TI-89 TI-92 Plus Guidebook for Advanced Mathematics Software Version 2.0 © 1999-2002 Texas Instruments 00_FRONT.
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TI-89 Shortcut Keys General Alpha Rules ¥O 2a j ¤ List of Flash applications Toggle between last two chosen applications or split screens ¥ |, ¥ « Lighten or darken contrast ¥¸ Calculate approximate answer ¥ C, ¥ D Move cursor to top or bottom (in editors) ¤ C, ¤ D Scroll tall objects in history ¤ A, ¤ B Highlight left or right from cursor 2 C, 2 D Page up or page down (in editors) 2 A, 2 B Move cursor far left or far right On-screen Keyboard Map ( ¥ ^ ) Press N to exit the map.
TI-92 Plus Shortcut Keys General ¥O 2a ¥D Editing List of Flash applications Toggle between last two chosen applications or split screens Copy graph coordinates to sysdata ¥F ¥H ¥N ¥O ¥S ¥ |, ¥ « ¥¸ ¥´ ¥1–¥9 Display FORMATS dialog box Copy graph coordinates to Home screen history Create new variable Open existing variable Save copy as Lighten or darken contrast Calculate approximate answer Turn off unit so that it returns to current application the next time you turn it on Run programs kbdprgm1() throu
Table of Contents This guidebook describes how to use the TI-89 / TI-92 Plus. The table of contents can help you locate "getting started" information as well as detailed information about the TI-89 / TI-92 Plus features. Appendix A provides one convenient location to find details about every TI-89 / TI-92 Plus function and instruction. Flash Applications...................................................................................... x Keystroke Differences ............................................
Chapter 3: Symbolic Manipulation Preview of Symbolic Manipulation ........................................................ 58 Using Undefined or Defined Variables .................................................. 59 Using Exact, Approximate, and Auto Modes ....................................... 61 Automatic Simplification......................................................................... 64 Delayed Simplification for Certain Built-In Functions........................
Chapter 8: Polar Graphing Preview of Polar Graphing.................................................................... 134 Overview of Steps in Graphing Polar Equations................................ 135 Differences in Polar and Function Graphing...................................... 136 Chapter 9: Sequence Graphing Preview of Sequence Graphing ............................................................ 140 Overview of Steps in Graphing Sequences .........................................
Chapter 12: Additional Graphing Topics Preview of Additional Graphing Topics .............................................. 202 Collecting Data Points from a Graph................................................... 203 Graphing a Function Defined on the Home Screen........................... 204 Graphing a Piecewise Defined Function............................................. 206 Graphing a Family of Curves ................................................................ 208 Using the Two-Graph Mode .....
Chapter 17: Programming Preview of Programming....................................................................... 276 Running an Existing Program............................................................... 278 Starting a Program Editor Session....................................................... 280 Overview of Entering a Program.......................................................... 282 Overview of Entering a Function.........................................................
Chapter 21: Memory and Variable Management Preview of Memory and Variable Management ................................. 350 Checking and Resetting Memory ......................................................... 353 Displaying the VAR-LINK Screen ......................................................... 355 Manipulating Variables and Folders with VAR-LINK ........................ 357 Pasting a Variable Name to an Application ........................................ 359 Archiving and Unarchiving a Variable..
Appendix B: Reference Information TI-89 / TI-92 Plus Error Messages ....................................................... 542 Modes....................................................................................................... 550 TI-89 / TI-92 Plus Character Codes ..................................................... 555 TI.89 Key Codes ..................................................................................... 556 TI.92 Plus Key Codes...................................................
Flash Applications Applications Flash functionality enables the ability to download different applications to a TI-89 / TI-92 Plus calculator from the enclosed CD-ROM, the TI web site, or from another calculator. Before downloading new applications to a TI-89 / TI-92 Plus, please read and accept the license agreement on the TI-89 / TI-92 Plus Applications CD-ROM. Hardware/Software Requirements Before installing Flash applications, you will need: • A computer with a CD-ROM drive and a serial port.
Transferring a Flash Application from another TI-89 / TI-92 Plus Note: This guidebook uses TI-89 screen shots. Backing up a Flash Application Note: For further information about transmitting applications to and from your computer using TI Connect, refer to the TI Connect online help. Do not attempt to transfer an application if a low-battery message appears on either the receiving or sending calculator. 1.
Keystroke Differences There are certain differences in keystrokes using the TI-89 / TI-92 Plus for various operations. The following table shows the keystrokes for major commands for the two calculators. › TI-92 Plus ³ TI-89 FUNCTION LETTERS One lowercase letter (a-s, u, v, w) j A-S, U-W A-S, U-W One lowercase letter (t, x, y, z) T, X, Y, Z T, X, Y, Z Several lowercase letters 2™ End several lowercase letters j Several uppercase letters ¤™ 2¢ End several uppercase letters j 2 ¢.
› TI-92 Plus ³ TI-89 FUNCTION SYMBOLS ú (Conversion triangle) 2 2 _ (Underscore) ¥ 2 θ (Theta) ¥Ï Ï | (“With”) Í 2Í ' (Prime) 2È 2È ° (Degree) 2v 2v ∠ (Angle) 2’ 2’ Σ (Sigma) ½Σ( 2> xê (Reciprocal) ½ ^-1 2V Space j Space bar Place data in sysdata variable ¥b ¥D Greek characters ¥ c j or ¥ c ¤ ¥ G or ¥G ¤ Keyboard map ¥^ ¥” 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)
What’s New? Introducing Advanced Mathematics Software Version 2.0 TI developed the Advanced Mathematics Software Version 2.0 to enable downloadable calculator software applications for the TI-89 and TI-92 Plus. For details, refer to: Chapter 21 and 22 Advanced Mathematics Software Version 2.0 is an infrastructure enhancement of the current Advanced Mathematics Software Version 1.xx. It has all the features of Version 1.xx.
Upgradability with Flash ROM The TI-89 / TI-92 Plus uses Flash technology, which lets you upgrade future software versions without buying a new calculator. For details, refer to: Chapter 22 As new functionality becomes available, you can electronically upgrade your TI-89 / TI-92 Plus. Future software versions include maintenance upgrades that will be released free of charge, as well as new applications and major future upgrades that will be available for purchase from the TI web site.
Chapter 1: Getting Started 1 Getting the TI.89 Ready to Use ................................................................ 2 Getting the TI.92 Plus Ready to Use........................................................ 3 Setting the Contrast and Selecting a Language...................................... 4 Performing Computations......................................................................... 8 Graphing a Function ................................................................................
Getting the TI-89 Ready to Use The TI-89 comes with four AAA batteries. This chapter describes how to install these batteries. It also describes how to turn the unit on for the first time, set the display contrast, select a language, and view the Home screen for both the TI-89 and the TI-92 Plus. Installing the AAA Batteries To install the four AAA batteries: 1. Place the TI-89 face down on a soft cloth to prevent scratching the display face. 2.
Getting the TI-92 Plus Ready to Use The TI-92 Plus comes with four AA batteries. This chapter describes how to install these batteries. It also describes how to turn the unit on for the first time, set the display contrast, select a language, and view the Home screen for both the TI-92 Plus and the TI-89. Installing the AA Batteries Important: When replacing batteries in the future, ensure that the TI-92 Plus is turned off by pressing 2 ®. To install the four AA alkaline batteries: 1.
Setting the Contrast and Selecting a Language Turning the Unit on and Adjusting the Display Contrast After you install the batteries in your TI-89 / TI-92 Plus, press ´. It is possible that the display contrast may be too dark or too dim to see anything. To adjust the display to your satisfaction, hold down ¥ (diamond symbol inside a green border) and momentarily press | (minus key) to lighten the display. Hold down ¥ and momentarily press « (plus key) to darken the display.
Localizing the TI-89 / TI-92 Plus 1. Press the cursor keys (D or C) to move the pointer to the language in which you would like to set your TI-89 / TI-92 Plus. (The list of languages on your calculator may vary from this example.) Note: Until you complete the localization process, the Select a Language dialog box will reappear when you turn the unit on. 2. Press ¸ to set the TI-89 / TI-92 Plus into the selected language. (Pressing N halts the localization process and displays the Home screen.) 3.
About the Home Screen After you select a language, a blank Home screen is displayed. The Home screen lets you execute instructions, evaluate expressions, and view results. The following example contains previously entered data and describes the main parts of the 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.
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. Last Entry "Pretty print" is ON. Exponents, roots, fractions, etc., are displayed in the same form in which they are traditionally written.
Performing Computations This section provides several examples for you to perform that demonstrate some of the computational features of the TI-89 / TI-92 Plus. 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. Steps ³ TI.89 Keystrokes › TI.92 Plus Keystrokes Display Showing Computations 1. Compute sin(p/4) and display the 2 W 2 T result in symbolic and numeric e4d¸ format.
Steps ³ TI.89 Keystrokes › TI.92 Plus Keystrokes Display Expanding Expressions 1. Expand the expression (xì 5) 3. You can enter “expand” on the entry line by typing EXPAND on the keyboard, or by pressing „ and selecting 3:expand(. „3 cX|5dZ3 d ¸ „3 cX|5dZ3 d ¸ 2. (Optional) Enter other expressions on your own. Reducing Expressions 1. Reduce the expression (x 2ì 2xì 5)/(xì 1) to its simplest form.
Steps ³ TI.89 Keystrokes › TI.92 Plus Keystrokes „1 XZ2|2X|6 Á2bXd ÍX 2Ã0 ¸ „1 XZ2|2X|6 Á2bXd 2ÍX 2Ã0 ¸ 2=cX|Y dZ3ecX« YdZ2bXd ¸ 2=cX|Y dZ3ecX« YdZ2bXd ¸ Display Solving Equations with a Domain Constraint 1. Solve the equation x 2ì 2xì 6=2 with respect to x where x is greater than zero. The “with” (I) operator provides domain constraint. TI.89: Í TI.92 Plus: 2 Í Finding the Derivative of Functions 1. Find the derivative of (xì y)3/(x+y) 2 with respect to x.
Graphing a Function The example in this section demonstrates some of the graphing capabilities of the TI-89 / TI-92 Plus. It illustrates how to graph a function using the Y= Editor. You will 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 / TI-92 Plus by graphing the function y=(|x 2ì 3|ì 10)/2. Steps 1. Display the Y= Editor. ³ TI.
Steps 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. 7. Set the upper bound. ³ TI.89 Keystrokes › TI.92 Plus Keystrokes B. . . B ¸ B...B ¸ B. . . B B...B ¸ ¸ Display Press B (right cursor) to move the tracing cursor until the upper bound for x is just to the right of the minimum node. 8. Find the minimum point on the graph between the lower and upper bounds.
Chapter 2: Operating the Calculator 2 Turning the TI.89 / TI.92 Plus On and Off ............................................ 14 Setting the Display Contrast ................................................................... 15 The TI.89 Keyboard ................................................................................. 16 The TI.92 Plus Keyboard......................................................................... 17 Modifier Keys.................................................................
