . . . . . . . 561 Y= Editor . . . . . . . . . . . . . . . . . . 559 PlotsOff, plots off . . . . . . . . . . . 311, 855 PlotsOn, plots on . . . . . . . . . . . 311, 855 plotStep window variable . . . . . . . . . 359 plotStrt window variable . . . . . . . . . . 359 point change, PtChg . . . . . . .
comment, | . . . . . . . . . . . . 581, 913 conditional tests . . . . . . . . . . . . . 603 copying . . . . . . . . . . . . . . . . . . . . 579 custom toolbar off, CustmOff . . . 230, 621, . . . . . . . . . . . . . . . . . . . 803 custom toolbar on, CustmOn . . . 230, 621, . . . . . . . . . . . . . . . . . . . 803 debugging . . . . . . . . . . . . . . . . . 636 define dialog box Dialog . . . 621, 811 define toolbar, Custom . . . . 621, 803 define toolbar, Toolbar . . . . 621, 892 define, Define . . .
menus . . . . . . . . . . . . . . . . 622, 626 multicommand lines . . . . . . . . . . 580 operations . . . . . . . . . . . . . . . . . 784 output . . . . . . . . . . . . . 574, 582, 620 output, Output . . . . . . 620, 627, 851 pass error, PassErr . . . . . . 636, 854 passing values . . . . . . . . . . . . . . 584 pause, Pause . . . . . . . 620, 636, 854 popup menu, PopUp . . . . . 619, 856 prompt, Prompt( ) . . . . . . . . 619, 857 request, Request . . . . 620, 622, 865 return, Return . . . . . . .
radian, R . . . . . . . . . . . . . . . . . . . . . . 910 rand( ), random number . . . . . . . . . . 862 randMat( ), random matrix . . . . 747, 863 randNorm( ), random norm . . . . . . . . 863 random matrix, randMat( ) . . . . . . . . 747, 863 norm, randNorm( ) . . . . . . . . . . . 863 number seed, RandSeed . . 747, 863 number, rand( ) . . . . . . . . . . . . . 862 polynomial, randPoly( ) . . . . . . . 863 randPoly( ), random polynomial . . . . 863 RandSeed, random number seed . .
rotate( ), rotate . . . . . . . . . . . . . 686, 866 rotate, rotate( ) . . . . . . . . . . . . . 603, 686 round( ), round . . . . . . . . . . . . . . . . . 867 row echelon form, ref( ) . . . . . . . . . . 864 rowAdd( ), matrix row addition . . . . . 867 rowDim( ), matrix row dimension . . . 867 rowNorm( ), matrix row norm . . . . . . 867 rowSwap( ), matrix row swap . . . . . . 868 RplcPic, replace picture . . . . . . 629, 868 rref( ), reduced row echelon form . . . 262, 747, . . . . . . . . . . . . . . . .
Shade (graph math tool) . . . . . . 332, 337 Shade, shade . . . . . . . . . . . . . . 632, 875 shade, Shade . . . . . . . . . . . . . . . . . . 632 Shift modifier key (7) description . . . . . . . . . . . . . . . . . . 13 status . . . . . . . . . . . . . . . . . . . . . . 38 shift( ), shift . . . . . . . . 533, 603, 687, 875 shift, shift( ) . . . . . . . . . . . . . . . . 603, 687 show statistical results, ShowStat . . 548, 876 ShowStat, show statistical results . . 548, 876 sign( ), sign . . . . . . . . .
status and open Apps . . . . . . . . . . 6 viewing . . . . . . . . . . . . . . . . . . . . . 18 square root, $( ) . . . . . . . . . . . . . . . . 909 standard annuity activity . . . . . . . . . . 769 standard deviation, stdDev( ) . . . . . . 883 start timer, startTmr( ) . . . . . . . . . . . . 882 startTmr( ), start timer . . . . . . . . . . . . 882 statistics . . . . . . . . . . . . . . . . . . 540–571 Box Plot . . . . . . . . . . . . . . . . . . . 556 Calculation Type . . . . . . . . 541, 546 categories .