Turning the TI-89 / TI-92 Plus On and Off You can turn the TI-89 / TI-92 Plus on and off manually by using the ´ and 2 ® (or ¥ ® ) keys. To prolong battery life, the APDé (Automatic Power Downé) feature lets the TI-89 / TI-92 Plus turn itself off automatically. Turning the TI-89 / TI-92 Plus On Turning the TI-89 / TI-92 Plus Off Note: ® is the second function of the ´ key. Press ´. ¦ If you turned the unit off by pressing 2 ®, the TI-89 / TI-92 Plus returns to the Home screen.
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 TI-89 / TI-92 Plus is turned off. Adjusting the Display Contrast You can adjust the display contrast to suit your viewing angle and lighting conditions.
The TI-89 Keyboard Use this section to familiarize yourself with the various keys on the TI-89 keyboard. Most keys can perform two or more functions, depending on whether you first press a modifier key. Overview of Some Important Keys ƒ through 2 Š function keys let you select toolbar menus. Used with ¥, you can also select applications (page 39). N cancels a menu or dialog box. A, B, C, and D move the cursor. 2, ¥, ¤, and j modify the action of other keys (page 18).
The TI-92 Plus Keyboard With the TI-92 Plus’s easy-to-hold shape and keyboard layout, you can quickly access any area of the keyboard even when you are holding the unit with two hands. Keyboard Areas The keyboard is divided into several areas of related keys. Cursor Pad Moves the display cursor in up to 8 directions, depending on the application. Function Keys Access the toolbar menus displayed across the top of the screen.
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) ¥ (diamond) ¤ (shift) Note: For information about using ¤ and j, refer to “Entering Alphabetic Characters” on page 21. j (TI-89 only) ‚ (hand) (TI-92 Plus only) Examples of 2 and ¥ Modifiers Activates keys that select certain applications (page 39), menu items, and other operations from the keyboard.
Some keys perform only one additional operation, which may require either 2 or ¥, 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, ¥ 5 accesses CUT , which is the same color as the ¥ key. When you press a modifier such as 2 or ¥, a 2ND or 2 indicator appears in the status line at the bottom of the display. If you press a modifier by accident, press it again (or press N ) to cancel its effect.
Important Keys (continued) Key Description TI.89: Enters the “with” operator, which is used in symbolic calculations (Chapter 3). Í TI.92 Plus: 2Í 2 <, 2= Performs integrations and derivatives (Chapter 3). 2’ Designates an angle in polar, cylindrical, and spherical coordinates. 2I Displays the MATH menu. 2¯ Displays the MEMORY screen (Chapter 21). 2 ° Displays the VAR-LINK screen for managing variables and Flash applications (Chapter 21). 2£ Recalls the contents of a variable (page 48).
Entering Alphabetic Characters Alphabetic characters are used in expressions such as xñ+yñ, to enter variable names (page 47), and in the Text Editor (Chapter 18). Entering a Letter Character on the TI-89 The letters x, y, z, and t are commonly used in algebraic expressions. So that you can type them quickly, these letters are primary keys on the TI-89 keyboard. X Y Z T Other letters are available as the j function of another key, similar to the 2 and ¥ modifiers described in the previous section.
Typing Alphabetic Characters … (continued) Automatic AlphaLock in TI-89 Dialog Boxes Note: To type a number, press j to turn alphalock off. Press j or 2 ™ to resume typing letters. On the TI-89, 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 alpha-lock off. After you type the character, alphalock remains on.
Home Screen When you first turn on your TI-89 / TI-92 Plus, the Home screen is displayed. The Home screen lets you execute instructions, evaluate expressions, and view results. Displaying the Home Screen When you turn on the TI-89 / TI-92 Plus after it has been turned off with 2 ®, the display always shows the Home screen. (If the TI-89 / TI-92 Plus turned itself off through APDé, the display shows the previous screen, which may or may not have been the Home screen.
Scrolling through the History Area Note: For an example of viewing a long answer, refer to page 28. History Information on the Status Line Normally, the cursor is in the entry line. However, you can move the cursor into the history area. To: Do this: View entries or answers that have scrolled off the screen 1. From the entry line, press C to highlight the last answer. 2. Continue using C to move the cursor from answer to entry, up through the history area.
Entering Numbers The keypad lets you enter positive and negative numbers for your calculations. You can also enter numbers in scientific notation. Entering a Negative Number 1. Press the negation key ·. (Do not use the subtraction key |.) 2. Type the number. To see how the TI-89 / TI-92 Plus evaluates a negation in relation to other functions, refer to the Equation Operating System (EOSé) hierarchy in Appendix B. For example, it is important to know that functions such as xñ are evaluated before negation.
Entering Expressions and Instructions You perform a calculation by evaluating an expression. You initiate an action by executing the appropriate instruction. Expressions are calculated and results are displayed according to the mode settings described on page 29. Definitions Expression Consists of numbers, variables, operators, functions, and their arguments that evaluate to a single answer. For example: prñ +3. ¦ Enter an expression in the same order that it normally is written.
Parentheses Expressions are evaluated according to the Equation Operating System (EOSé) hierarchy described in Appendix B. To change the order of evaluation or just to ensure that an expression is evaluated in the order you require, use parentheses. Calculations inside a pair of parentheses are completed first. For example, in 4(1+2), EOS first evaluates (1+2) and then multiplies the answer by 4. Entering an Expression Type the expression, and then press ¸ to evaluate it.
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. If an entry or answer is too long to fit on one line, ú is displayed at the end of the line. To view the entire entry or answer: 1. Press C to move the cursor from the entry line up into the history area. This highlights the last answer. 2. As necessary, use C and D to highlight the entry or answer you want to view.
Formats of Displayed Results A result may be calculated and displayed in any of several formats. This section describes the TI-89 / TI-92 Plus modes and their settings that affect the display formats. To check or change your current mode settings, refer to page 40. 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.
Exact/Approx (continued) APPROXIMATE — All numeric results, where possible, are displayed in floating-point (decimal) form. Fractional results are evaluated numerically. Note: Results are rounded to the precision of the TI-89 / TI-92 Plus and displayed according to current mode settings. 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, prñ = 3.14159⋅rñ.
Display Digits Mode By default, Display Digits = FLOAT 6, which means that results are rounded to a maximum of six digits. You can use 3 to select different settings. The settings apply to all exponential formats. Internally, the TI-89 / TI-92 Plus calculates and retains all decimal results with up to 14 significant digits (although a maximum of 12 are displayed). Setting Example FIX (0 – 12) 123. 123.5 123.46 123.457 FLOAT 123.456789012 Number of decimal places varies, depending on the result.
Editing an Expression in the Entry Line Knowing how to edit an entry can be a real time-saver. If you make an error while typing an expression, it’s often easier to correct the mistake than to retype the entire expression. Removing the Highlight from the Previous Entry After you press ¸ to evaluate an expression, the TI-89 / TI-92 Plus leaves that expression on the entry line and highlights it.
Inserting or Overtyping a Character The TI-89 / TI-92 Plus has both an insert and an overtype mode. By default, the TI-89 / TI-92 Plus is in the insert mode. To toggle between the insert and overtype modes, press 2 /. If the TI.89 / TI.92 Plus is in: The next character you type: Will be inserted at the cursor. Tip: Look at the cursor to see if you’re in insert or overtype mode. Thin cursor between characters Will replace the highlighted character.
Menus To leave the keyboard uncluttered, the TI-89 / TI-92 Plus uses menus to access many operations. This section gives an overview of how to select an item from any menu. Specific menus are described in the appropriate chapters of this guidebook. 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 APPLICATIONS menu — Lets you select from a list of applications.
Items Ending with ú (Submenus) If you select a menu item ending with ú, a submenu is displayed. You then select an item from the submenu. Note: Because of limited screen size, the TI-89 overlaps these menus as: For example, List displays a submenu that lets you select a specific List function. ï indicates that you can 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. Items Containing “. . .
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.
Using the Custom Menu The TI-89 / TI-92 Plus has a custom menu that you can turn on and off at any time. You can use the default custom menu or create your own as described in Chapter 17: Programming. 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 Home screen’s normal toolbar menu, press 2 ¾ to toggle the custom menu on and off.
Selecting an Application The TI-89 / TI-92 Plus has different applications that let you solve and explore a variety of problems. You can select an application from a menu, or you can access commonly used applications directly from the keyboard. From the 1. Press O to display a menu that lists the applications. APPLICATIONS Menu 2. Select an application. Either: ¦ Note: To cancel the menu without making a selection, press N.
From the Keyboard You can access commonly used applications from the keyboard. On the TI-89 for example, ¥ # is the same as pressing ¥ and then ƒ. This guidebook uses the notation ¥ #, similar to the notation used in second functions. TI-89 Application: Press: Home TI.89: " TI.92 Plus: ¹ " Y= Editor ¥# Applications listed above ƒ, „ etc., are printed in the same color as ¥.
Setting Modes Modes control how numbers and graphs are displayed and interpreted. Mode settings are retained by the Constant Memoryé feature when the TI-89 / TI-92 Plus is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings. Checking Mode Settings Press 3 to display the MODE dialog box, which lists the modes and their current settings. There are three pages of mode listings. Press ƒ, „, or … to quickly display a particular page.
Overview of the Modes Note: For detailed information about a particular mode, look in the applicable section of this guidebook. Mode Description Graph Type of graphs to plot: FUNCTION, PARAMETRIC, POLAR, SEQUENCE, 3D, or DE. Folder used to store and recall variables. Unless you have created additional folders, only the MAIN folder is available. Refer to “Using Folders to Store Independent Sets of Variables” in Chapter 5.
Modes (continued) Mode Description Base Lets you perform calculations by entering numbers in decimal (DEC), hexadecimal (HEX), or binary (BIN) form. 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. Lets you select custom defaults. The mode is dimmed until you select Unit System, 3:CUSTOM.
Using the Clean Up Menu to Start a New Problem On the Home screen, the Clean Up toolbar menu lets you start a new calculation from a cleared state without resetting the TI-89 / TI-92 Plus’s memory. Clean Up Toolbar Menu From the Home screen, display the Clean Up menu by pressing: TI.89: 2 ˆ TI.92 Plus: ˆ Menu Item Description Clear a–z Clears (deletes) all single-character variable names in the current folder, unless the variables are locked or archived.
Using the Catalog Dialog Box The CATALOG provides a way to access any built-in TI-89 / TI-92 Plus command (functions and instructions) from one convenient list. In addition, the CATALOG dialog box lets you select functions used in Flash applications or user-defined functions (if any have been loaded or defined). Displaying the CATALOG To display the CATALOG dialog box, press: TI.89: ½ TI.
3. Move the ú indicator to the command, and press ¸. To move the ú indicator: Tip: From the top of the list, press C to move to the bottom. From the bottom, press D to move to the top. Information about Parameters Press or type: One command at a time D or C One page at a time 2 D or 2 C To the first command that begins with a specified letter The letter key. (On the TI-89, do not press j first. If you do, you need to press j or 2 ™ again before you can type a letter.
3. Move the ú indicator to the function, and press ¸. Selecting a User-Defined Function or Program To move the ú indicator: Press or type: One function 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, do not press j first. If you do, you need to press j or 2 ™ again before you can type a letter.) You can create your own functions or programs and then use † User-Defined to access them.
Storing and Recalling Variable Values When you store a value, you store it as a named variable. You can then use the name instead of the value in expressions. When the TI-89 / TI-92 Plus encounters the name in an expression, it substitutes the variable’s stored value. Rules for Variable Names A variable name: ¦ Can use 1 to 8 characters consisting of letters and digits. This includes Greek letters (but not p), accented letters, and international letters. Do not include spaces.
Storing a Value in a Variable 1. Enter the value you want to store, which can be an expression. Note: TI-89 users should use j as necessary when typing variable names. 3. Type the variable name. 2. Press §. The store symbol (! ) is displayed. 4. Press ¸. To store to a variable temporarily, you can use the “with” operator. Refer to “Substituting Values and Setting Constraints” in Chapter 3. Displaying a Variable 1. Type the variable name. 2. Press ¸ .
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 / TI-92 Plus leaves that expression on the entry line and highlights it. You can type over the entry, or you can reuse it as necessary.
Tip: Editing an entry lets you make minor changes without retyping the entire entry. Using the equation A=pr 2, use trial and error to find the radius of a circle that covers 200 square centimeters. 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 7.95 and continue until the answer is as accurate as you want. On the TI.89: On the TI.
Recalling the Last Answer Each time you evaluate an expression, the TI-89 / TI-92 Plus 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 4.2 ¸ 2. Find the yield. 147 e 2 ± ¸ Note: Refer to ans() in Appendix A.
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 ² and 2 ± as described in the previous section, but there are differences.
Status Line Indicators in the Display The status line is displayed at the bottom of all application screens. It shows information about the current state of the TI-89 / TI-92 Plus, including several important mode settings. Status Line Indicators Current Folder Modifier Key Angle Mode Exact/Approx Mode Note: To cancel 2, ¥, j, or ¤, press the same key again or press a different modifier key.
Status Line (continued) Indicator Meaning Exact/ Approx Mode Shows how answers are calculated and displayed. Refer to page 29. 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 — GR1 or GR2. (Displays G#1 or G#2 on the TI-92 Plus.) Graph Mode Indicates the type of graphs that can be plotted. To change the Graph mode, use the 3 key.
Finding the Software Version and ID Number In some situations, you may need to find out information about your TI-89 / TI-92 Plus, particularly the software version and the unit’s ID number. Displaying the “About” Screen From the Home screen, press ƒ and then select A:About. Your screen will be different than the one shown to the right. Press ¸ or N to close the screen.
56 Chapter 2: Operating the Calculator 02OPER.
Chapter 3: Symbolic Manipulation 3 Preview of Symbolic Manipulation ........................................................ 58 Using Undefined or Defined Variables .................................................. 59 Using Exact, Approximate, and Auto Modes ....................................... 61 Automatic Simplification......................................................................... 64 Delayed Simplification for Certain Built-In Functions........................
Preview of Symbolic Manipulation Solve the system of equations 2x ì 3y = 4 and ë x + 7y = ë 12. Solve the first equation so that x is expressed in terms of y. Substitute the expression for x into the second 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 ³ TI.89 Keystrokes › TI.92 Plus Keystrokes " MM „1 2X|3YÁ4 bXd¸ ¥" MM „1 2X|3YÁ4 bXd¸ 2. Begin to solve the equation ë x + 7y = ë 12 for y, but do not press ¸ yet.
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 Tip: 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.
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 Chapter 21. 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 Chapter 5.
Using Exact, Approximate, and Auto Modes The Exact/Approx mode settings, which are described briefly in Chapter 2, directly affect the precision and accuracy with which the TI-89 / TI-92 Plus calculates a result. This section describes these mode settings as they relate to symbolic manipulation. EXACT Setting When Exact/Approx = EXACT, the TI-89 / TI-92 Plus uses exact rational arithmetic with up to 614 digits in the numerator and 614 digits in the denominator.
APPROXIMATE Setting When Exact/Approx = APPROXIMATE, the TI-89 / TI-92 Plus converts rational numbers and irrational constants to floating-point. However, there are exceptions: ¦ Certain built-in functions that expect one of their arguments to be an integer will convert that number to an integer if possible. For example: d(y(x), x, 2.0) transforms to d(y(x), x, 2). ¦ Whole-number floating-point exponents are converted to integers. For example: x 2.0 transforms to x 2 even in the APPROXIMATE setting.
AUTO Setting When Exact/Approx = AUTO, the TI-89 / TI-92 Plus uses exact rational arithmetic wherever all of the operands are rational numbers. Otherwise, floating-point arithmetic is used after 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.
Automatic Simplification When you type an expression on the entry line and press ¸, the TI-89 / TI-92 Plus 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.
¦ Identities involving zeros and ones are exploited. ¦ Polynomial greatest common divisors are canceled. ¦ Polynomials are expanded unless no key cancellation can occur. This floating-point number causes numeric results to be shown as floating-point. If a floating-point whole number is entered as an exponent, it is treated as an integer (and does not produce a floating-point result). No key cancellation ¦ Common denominators are formed unless no key cancellation can occur.
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.
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: TI.89: Í TI.92 Plus: 2 Í Substituting for a Variable For every occurrence of a specified variable, you can substitute a numeric value or an expression. First derivative of xìò at x = 5 To substitute for multiple variables at the same time, use the Boolean and operator.
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.
Specifying Domain Constraints Many identities and transformations are valid for only a particular domain. For example: ln(xù y) = ln(x) + ln(y) only if x and/or y is not negative sinê (sin(q)) = q only if q ‚ ë p/2 and q p/2 radians Use the “with” operator to specify the domain constraint. Because ln(x ù y) = ln(x) + ln(y) is not always valid, the logarithms are not combined. Tip: Enter ln(xù y) instead of ln(xy); otherwise, xy is interpreted as a single variable named xy.
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 Appendix A. 70 Menu Item Description solve Solves an expression for a specified variable.
Menu Item Description Trig Displays the submenu: Complex 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. 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.
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 Appendix A. Some algebraic operations do not require a special function. Adding or Dividing Polynomials You can add or divide polynomials directly, without using a special function. Factoring and Expanding Polynomials Use the factor ( „ 2) and expand ( „ 3) functions.
Solving an Equation Use the solve ( „ 1) function to solve an equation for a specified variable. solve(equation, var) Solve x + y ì 5 = 2x ì 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 Note: An operation such as | 2 Ù subtracts 2x from both sides.
Finding the Zeros of an Expression Use the zeros ( „ 4) function. Tip: For ‚ or , type ¥ Ã or ¥ Â.You can also use 2 I 8 or 2 ¿ 2 to select them from a menu. Use the expression x ù sin(x) + cos(x). Finding Proper Fractions and Common Denominators zeros(expression, var) Find the zeros with respect to x in the interval 0 x and x 3. Use the “with” operator to specify the interval. Use the propFrac ( „ 7) and comDenom ( „ 6) functions.
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 Appendix A. 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 Appendix A. Integrating and Differentiating Use the ‰ integrate ( … 2) and d differentiate ( … 1) functions. ‰ (expression, var [,low] [,up]) lets you specify limits or a constant of integration d (expression, var [,order]) Note: You can integrate an expression only; you can differentiate an expression, list, or matrix.
User-Defined Functions and Symbolic Manipulation You can use a user-defined function as an argument for the TI-89 / TI-92 Plus’s built-in algebra and calculus functions. For Information about Creating a User-Defined Function Refer to: ¦ “Creating and Evaluating User-Defined Functions” in Chapter 5. ¦ “Graphing a Function Defined on the Home Screen” and “Graphing a Piecewise Defined Function” in Chapter 12. ¦ “Overview of Entering a Function” in Chapter 17.
Multi-Statement vs. Single-Statement Functions Tip: You can use your computer keyboard to type lengthy text and then use TI-GRAPH LINK to send it to the TI-89 / TI 92-Plus. See Chapter 18 for more information. Multi-statement user-defined functions should be used as an argument for numeric functions (such as nDeriv and nInt) only. In some cases, you may be able to create an equivalent singlestatement function. For example, consider a piecewise function with two pieces.
If You Get an Out-of-Memory Error The TI-89 / TI-92 Plus stores intermediate results in memory and then deletes them when the calculation is complete. Depending on the complexity of the calculation, the TI-89 / TI-92 Plus may run out of memory before a result can be calculated. Freeing Up Memory ¦ Delete unneeded variables and/or Flash applications, particularly large-sized ones. − Use 2 ° as described in Chapter 21 to view and delete variables and/or Flash applications.
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. x=x is true for any value of x. true, false These indicate the result of an identity or a Boolean expression. 5<3 is false. @n1 ... @n255 For @, press: TI.89: ¥ § TI.92 Plus: 2 R ˆ, e This notation indicates an “arbitrary integer” that represents any integer.
Chapter 4: Constants and Measurement Units 4 Preview of Constants and Measurement Units .................................... 82 Entering Constants or Units ................................................................... 83 Converting from One Unit to Another................................................... 85 Setting the Default Units for Displayed Results .................................. 87 Creating Your Own User-Defined Units ................................................
Preview of Constants and Measurement Units Using the equation f = mù a, calculate the force when m = 5 kilograms and a = 20 meters/secondñ. What is the force when a = 9.8 meters/secondñ. (This is the acceleration due to gravity, which is a constant named _g). Convert the result from newtons to kilograms of force. Steps ³ TI-89 Keystrokes 3…B1 1. Display the MODE dialog box, ¸ Page 3. For Unit System mode, select SI for the metric system of measurements.
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: TI.89: 2 À TI.92 Plus: ¥ 9 Tip: Use 2 D and 2 C to scroll one page at a time through the categories.
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. Tip: Create a user-defined unit (page 88) for frequently used combinations. You can enter meters per second by combining _m and _s from the Length and Time categories, respectively.
Converting from One Unit to Another You can convert from one unit to another in the same category, including any user-defined units (page 88). 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 (page 87).
To enter meters per second squared: 27_m/_s^2 To convert meters per second squared from seconds to hours: 27_m/_s^2 41/_hr^2 For Temperature Values To convert a temperature value, you must use tmpCnv() instead of the 4 operator. tmpCnv(expression_¡tempUnit1, _¡tempUnit2) For ¡, press 2 “. For example, to convert 100_¡C to _¡F: tmpCnv(100_¡c, _¡f) 0 100 32 212 _oC _oF For Temperature Ranges For @, press: TI.89: ¥ c ¤ [D] TI.
Setting the Default Units for Displayed Results All results involving units are displayed in the default unit for that category. For example, if the default unit for Length is _m, any length result is displayed in meters (even if you entered _km or _ft in the calculation). 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 builtin default units, which you cannot change. To find the default units for these systems, refer to page 89.