character code, ord( ) . . . . . . . . . 602 character string, char( ) . . . 602, 792 dimension, dim( ) . . . . . . . . . . . . 602 expression to string, string( ) . . . 603, 884 format, format( ) . 602, 620, 627, 823 indirection, # . . . . . . . . 602, 909, 944 inputting, InputSt . . . . 601, 619, 728 left, left( ) . . . . . . . . . . . . . . 602, 835 mid-string, mid( ) . . . . . . . . 602, 844 operations . . . . . . . . . 600, 602, 785 right, right( ) . . . . . . . . . . . . 603, 866 rotate, rotate( ) . .
tan( ), tangent . . . . . . . . . . . . . . . . . . 887 tan/( ), arctangent . . . . . . . . . . . . . . 888 Tangent (graph math tool) 331, 336, 346, 353 tangent, tan( ) . . . . . . . . . . . . . . . . . . 887 tanh( ), hyperbolic tangent . . . . . . . . 888 tanh/( ), hyperbolic arctangent . . . . . 889 Taylor polynomial, taylor( ) 266, 269, 889 taylor( ), Taylor polynomial . . . . . . . . 889 tblStart, table start . . . . . . . . . . . . . . 456 tCollect( ), trigonometric collection . .
status . . . . . . . . . . . . . . . . . . . . . . 36 tplot window variable . . . . . . . . . . . . 417 Trace, trace . . . 751, 761, 763, 766, 892 trace, Trace 321, 628, 751, 761, 763, 766 tracing 87, 321, 324, 346, 353, 362, 381, 420 transmitting. See linking and transmitting transpose, T . . . . . . . . . . . . . . . . . . . 886 Trig menu . . . . . . . . . . . . . . . . . . . . . 257 trigonometric collection, tCollect( ) . . . . . . . . . . 257 expansion, tExpand( ) . . . . . . . .
V Value (graph math tool) . .331, 332, 353, 382, . . . . . . . . . . . . . . . . . . . . . . 420 variables . . . . . . . . . . . . . . . 39, 197, 199 archiving and unarchiving . 707, 708 archiving, Archive 596, 708, 709, 789 clearing . . . . . . . . . . . . . . . . . . . . 679 copy, CopyVar . . . . . . 596, 703, 796 copying . . . . . . . . . . . . . . . . . . . . 703 data . . . . . . . . . . . . . . . . . . . . . . 517 defined . . . . . . . . . . . . . . . . 235, 671 delayed simplification . . . . . . . .
while, While . . . . . . . . . . . . . . . . . . . 613 Window Editor . . . . . . . . . . . . . . . . . . 58 window variables (x . . . . . . . . . . . . . . . . . . . . . . . . 941 (y . . . . . . . . . . . . . . . . . . . . . . . . 941 diftol . . . . . . . . . . . . . . . . . . . . . . 418 dtime . . . . . . . . . . . . . . . . . . . . . 418 Estep . . . . . . . . . . . . . . . . . . . . . 418 eyeφ (z axis) . . . . . . . . 378, 387, 389 eyeθ (x axis) . . . . . . . . 378, 387, 389 eyeψ (rotation) . . . . . .
ymax window variable . . .313, 344, 359, 379, . . . . . . . . . . . . . . . . . . 417, 941 ymin window variable 313, 344, 351, 359, . . . . . . . . . . . . . . . . . . 379, 417, 941 yscl window variable 314, 344, 352, 359, 417 Z Zero (graph math tool) . . . . . . . 331, zeroes activity . . . . . . . . . . . . . . . . . . . . zeroes, zeroes( ) . . . . . . . . 240, 256, zeroes, zeros( ) . . . . . . . . . . . . . 743, zeros( ), zeroes . . . . . . . . . . . . . 743, zmax window variable . . . . . . . . . . .