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. Why Use Your Own Units? Some example reasons to create a unit are: ¦ You want to enter length values in dekameters. Define 10_m as a new unit named _dm. Note: If you create a userdefined unit for an existing category, you can select it from the UNITS dialog box menu.
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.
Volume _cup........ cup _floz........ fluid ounce _flozUK .. British fluid ounce _gal ......... gallon _galUK.... British gallon _l ............. liter _ml ..........milliliter _pt ...........pint _qt ...........quart _tbsp .......tablespoon _tsp .........teaspoon NONE (SI) (ENG/US) Time _day ........ day _hr........... hour _min........ minute _ms ......... millisecond _ns .......... nanosecond _s.............second (SI) (ENG/US) _week .....week _yr ...........year _ms ..........
Pressure _atm........ atmosphere _bar......... bar _inH2O ... inches of water _inHg ...... inches of mercury _mmH2O.. millimeters of water Viscosity, Kinematic _St........... stokes Viscosity, Dynamic _P ............ poise Frequency _GHz....... gigahertz _Hz.......... hertz (SI) (ENG/US) _kHz........kilohertz _MHz ......megahertz Electric Current _A............ ampere (SI) (ENG/US) _kA ......... kiloampere _mA ........ milliampere _mA..........microampere Charge _coul.......
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Chapter 5: Additional Home Screen Topics 5 Saving the Home Screen Entries as a Text Editor Script ................... 94 Cutting, Copying, and Pasting Information .......................................... 95 Creating and Evaluating User-Defined Functions ............................... 97 Using Folders to Store Independent Sets of Variables ..................... 100 If an Entry or Answer Is “Too Big” ......................................................
Saving the Home Screen Entries as a Text Editor Script To save all the entries in the history area, you can save the Home screen to a text variable. When you want to reexecute those entries, use the Text Editor to open the variable as a command script. Saving the Entries in the History Area From the Home screen: Note: Only the entries are saved, not the answers. 2. Specify a folder and text variable that you want to use to store the entries. Note: For information about folders, refer to page 100. 1.
Cutting, Copying, and Pasting Information Cut, copy, and paste operations let you move or copy information within the same application or between different applications. These operations use the TI-89 / TI-92 Plus’s clipboard, which is an area in memory that serves as a temporary storage location. Auto-paste vs. Cut/Copy/Paste Auto-paste, described in Chapter 2, is a quick way to copy an entry or answer in the history area and paste it to the entry line. 1.
Pasting Information from the Clipboard A paste operation inserts the contents of the clipboard at the current cursor location on the entry line. This does not change the contents of the clipboard. 1. Position the cursor where you want to paste the information. 2. Press ƒ and select 6:Paste, or use the key shortcut: TI.89: ¥ 7 TI.92 Plus: ¥ V Example: Copying and Pasting Suppose you want to reuse an expression without retyping it each time. 1. Copy the applicable information. a.
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 / TI-92 Plus’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.
Creating a MultiStatement Function Note: For information about similarities and differences between functions and programs, refer to Chapter 17. 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. For example, suppose you want to create a function that sums a series of reciprocals based on an entered integer (n): 1 1 1 + + ...
Displaying and Editing a Function Definition To: Do this: Display a list of all user-defined functions Press 2 ° to display the VAR-LINK screen. You may need to use the „ View toolbar menu to specify the Function variable type. (Refer to Chapter 21.) — or — Press: TI.89: ½ † TI.92 Plus: 2 ½ † Note: You can view a userdefined function in the CATALOG dialog box, but you cannot use the CATALOG to view or edit its definition.
Using Folders to Store Independent Sets of Variables The TI-89 / TI-92 Plus has one built-in folder named MAIN, and all variables are stored in that folder. By creating additional folders, you can store independent sets of user-defined variables (including user-defined functions). Folders and Variables Folders give you a convenient way to manage variables by organizing them into related groups.
Creating a Folder from the Home Screen Enter the NewFold command. Creating a Folder from the VAR-LINK Screen The VAR-LINK screen, which is described in Chapter 21, lists the existing variables and folders. NewFold folderName Folder name to create. This new folder is set automatically as the current folder. 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.
Using Variables in Different Folders You can access a user-defined variable or function that is not in the current folder. Specify the complete pathname instead of only the variable name. A pathname has the form: folderName \ variableName — or — folderName \ functionName For example: If Current Folder = MAIN Note: This example assumes that you have already created a folder named MATH.
If an Entry or Answer Is “Too Big” In some cases, an entry or answer may be “too long” and/or “too tall” to be displayed completely in the history area. In other cases, the TI-89 / TI-92 Plus may not be able to display an answer because there is not enough free memory. 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.
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Chapter 6: Basic Function Graphing 6 Preview of Basic Function Graphing................................................... 106 Overview of Steps in Graphing Functions .......................................... 107 Setting the Graph Mode......................................................................... 108 Defining Functions for Graphing ......................................................... 109 Selecting Functions to Graph ...............................................................
Preview of Basic Function Graphing 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. ³ TI-89 Keystrokes Steps › TI-92 Plus Keystrokes 1. Display the MODE dialog box. For Graph mode, select FUNCTION. 3 B1 ¸ 3 B1 ¸ 2. Display the Home screen. Then store the radius, 5, in variable r. " 5§jR ¸ ¥" 5§R ¸ 3. Display and clear the Y= Editor.
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 Set Graph mode (3) to FUNCTION . Also set Angle mode, if necessary. Define functions on Y= Editor (¥ #). Tip: To turn off any stat data plots (Chapter 16), press ‡ 5 or use † to deselect them. Select (†) which defined functions to graph.
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 / TI-92 Plus 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 Chapter 2. Note: For graphs that do not use complex numbers, set Complex Format = REAL.
Defining Functions for Graphing In FUNCTION graphing mode, you can graph functions named y1(x) through y99(x). To define and edit these functions, use the Y= Editor. (The Y= Editor lists function names for the current graphing mode. For example, in POLAR graphing mode, function names are r1(q), r2(q), etc.) Defining a New Function 1. Press ¥ # or O 2 to display the Y= Editor. Plots — You can scroll above y1= to see a list of stat plots. See Chapter 16.
Clearing a Function Note: ƒ 8 does not erase any stat plots (Chapter 16). 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 ¸. You don’t have to clear a function to prevent it from being graphed.
Selecting Functions to Graph Regardless of how many functions are defined in the Y= Editor, you can select the ones you want to graph. Press ¥ # or O 2 to display the Y= Editor. Selecting or Deselecting Functions A “Ÿ” indicates which functions will be graphed the next time you display the Graph screen. If PLOT numbers are displayed, those stat plots are selected. Selected Deselected In this example, Plots 1 and 2 are selected. To view them, scroll above y1=.
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. Displaying or Changing a Function’s Style From the Y= Editor: 1. Move the cursor to highlight the applicable function. 2. Select the Style menu: TI.89: Press 2 ˆ. TI.92 Plus: Press ˆ.
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. Displaying Window Variables in the Window Editor Press ¥ $ or O 3 to display the Window Editor.
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. Displaying Graph Format Settings From the Y= Editor, Window Editor, or Graph screen, press ƒ and select 9:Format. Tip: You also can display the GRAPH FORMATS dialog box from the Y= Editor, Window Editor, or Graph screen. Press: TI.89: ¥ Í TI.
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 ¥ % or O 4. The TI-89 / TI-92 Plus automatically graphs the selected functions. Note: If you select an „ Zoom operation from the Y= Editor or Window Editor, the TI-89 / TI-92 Plus automatically displays the Graph screen. BUSY indicator shows while graphing is in progress.
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.
Tracing a Function To display the exact coordinates of any plotted point on a graphed function, use the … Trace tool. Unlike the freemoving 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.
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. 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. There is a slight pause while the new portion of the graph is drawn.
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. Note: If you select a Zoom tool from the Y=Editor or Window Editor, the TI-89 / TI-92 Plus automatically displays the Graph screen.
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) Tip: To move the cursor in larger increments, use 2 B, 2 D, etc. The cursor changes to a small square, and the screen prompts for 2nd Corner? 3. Move the cursor to the opposite corner of the zoom box. As you move the cursor, the box stretches. Tip: You can cancel ZoomBox by pressing N before you press ¸.
Changing Zoom Factors The Zoom factors define the magnification and reduction used by ZoomIn and ZoomOut. 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. Tip: 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.
Using Math Tools to Analyze Functions On the Graph screen, the ‡ Math toolbar menu has several tools that help you analyze graphed functions. 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.). Note: For Math results, cursor coordinates are stored in system variables xc and yc (rc and qc if you use polar coordinates).
Finding y(x) at a Specified Point 1. From the Graph screen, press ‡ and select 1:Value. 2. Type the x value, which must be a real value between xmin and xmax. The value can be an expression. y1(x)=1.25xùcos(x) 3. Press ¸. Tip: You can also display function coordinates by tracing the function ( …), typing an x value, and pressing ¸. The cursor moves to that x value on the first function selected in the Y= Editor, and its coordinates are displayed. 4.
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 ¸. The derivative at that point is displayed. Finding the Numerical Integral over an Interval Tip: Typing x values is a quick way to set the limits. 1. From the Graph screen, press ‡ and select 7:‰f(x)dx. 2.
Finding the Distance between Two Points 1. From the Graph screen, press ‡ and select 9:Distance. 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 ¸.
Shading the Area between a Function and the X Axis You must have only one function graphed. If you graph two or more functions, the Shade tool shades the area between two functions. 1. From the Graph screen, press ‡ and select C:Shade. The screen prompts for Above X axis? 2. Select one of the following. To shade the function’s area: ¦ ¦ Above the x axis, press ¸. Below the x axis, press: TI.89: j [N] TI.
Chapter 7: Parametric Graphing 7 Preview of Parametric Graphing.......................................................... 128 Overview of Steps in Graphing Parametric Equations ..................... 129 Differences in Parametric and Function Graphing ........................... 130 This chapter describes how to graph parametric equations on the TI-89 / TI-92 Plus. Before using this chapter, you should be familiar with Chapter 6: Basic Function Graphing.
Preview of 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? ³ TI-89 Keystrokes Steps › TI-92 Plus Keystrokes 1. Display the MODE dialog box. For Graph mode, select PARAMETRIC. 3 B2 ¸ 3 B2 ¸ 2. Display and clear the Y= Editor.
Overview of Steps in Graphing Parametric Equations To graph parametric equations, use the same general steps used for y(x) functions as described in Chapter 6: Basic Function Graphing. Any differences that apply to parametric equations are described on the following pages. Graphing Parametric Equations Set Graph mode (3) to PARAMETRIC . Also set Angle mode, if necessary. Define x and y components on Y= Editor (¥ #). Select (†) which defined equations to graph. Select the x or y component, or both.
Differences in Parametric and Function Graphing This chapter assumes that you already know how to graph y(x) functions as described in Chapter 6: Basic Function Graphing. This section describes the differences that apply to parametric equations. Setting the Graph Mode Use 3 to set Graph = PARAMETRIC 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.
Selecting Parametric Equations To graph a parametric equation, select either its x or y component or both. When you enter or edit a component, it is selected automatically. Selecting x and y components separately can be useful for tables as described in Chapter 13. With multiple parametric equations, you can select and compare all the x components or all the y components. Selecting the Display Style You can set the style for either the x or y component.
Exploring a Graph As in function graphing, you can explore a graph by using the following tools. Tool For Parametric Graphs: Free-Moving Works just as it does for function graphs. Cursor „ Zoom Tip: During a trace, you can also evaluate x(t) and y(t) by typing the t value and pressing ¸. … Trace Tip: You can use QuickCenter at any time during a trace, even if the cursor is still on the screen.
Chapter 8: Polar Graphing 8 Preview of Polar Graphing.................................................................... 134 Overview of Steps in Graphing Polar Equations................................ 135 Differences in Polar and Function Graphing...................................... 136 This chapter describes how to graph polar equations on the TI-89 / TI-92 Plus. Before using this chapter, you should be familiar with Chapter 6: Basic Function Graphing. Consider a point (x,y) as shown below.
Preview of Polar Graphing The graph of the polar equation 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 ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 1. Display the MODE dialog box. For Graph mode, select POLAR. For Angle mode, select RADIAN. 3 B3 DDDB1 ¸ 3 B3 DDDB1 ¸ 2. Display and clear the Y= Editor. Then define the polar equation r1(q) = A sin Bq. ¥# ƒ8¸ ¸ 82W2.5 ¥Ïd¸ ¥# ƒ8¸ ¸ 8W2.
Overview of Steps in Graphing Polar Equations To graph polar equations, use the same general steps used for y(x) functions as described in Chapter 6: Basic Function Graphing. Any differences that apply to polar equations are described on the following pages. Graphing Polar Equations Set Graph mode (3) to POLAR . Also set Angle mode, if necessary. Define polar equations on Y= Editor (¥ #). Tip: To turn off any stat data plots (Chapter 16), press ‡ 5 or use † to deselect them.
Differences in Polar and Function Graphing This chapter assumes that you already know how to graph y(x) functions as described in Chapter 6: Basic Function Graphing. This section describes the differences that apply to polar equations. Setting the Graph Mode Use 3 to set Graph = POLAR 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.
Window Variables Note: You can use a negative qstep. If so, qmin must be greater than qmax. The Window Editor maintains an independent set of Window variables for each Graph mode setting (just as the Y= Editor maintains independent function lists). Polar graphs use the following Window variables. Variable Description qmin, qmax Smallest and largest q values to evaluate. qstep Increment for the q value. Polar equations are evaluated at: r(qmin) r(qmin+qstep) r(qmin+2(qstep)) ... not to exceed ...
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: Free-Moving Works just as it does for function graphs. Cursor „ Zoom Tip: During a trace, you can also evaluate r(q) by typing the q value and pressing ¸. … Trace Tip: You can use QuickCenter at any time during a trace, even if the cursor is still on the screen.
Chapter 9: Sequence Graphing 9 Preview of Sequence Graphing ............................................................ 140 Overview of Steps in Graphing Sequences ......................................... 141 Differences in Sequence and Function Graphing .............................. 142 Setting Axes for Time, Web, or Custom Plots .................................... 146 Using Web Plots...................................................................................... 147 Using Custom Plots.........
Preview of 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. Does it stabilize at a certain number? Initially After 1 Year 4000 .8 x 4000 + 1000 After 2 Years After 3 Years ... .8 x (.8 x 4000 + 1000) .8 x (.8 x (.8 x 4000 + 1000) + 1000) + 1000 + 1000 Steps ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 1.
Overview of Steps in Graphing Sequences To graph sequences, use the same general steps used for y(x) functions as described in Chapter 6: Basic Function Graphing. Any differences are described on the following pages. Graphing Sequences Set Graph mode (3) to SEQUENCE . Also set Angle mode, if necessary. Define sequences and, if needed, initial values on Y= Editor (¥ #). Select (†) which defined sequences to graph. Do not select initial values.
Differences in Sequence and Function Graphing This chapter assumes that you already know how to graph y(x) functions as described in Chapter 6: 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.
Selecting Sequences With TIME and WEB axes, the TI-89 / TI-92 Plus 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 (Continued) Standard values (set when you select 6:ZoomStd from the „ Zoom toolbar menu) are: nmin = 1. nmax = 10. plotStrt = 1. plotStep = 1. xmin = ë 10. xmax = 10. xscl = 1. ymin = ë 10. 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 a graph, look at the following examples of a recursive sequence. This graph is plotted beginning with the 1st term.
Exploring a Graph As in function graphing, you can explore a graph by using the following tools. Any displayed coordinates are shown in rectangular or polar form as set in the graph format. Tool For Sequence Graphs: Free-Moving Works just as it does for function graphs. Cursor „ Zoom Tip: During a trace, you can evaluate a sequence by typing a value for n and pressing ¸. … Trace Works just as it does for function graphs.
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 chapter. Displaying the AXES Dialog Box From the Y= Editor, Axes: ¦ Depending on the current Axes setting, some items may be dimmed. ¦ To exit without making any changes, press N. Item Description Axes TIME — Plots u(n) on the y axis and n on the x axis. WEB — Plots u(n) on the y axis and u(n-1) on the x axis.
Using Web Plots A web plot graphs u(n) vs. u(nì 1), 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. Valid Functions for Web Plots When You Display the Graph Screen A sequence must meet the following criteria; otherwise, it will not be graphed properly on WEB axes. The sequence: ¦ Must be recursive with only one recursion level; u(nì 1) but not u(nì 2). ¦ Cannot reference n directly.
Example: Convergence 1. On the Y= Editor ( ¥ # ), define u1(n) = ë.8u1(nì 1) + 3.6. Set initial value ui1 = ë 4. 2. Set Axes = TIME. 3. On the Window Editor ( ¥ $ ), set the Window variables. 4. Graph the sequence ( ¥ %). nmin=1. nmax=25. plotstrt=1. plotstep=1. xmin=0. ymin= ë 10. xmax=25. ymax=10. xscl=1. yscl=1. u(n) n By default, a sequence uses the Square display style. 5. On the Y= Editor, set Axes = WEB and Build Web = AUTO. 6. On the Window Editor, change nmin=1. nmax=25. the Window variables.
5. On the Y= Editor, set Axes = WEB and Build Web = AUTO. 6. On the Window Editor, change nmin=0. nmax=10. the Window variables. plotStrt=1. xmin= ë 10. ymin= ë 10. xmax=10. ymax=10. xscl=1. yscl=1. plotStep=1. u(n) 7. Regraph the sequence. The web plot shows how quickly the sequence diverges to large negative values. Example: Oscillation u(nì1) y=x y=3.2xì.8xñ This example shows how the initial value can affect a sequence. 1.
Using Custom Plots CUSTOM axes give you great flexibility in graphing sequences. As shown in the following example, CUSTOM axes are particularly effective for showing relationships between one sequence and another. Example: PredatorPrey Model Using the predator-prey model in biology, determine the numbers of rabbits and foxes that maintain population equilibrium in a certain region. R M K W G D = = = = = = Number of rabbits Growth rate of rabbits if there are no foxes (use .
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 Chapter 13 for detailed information about tables. 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 ( ¥ # ), define the sequence and set the initial values as shown. You must enter {1,1}, although {1 1} is shown in the sequence list.
152 Chapter 9: Sequence Graphing 09SEQUEN.
Chapter 10: 3D Graphing 10 Preview of 3D Graphing ........................................................................ 154 Overview of Steps in Graphing 3D Equations .................................... 156 Differences in 3D and Function Graphing .......................................... 157 Moving the Cursor in 3D ....................................................................... 160 Rotating and/or Elevating the Viewing Angle.....................................
Preview of 3D Graphing Graph the 3D equation z(x,y) = (xò y ì yò x) / 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 ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 1. Display the MODE dialog box. For Graph mode, select 3D. 3 B5 ¸ 3 B5 ¸ 2. Display and clear the Y= Editor. Then define the 3D equation z1(x,y) = (xò y ì yò x) / 390.
³ TI-89 Keystrokes Steps › TI-92 Plus Keystrokes Display 0 (zero, not the 0 (zero, not the 6. Return the graph to its initial letter O) letter O) orientation. Then move the AAA viewing angle along the “viewing A A A orbit” around the graph. For information about the viewing orbit, refer to page 164. X X Y Y Z Z 8. Return to the initial orientation. 0 0 9. Display the graph in different graph format styles.
Overview of Steps in Graphing 3D Equations To graph 3D equations, use the same general steps used for y(x) functions as described in Chapter 6: Basic Function Graphing. Any differences that apply to 3D equations are described on the following pages. Graphing 3D Equations Set Graph mode (3) to 3D. Also set Angle mode, if necessary. Define 3D equations on Y= Editor (¥ #). Tip: To turn off any stat data plots (Chapter 16), press ‡ 5 or use † to deselect them. Select (†) which equation to graph.
Differences in 3D and Function Graphing This chapter assumes that you already know how to graph y(x) functions as described in Chapter 6: 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.
Window Variables Note: If you enter a fractional number for xgrid or ygrid, it is rounded to the nearest whole number ‚ 1. The Window Editor maintains an independent set of Window variables for each Graph mode setting (just as the Y= Editor maintains independent function lists). 3D graphs use the following Window variables. Variable Description eyeq, eyef, eyeψ Angles (always in degrees) used to view the graph. Refer to “Rotating and/or Elevating the Viewing Angle” on page 162.
Setting the Graph Format The Axes and Style formats are specific to the 3D graphing mode. Refer to “Changing the Axes and Style Formats” on page 165. Exploring a Graph As in function graphing, you can explore a graph by using the following tools. Any displayed coordinates are shown in rectangular or cylindrical form as set in the graph format.
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. 3D graphs have two independent variables (x,y) instead of one, and the x and y axes have a different orientation than other graphing modes. How to Move the Cursor On a 3D surface, the cursor always follows along a grid wire. Cursor Key Note: You can move the cursor only within the x and y boundaries set by Window variables xmin, xmax, ymin, and ymax.
Example of the Cursor on a Hidden Surface On more complex shapes, the cursor may appear as if it is not on a grid point. This is an optical illusion caused when the cursor is on a hidden surface. For example, consider a saddle shape z1(x,y) = (xñ ì yñ ) / 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). Tip: To cut away the front of the saddle in this example, set xmax=0 to show only negative x values.
Rotating and/or Elevating the Viewing Angle In 3D graphing mode, the eyeq and eyef Window variables let you set viewing angles that determine your line of sight. The eyeψ Window variable lets you rotate the graph around that line of sight. How the Viewing Angle Is Measured Z The viewing angle has three components: ¦ eyeq — angle in degrees from the positive x axis. ¦ eyef — angle in degrees from the positive z axis. eyef eyeψ X Note: When eyeψ=0, the z axis is vertical on the screen.
Effect of Changing eyef 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 Note: This example starts on the xy plane (eyef = 90) and decrements eyef by 20 to elevate the viewing angle. In this example, eyeq = 20 eyef = 90 eyef = 70 eyef = 50 Effect of Changing eyeψ Note: During rotation, the axes expand or contract to fit the screen’s width and height.
Animating a 3D Graph Interactively After plotting any 3D graph, you can change the viewing angle interactively by using the cursor. Refer to the preview example on page 154. The Viewing Orbit When using A and B to animate a graph, think of it as moving the viewing angle along its “viewing orbit” around the graph. Note: The viewing orbit affects the eye Window variables in differing amounts.
Changing the Axes and Style Formats With its default settings, the TI-89 / TI-92 Plus displays hidden surfaces on a 3D graph but does not display the axes. However, you can change the graph format at any time. Displaying the From the Y= Editor, Window Editor, or Graph screen, press: GRAPH FORMATS ƒ9 — or — TI-89: ¥ Í TI-92 Plus: ¥ F Dialog Box ¦ The dialog box shows the current graph format settings. ¦ To exit without making a change, press N.
Examples of Style Settings To display the valid Style settings, highlight the current setting and press B. ¦ Tip: WIRE FRAME is faster to graph and may be more convenient when you’re experimenting with different shapes. WIRE FRAME — Shows the 3D shape as a transparent wire frame. ¦ HIDDEN SURFACES — Uses shading to differentiate the two sides of the 3D shape. Later sections in this chapter describe CONTOUR LEVELS, WIRE AND CONTOUR (page 167) and IMPLICIT PLOT (page 171).
Contour Plots In a contour plot, a line is drawn to connect adjacent points on the 3D graph that have the same z value. This section discusses the CONTOUR LEVELS and WIRE AND CONTOUR graph format styles. 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.
How Are Z Values Determined? You can set the ncontour Window variable ( ¥ $ ) to specify the number of contours that will be evenly distributed along the displayed range of z values, where: zmax ì 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. If ncontour=5 and you use the standard viewing window (zmin=ë 10 and zmax=10) , the increment is 3.333.
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: Tip: To remove the default contours, use ¥ $ and set ncontour=0. DrwCtour 5 Draws a contour for z=5. DrwCtour {1,2,3} Draws contours for z=1, 2, and 3.
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). Example In this example, let f(x)=x 3+1. By substituting the general complex form x+yi for x, you can express the complex surface equation as z(x,y)=abs((x+yù i)3+1). 1. Use 3 to set Graph=3D. 2. Press ¥ #, and define the equation: z1(x,y)=abs((x+yù i)^3+1) 3. Press ¥ $, and set the Window variables as shown. 4.
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. Explicit and Implicit Forms In 2D function graphing mode, equations have an explicit form y=f(x), where y is unique for each value of x. Many equations, however, have an implicit form f(x,y)=g(x,y), where you cannot explicitly solve for y in terms of x or for x in terms of y.
¦ 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. Style 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.
Example: Implicit Plot of a More Complicated Equation You can use the IMPLICIT PLOT graph format style to plot and animate a complicated equation that cannot be graphed otherwise. Although it may take a long time to evaluate such a graph, the visual results can justify the time required. Example Graph the equation sin(x 4+yìx 3 y) = .1. 1. Use 3 to set Graph=3D. 2. Press ¥ #, and define the equation: z1(x,y)=sin(x^4+yì x^3y)ì.1 3. Press ¥ $, and set the Window variables as shown. 4.
174 Chapter 10: 3D Graphing 10_3D.
Chapter 11: Differential Equation Graphing 11 Preview of Differential Equation Graphing ........................................ 176 Overview of Steps in Graphing Differential Equations..................... 178 Differences in Diff Equations and Function Graphing...................... 179 Setting the Initial Conditions ................................................................ 184 Defining a System for Higher-Order Equations ................................. 186 Example of a 2nd-Order Equation ......
Preview of Differential Equation Graphing Graph the solution to the logistic 1st-order differential equation y' = .001yù (100ì y). Start by drawing only the slope field. Then enter initial conditions in the Y= Editor and interactively from the Graph screen. Steps ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 1. Display the MODE dialog box. For Graph mode, select DIFF EQUATIONS. 3 B6 ¸ 3 B6 ¸ 2. Display and clear the Y= Editor. Then define the 1st-order differential equation: ¥# ƒ8¸ ¸.
Steps 6. Return to the Y= Editor and enter an initial condition: yi1=10 7. Return to the Graph screen. ³ TI-89 Keystrokes › TI-92 Plus Keystrokes ¥# ¸10 ¸ ¥# ¸10 ¸ ¥% ¥% Display Initial conditions entered in the Y= Editor always occur at t0. The graph begins at the initial condition and plots to the right. Then it plots to the left. The initial condition is marked with a circle. ¥#C ¸2[ 10b202\ ¸ ¥#C ¸2[ 10b202\ ¸ 9. Return to the Graph screen. ¥% ¥% 10.
Overview of Steps in Graphing Differential Equations To graph differential equations, use the same general steps used for y(x) functions as described in Chapter 6: Basic Function Graphing. Any differences are described on the following pages. Graphing Differential Equations Set Graph mode (3) to DIFF EQUATIONS . Also set Angle mode, if necessary. Define equations and, optionally, initial conditions on Y= Editor (¥ #). Tip: To turn off any stat data plots, press ‡ 5 or use † to deselect them.
Differences in Diff Equations and Function Graphing This chapter assumes that you already know how to graph y(x) functions as described in Chapter 6: 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.
Setting Graph Formats From the Y= Editor, Window Editor, or Graph screen, press: ƒ9 — or — TI-89: ¥ Í TI-92 Plus: ¥ F The formats affected by differential equations are: Graph format Description Graph Order Not available. Solution Method Specifies the method used to solve the differential equations. ¦ RK — Runge-Kutta method. For information about the algorithm used for this method, refer to Appendix B. ¦ EULER — Euler method. The method lets you choose either greater accuracy or speed.
Setting Axes In the Y= Editor, Axes may or may not be available, depending on the current graph format. If it is available, you can select the axes that are used to graph the differential equations. For more information, refer to page 190. TI-89: 2 ‰ TI-92 Plus: ‰ Window Variables Note: If tmax < t0, tstep must be negative. 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 (Continued) xmin, xmax, ymin, ymax Boundaries of the viewing window. xscl, yscl Distance between tick marks on the x and y axes. ncurves Number of solution curves (0 through 10) that will be drawn automatically if you do not specify an initial condition. By default, ncurves = 0.
The fldpic System Variable When a slope or direction field is drawn, a picture of the field is stored automatically to a system variable named fldpic. If you perform an operation that regraphs the plotted equations but does not affect the field, the TI-89 / TI-92 Plus reuses the picture in fldpic instead of having to redraw the field. This can speed up the regraphing time significantly.
Setting the Initial Conditions You can enter initial conditions in the Y= Editor, let the TI-89 / TI-92 Plus 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.
Selecting an Initial Condition Interactively from the Graph Screen Note: With SLPFLD or DIRFLD, you can select initial conditions interactively regardless of whether you enter initial conditions in the Y= Editor. 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 1. Press: TI-89: 2 Š TI-92 Plus: Š 2. Specify an initial condition.
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 n th-order equation, you must transform it into a system of n 1st-order equations. Transforming an Equation into a 1stOrder System Note: To produce a 1storder equation, the right side must contain nonderivative variables only. A system of equations can be defined in various ways, but the following is a general method. y'' + y' + y = e x 1.
Example of a 2nd-Order Equation The 2nd-order differential equation y''+y = 0 represents a simple harmonic oscillator. Transform this into a system of equations for the Y= Editor. Then, graph the solution for initial conditions y(0) = 0 and y'(0) = 1. Example 1. Press 3 and set Graph=DIFF EQUATIONS. 2. Define a system of equations for the 2nd-order equation as described on page 186. Rewrite the equation and make the necessary substitutions. Note: t0 is the time at which the initial conditions occur.
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). Note: To display different graphs in both parts of a split screen, you must use the 2-graph mode. 9. Press 3 and change the mode settings on Page 2 as shown. Then close the MODE dialog box, which redraws the graph. 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.
Example of a 3rd-Order Equation For the 3rd-order differential equation y'''+2y''+2y'+y = sin(x), write a system of equations to enter in the Y= Editor. Then graph the solution as a function of time. Use initial conditions y(0) = 0, y'(0) = 1, and y''(0) = 1. Example 1. Press 3 and set Graph=DIFF EQUATIONS. 2. Define a system of equations for the 3rd-order equation as described on page 186. Rewrite the equation and make the necessary substitutions.
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: TI-89: 2 ‰ TI-92 Plus: ‰ If Fields = SLPFLD, Axes is unavailable. TI-89: 2 ‰ TI-92 Plus: ‰ Item Description Axes TIME — Plots t on the x axis and y (solutions to all selected differential equations) on the y axis.
Example of Time and Custom Axes Using the predator-prey model from biology, determine the numbers of rabbits and foxes that maintain population equilibrium in a certain region. Graph the solution using both time and custom axes. Predator-Prey Model Use the two coupled 1st-order differential equations: y1' = ë y1 + 0.1y1 ù y2 and y2' = 3y2 ì y1 ù y2 where: y1 yi1 y2 yi2 = = = = Population of foxes Initial population of foxes (2) Population of rabbits Initial population of rabbits (5) 1.
Note: In this example, DIRFLD is used for two related differential equations that do not represent a 2ndorder equation. 8. Return to the Y= Editor. Press: ƒ9 — or — TI-89: ¥ Í TI-92 Plus: ¥ F Set Fields = DIRFLD. 9. Press: TI-89: 2 ‰ TI-92 Plus: ‰ 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. Tip: Use a list to specify more than one initial condition. 12.
Example Comparison of RK and Euler Consider a logistic growth model dP/dt = .001ù Pù (100ì P), with the initial condition P(0) = 10. Use the BldData instruction to compare the graphing points calculated by the RK and Euler solution methods. Then plot those points along with a graph of the equation’s exact solution. Example 1. Press 3 and set Graph=DIFF EQUATIONS. 2. Express the 1st-order equation in terms of y1' and y1. y1'=.
9. Return to the Home screen, and use BldData to create a data variable containing the Euler graphing points. Note: errorlog lets you combine the data in rklog and eulerlog so that you can view the two sets of data side by side. 10. Use the Data/Matrix Editor ( O 6 3 ) to create a new data variable named errorlog. Note: rklog[1] and rklog[2] refer to column 1 and 2 in rklog, respectively. Likewise with eulerlog[2]. 11.
16. In the Window Editor, set the Window variables. Note: The fuzzy line on the graph indicates differences between the RK and Euler values. xmin=ë 10. ymin=ë 10. xres=2. xmax=100. ymax=120. xscl=10. yscl=10. 17. Display the Graph screen ( ¥ % ). 18. In the Window Editor, set the Window variables to zoom in so that you can examine the differences in more detail. xmin=39.7 ymin=85.5 xmax=40.3 ymax=86. xscl=.1 yscl=.1 xres=2. Euler (Plot 2) 19. Return to the Graph screen. RK (Plot 1) 20.
Example of the deSolve( ) Function The deSolve() function lets you solve many 1st- and 2ndorder ordinary differential equations exactly. Example For a general solution, use the following syntax. For a particular solution, refer to Appendix A. deSolve(1stOr2ndOrderODE, independentVar, dependentVar) Using the logistic 1st-order differential equation from the example on page 176, find the general solution for y with respect to t. Tip: For maximum accuracy, use 1/1000 instead of .001.
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.
Fields=DIRFLD In the Y= Editor Enter a valid system of two 1st-order equations. For information about defining a valid system for a 2ndorder equation, refer to page 186. Set Axes = CUSTOM: TI-89: 2 ‰ TI-92 Plus: ‰ 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.
Fields=FLDOFF In the Y= Editor If you enter a 2nd- or higher-order equation, enter it as a valid system of equations as described on page 186. All equations (selected or not) must have the same number of initial conditions. Otherwise, a Dimension error occurs when you graph. To set Axes = TIME or CUSTOM, press: TI-89: 2 ‰ TI-92 Plus: ‰ 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).
200 Chapter 11: Differential Equation Graphing 11DIFFEQ.
Chapter 12: Additional Graphing Topics 12 Preview of Additional Graphing Topics .............................................. 202 Collecting Data Points from a Graph................................................... 203 Graphing a Function Defined on the Home Screen........................... 204 Graphing a Piecewise Defined Function............................................. 206 Graphing a Family of Curves ................................................................ 208 Using the Two-Graph Mode .
Preview of Additional Graphing Topics From the Home screen, graph the piecewise defined function: y = ìx 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 ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 1. Display the MODE dialog box. For Graph mode, select FUNCTION. For Angle mode, select RADIAN. 3 B1 DDD B1 ¸ 3 B1 DDD B1 ¸ 2. Display the Home screen.
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.
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. What Is the “Native” Independent Variable? On the Y= Editor, all functions must be defined in terms of the current graph mode’s “native” independent variable.
Graphing Directly from the Home Screen Tip: Graph is available from the Home screen’s † toolbar menu. Note: Graph uses the current Window variable settings. Tip: To create a table from the Home screen, use the Table command. It is similar to Graph. Both share the same expressions. The Graph command lets you graph an expression from the Home screen without using the Y= Editor.
Graphing a Piecewise Defined Function To graph a piecewise function, you must first define the function by specifying boundaries and expressions for each piece. The when function is extremely useful for two-piece functions. For three or more pieces, it may be easier to create a multi-statement, user-defined function. Using the When Function To define a two-piece function, use the syntax: Tip: Graph math results may vary. For example, suppose you want to graph a function with two pieces.
Using a MultiStatement, UserDefined 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 < ìp 4 sin(x) x ‚ ìp and x < 0 2x + 6 x‚0 6 ìxñ Note: For information about similarities and differences between functions and programs, refer to Chapter 17. A multi-statement, user-defined function can have many of the control and decision-making structures (If, ElseIf, Return, etc.
Graphing a Family of Curves By entering a list in an expression, you can plot a separate function for each value in the list. (You cannot graph a family of curves in SEQUENCE or 3D graphing mode.) Examples Using the Y= Editor Enter the expression {2,4,6} sin(x) and graph the functions. Tip: Graph math results may vary. Tip: Enclose list elements in braces (2 [ and 2 \) and separate them with commas.
Using the Two-Graph Mode In two-graph mode, the TI-89 / TI-92 Plus’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 Chapter 14. 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.
Independent GraphRelated Features Note: The Y= Editor is completely independent only when the two sides use different graphing modes (as described below). Both Graph 1 and Graph 2 have independent: ¦ Graph modes (FUNCTION, POLAR, etc.). Other modes such as Angle, Display Digits, etc., are shared and affect both graphs. ¦ Window Editor variables. ¦ Table setup parameters and Table screens. ¦ Graph formats such as Coordinates, Axes, etc. ¦ Graph screens. ¦ Y= Editors.
Using a Split Screen Note: You can display nongraph-related applications (such as the Home screen) on only one side at a time. For more complete information about split screens, refer to Chapter 14. ¦ To switch from one graph side to the other, press 2 a (second function of O). ¦ To display different applications: − Switch to the applicable graph side and display the application as you normally would. — or — − Use 3 to change Split 1 App and/or Split 2 App.
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. You cannot draw a function or equation interactively from the Graph screen.
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. (Some objects are not available for 3D graphs.) Clearing All Drawings A drawn object is not part of the graph itself. It is drawn “on top of” the graph and remains on the screen until you clear it. From the Graph screen: Tip: You can also enter ClrDraw on the Home screen’s entry line.
Erasing Individual Parts of a Drawing Object From the Graph screen: 1. TI-89: 2 ‰ TI-92 Plus: ‰ and select 2:Eraser. The cursor is shown as a small box. 2. Move the cursor to the applicable location. Note: These techniques also erase parts of graphed functions. To erase: Do this: Area under the box Press ¸. Along a freehand line TI-89: Press and hold ¤, and move the cursor to erase the line. TI-92 Plus: Press and hold ‚, and move the cursor to erase the line. To quit, release ¤ or ‚.
Drawing a Horizontal or Vertical Line From the Graph screen: 1. TI-89: 2 ‰ TI-92 Plus: ‰ 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. Tip: Use 2 to move the cursor in larger increments; 2 B, etc. 2. Use the cursor pad to move the line to the appropriate position. Then press ¸.
Typing Text Labels From the Graph screen: 1. TI-89: 2 ‰ TI-92 Plus: ‰ and select 7:Text. Tip: The text cursor indicates the upper-left corner of the next character you type. 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. From the Home Screen or a Program ¦ To continue, move the cursor to another location. ¦ To quit, press ¸ or N.
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.
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. Note: If a variable name is not shown on the dialog box, there are no graph pictures in the folder. 2. Select the type (Picture), folder, and variable that contain the graph picture you want to open. 3. Press ¸.
Animating a Series of Graph Pictures As described earlier in this chapter, you can save a picture of a graph. By using the CyclePic command, you can flip through a series of graph pictures to create an animation. CyclePic Command Before using CyclePic, you must have a series of graph pictures that have the same base name and are sequentially numbered starting with 1 (such as pic1, pic2, pic3, . . . ).
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. Elements in a Graph Database A graph database consists of: ¦ Mode settings (3) for Graph, Angle, Complex Format, and Split Screen (only if you are using the two-graph mode). Note: In two-graph mode, the elements for both graphs are saved in a single database.
Chapter 13: Tables 13 Preview of Tables................................................................................... 222 Overview of Steps in Generating a Table............................................ 223 Setting Up the Table Parameters ......................................................... 224 Displaying an Automatic Table ............................................................ 226 Building a Manual (Ask) Table .............................................................
Preview of Tables Evaluate the function y=x 3ì 2x at each integer between ë 10 and 10. How many sign changes are there, and where do they occur? Steps ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 1. Display the MODE dialog box. For the Graph mode, select FUNCTION. 3 B1 ¸ 3 B1 ¸ 2. Display and clear the Y= Editor. Then define y1(x) = x 3 – 2x. ¥# ƒ8¸ ¸ XZ3|2X ¸ ¥# ƒ8¸ ¸ XZ3|2X ¸ 3.
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 Set Graph mode and, if necessary, Angle mode (3). Note: Tables are not available in 3D Graph mode. Define functions on Y= Editor (¥ #). Tip: For information on defining and selecting functions with the Y= Editor, refer to Chapter 6.
Setting Up the Table Parameters To set up the initial parameters for a table, use the TABLE SETUP dialog box. After the table is displayed, you can also use this dialog box to change the parameters. Displaying the TABLE SETUP To display the TABLE SETUP dialog box, press ¥ &. From the Table screen, you can also press „. Dialog Box Setup Parameter Description Note: The table initially starts at tblStart, but you can use C to scroll to prior values.
Which Setup Parameters to Use To generate: tblStart @tbl Graph < - > Table Independent value value OFF AUTO — — ON AUTO — — — ASK An automatic table ¦ Based on initial values ¦ That matches Graph screen A manual table “—” means that any value entered for this parameter is ignored for the indicated type of table. In SEQUENCE graphing mode (Chapter 9), use integers for tblStart and @tbl. Changing the Setup Parameters From the TABLE SETUP dialog box: 1.
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. Before You Begin Define and select the applicable functions on the Y= Editor (¥ #). This example uses y1(x) = xò ì x/3. Then enter the initial table parameters (¥ &).
Changing the Cell Width Note: By default, the cell width is 6. 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. To change the cell width from the Table screen: 1. Press ƒ 9 — or — TI-89: ¥ Í TI-92 Plus: ¥ F. 2. Press B or A to display a menu of valid widths (3 – 12). 3. Move the cursor to highlight a number and press ¸.
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. The table’s header row shows the function names (y1, etc.). 2. Press † to move the cursor to the entry line, where the function is displayed and highlighted. Tip: You can use this feature to view a function without leaving the table. Tip: To cancel any changes and return the cursor to the table, press N instead of ¸. 3.
Building a Manual (Ask) Table If Independent = ASK on the TABLE SETUP dialog box, the TI-89 / TI-92 Plus lets you build a table manually by entering specific values for the independent variable. Displaying the Table Screen To display the Table screen, press ¥ ' or O 5. If you set Independent = ASK (with ¥ & ) before displaying a table for the first time, a blank table is displayed. The cursor highlights the first cell in the independent variable column.
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: Note: If the independent variable column contains existing values, they are shown as a list (which you can edit). x={1,1.5,1.75,2} You can also enter a list variable or an expression that evaluates to a list. 4.
Chapter 14: Split Screens 14 Preview of Split Screens........................................................................ 232 Setting and Exiting the Split Screen Mode ......................................... 233 Selecting the Active Application .......................................................... 235 On the TI-89 / TI-92 Plus, you can split the screen to show two applications at the same time.
Preview of Split Screens Split the screen to show the Y= Editor and the Graph screen. Then explore the behavior of a polynomial as its coefficients change. Steps ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 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. 3 B1 „B3 DB2 DB4¸ 3 B1 „B3 DB2 DB4¸ 2. Clear the Y= Editor and turn off any stat data plots. Then define y1(x) = .1x 3–2x+6. ƒ8¸ ‡5 ¸ .
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.
Other Modes that Affect a Split Screen Mode Description Number of Graphs Lets you set up and display two independent sets of graphs. Note: Leave this set to 1 unless you have read the applicable section in Chapter 12. Split Screens and Pixel Coordinates This is an advanced graphing feature as described in “Using the Two-Graph Mode” in Chapter 12. The TI-89 / TI-92 Plus has commands that use pixel coordinates to draw lines, circles, etc., on the Graph 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.
Using 2 K to Display the Home Screen Tip: Pressing 2 K twice always exits the split screen mode. When Using a Top-Bottom Split 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.
Chapter 15: Data/Matrix Editor 15 Preview of the Data/Matrix Editor....................................................... 238 Overview of List, Data, and Matrix Variables..................................... 239 Starting a Data/Matrix Editor Session................................................. 241 Entering and Viewing Cell Values ........................................................ 243 Inserting and Deleting a Row, Column, or Cell..................................
Preview of the 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). ³ TI-89 Keystrokes Steps 1. Start the Data/Matrix Editor and O 6 3 create a new list variable named B 3 TEMP. DD TEMP ¸¸ 2. Enter a column of numbers.
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: Note: If you enter more than one column of elements in a list variable, it is converted automatically into a data variable.
Data Variable (Continued) From the Home screen or a program, you can use the NewData command to create a data variable that consists of existing lists. Although you cannot directly display a data variable on the Home screen, you can display a specified column or element. NewData data1,list1,list2 Names of existing list variables Name of data variable to create Name of data variable Column number data1[1] (data1[1])[1] Element number in the column Column number Displays column 1 of the variable data1.
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 6:Data/Matrix Editor. 2. Select 3:New. 3. Specify the applicable information for the new variable.
Using the Current Variable You can leave the Data/Matrix Editor and go to another application at any time. To return to the variable that was displayed when you left the Data/Matrix Editor, press O 6 and select 1:Current. 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.
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). If you open an existing variable, the values in that variable are displayed. You can then enter additional values or edit the existing ones. The Data/Matrix Editor Screen A blank Data/Matrix Editor screen is shown below. When the screen is displayed initially, the cursor highlights the cell at row 1, column 1.
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 ¥ C or Go to row 1 in the current ¥D 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, ¥ D goes to row 999. Go to column 1 or to the last column that contains data, respectively. If the cursor is in or past that last column, ¥ B goes to column 99.
¦ In a matrix variable, when you enter a value in a cell outside the current boundaries, additional rows and/or columns are added automatically to the matrix to include the new cell. Other cells in the new rows and/or columns are filled with zeros. Note: Although you specify the size of a matrix when you create it, you can easily add additional rows and/or columns. Changing the Cell Width Tip: Remember, to see a number in full precision, you can always highlight the cell and look at the entry line.
Inserting and Deleting a Row, Column, or Cell The general procedures for inserting and deleting a cell, row, or column are simple and straightforward. You can have up to 99 columns with up to 999 elements in each column. Note About Column Titles and Headers You cannot delete the rows or cells that contain column titles or headers. Also, you cannot insert a row or cell before a column title or header.
Inserting a Cell The new cell is inserted before the highlighted cell in the same column. (You cannot insert a cell into a locked column, which is defined by a function in the column header. Refer to page 248.) In the Data/Matrix Editor: 1. Move the cursor to the applicable cell. 2. TI-89: 2 ˆ TI-92 Plus: ˆ and select 1:Insert. 3. Select 1:cell. Note: For a matrix variable, you cannot insert a cell because the matrix must retain a rectangular shape. The inserted cell is undefined.
Defining a Column Header with an Expression For a list variable or a column in a data variable, you can enter a function in the column header that automatically generates a list of elements. In a data variable, you can also define one column in terms of another. Entering a Header Definition Tip: To view an existing definition, press † or move the cursor to the header cell and look at the entry line. In the Data/Matrix Editor: 1. Move the cursor to any cell in the column and press †.
Using an Existing List as a Column Note: If you have a CBL 2é/CBL™ or CBRé, use these techniques for your collected lists. Tip: Use 2 ° to see existing list variables. 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. Refer to the existing list variable.
Using Shift and CumSum Functions in a Column Header When defining a column header, you can use the shift and cumSum functions as described below. These descriptions differ slightly from Appendix A. This section describes how to use the functions in the Data/Matrix Editor. Appendix A gives a more general description for the Home screen or a program. Using the Shift Function The shift function copies a base column and shifts it up or down by a specified number of elements.
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. TI-89: 2 ˆ TI-92 Plus: ˆ and select 3:Sort Column. Numbers are sorted in ascending order. Character strings are sorted in alphabetical order.
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 Note: A list is automatically converted to a data variable if you enter more than one column of information. Data Data Data column List Matrix Matrix Procedure From the Data/Matrix Editor: 1.
Chapter 16: Statistics and Data Plots 16 Preview of Statistics and Data Plots.................................................... 254 Overview of Steps in Statistical Analysis............................................ 258 Performing a Statistical Calculation.................................................... 259 Statistical Calculation Types ................................................................ 261 Statistical Variables.........................................................................
Preview of 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 ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 1. Display the MODE dialog box. For Graph mode, select FUNCTION.
Steps ³ TI-89 Keystrokes › TI-92 Plus Keystrokes ‡ B7D Cj1D jC2D BD¸ ‡ B7D C1D C2D BD¸ ¸ ¸ 8. Close the STAT VARS screen. ¸ The Data/Matrix Editor displays. ¸ 6. Display the Calculate dialog box. Set: Calculation Type = MedMed x = C1 y = C2 Store RegEQ to = y1(x) 7. Perform the calculation to display the MedMed regression equation. Display As specified on the Calculate dialog box, this equation is stored in y1(x). ‡ B5D D D BD¸ ‡ B5D D D BD¸ ¸ ¸ 11. Close the STAT VARS screen.
Steps 15. Display the Y= Editor. For y1(x), the MedMed regression equation, set the display style to Dot. ³ TI-89 Keystrokes › TI-92 Plus Keystrokes ¥# 2ˆ2 ¥# ˆ2 C C „9 „9 O61 O61 Display 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. 16. Scroll up to highlight Plot 1.
Steps ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 22. Enter a title for column 6. Define B C 2 ™ RESIDj column 6’s header as the ¸ residuals for LinReg. †jC2| jC5¸ BC RESID ¸ †C2| C5¸ 23. Display the Plot Setup screen and „ † deselect Plot 1. „† Dƒ D D Cj1D jC4¸ ¸ Dƒ D D C1D C4¸ ¸ Dƒ D B3D Cj1D jC6¸ ¸ Dƒ D B3D C1D C6¸ ¸ ¥# ‡3 ¥# ‡3 „9 „9 28. Display the Home screen. " ¥" 29. Use the MedMed (y1(x)) and LinReg (y2(x)) regression equations to calculate values for x = 300 (300,000 population).
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. Calculating and Plotting Stat Data Set Graph mode (3) to FUNCTION . Note: Refer to Chapter 15 for details on entering data in the Data/Matrix Editor. Enter stat data in the Data/Matrix Editor (O 6). Perform stat calculations to find stat variables or fit data to a model (‡).
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.
The Calculate Dialog Box Item Description Freq Type the column number that contains a “weight” value for each data point. If you do not enter a column number, all data points are assumed to have the same weight (1). Category Type the column number that contains a category value for each data point. Include Categories If you specify a Category column, you can use this item to limit the calculation to specified category values.
Statistical Calculation Types As described in the previous section, the Calculate dialog box lets you specify the statistical calculation you want to perform. This section gives more information about the calculation types. 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.
Selecting the Calculation Type Calc Type Description MedMed Median-Median — Fits the data to the model y=ax+b (where a is the slope, and b is the y-intercept) using the median-median line, which is part of the resistant line technique. (Continued) Summary points medx1, medy1, medx2, medy2, medx3, and medy3 are calculated and stored to variables, but they are not displayed on the STAT VARS screen.
Statistical Variables Statistical calculation results are stored to variables. To access these variables, type the variable name or use the VAR-LINK screen as described in Chapter 21. All statistical variables are cleared when you edit the data or change the calculation type. Other conditions that clear the variables are listed on page 260. Calculated Variables Statistical variables are stored as system variables. However, regCoef and regeq are treated as a list and a function variable, respectively.
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. Note: This dialog box is similar to the Calculate dialog box.
Note: For an example of using Freq, Category, and Include Categories, refer to page 270. Item Description Freq Type the column number that contains a “weight” value for each data point. If you do not enter a column number, all data points are assumed to have the same weight (1). Category Type the column number that contains a category value for each data point. Include Categories If you specify a Category, you can use this to limit the calculation to specified category values.
Statistical Plot Types When you define a plot as described in the previous section, the Plot Setup screen lets you select the plot type. This section gives more information about the available plot types. Scatter xyline 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.
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. ¦ xmax ì xmin When defining the plot, you can specify the Hist. Bucket Number of bars = Hist. Bucket Width 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.
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 ¥ # 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.
Graphing and Tracing a Defined Stat Plot After entering the data points and defining the stat plots, you can graph the selected plots by using the same methods you used to graph a function from the Y= Editor (as described in Chapter 6). 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 ¥ $ to display the Window Editor.
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. Example of a Frequency Column In a data variable, you can use any column in the Data/Matrix Editor to specify a frequency value (or weight) for the data points on each row.
Suppose you enter the test scores from a class that has 10th and 11th grade students. You want to analyze the scores for the whole class, but you also want to analyze categories such as 10th grade girls, 10th grade boys, 10th grade girls and boys, etc. First, determine the category values you want to use. Note: You do not need a category value for the whole class. Also, you do not need category values for all 10th graders or all 11th graders since they are combinations of other categories.
If You Have a CBL 2/CBL or CBR The Calculator-Based Laboratoryé System (CBL 2é/CBL™) and Calculator-Based Rangeré System (CBRé) are optional accessories, available separately, that let you collect data from a variety of real-world experiments. TI-89 / TI-92 Plus CBL 2/CBL and CBR programs are available from the TI web site at: http://www.ti.com/calc/cbl and http://www.ti.
Creating a Data Variable with the CBL 2/CBL Lists You can create a new data variable that consists of the necessary CBL 2/CBL list variables. ¦ From the Home screen or a program, use the NewData command. NewData dataVar, list1 [,list2 ] [,list3 ] ... CBL 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.
274 Chapter 16: Statistics and Data Plots 16STATS.
Chapter 17: Programming 17 Preview of Programming....................................................................... 276 Running an Existing Program............................................................... 278 Starting a Program Editor Session....................................................... 280 Overview of Entering a Program.......................................................... 282 Overview of Entering a Function.........................................................
Preview of 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 1. Start a new program on the Program Editor. ³ TI.89 Keystrokes O73 › TI.92 Plus Keystrokes Display O73 2. Type PROG1 (with no spaces) as D D PROGj1 the name of the new program variable. DD PROG1 3. Display the “template” for a new ¸ ¸ program. The program name, Prgm, and EndPrgm are shown automatically.
› TI-92 Plus Keystrokes ³ TI-89 Keystrokes Steps " 5. Go to the Home screen. Enter the program name, followed by a 2 ™ P R O G j1 set of parentheses. cd¸ You must include ( ) even when there ¥" PROG 1 cd¸ Display prog1() are no arguments for the program. The program displays a dialog box with the prompt specified in the program. 6. Type 5 in the displayed dialog box. 5 5 7. Continue with the program. The Disp command displays the result on the Program I/O screen.
Running an Existing Program After a program is created (as described in the remaining sections of this chapter), 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. Tip: Use 2 ° to list existing PRGM variables. Highlight a variable and press ¸ to paste its name to the entry line. Note: Arguments specify initial values for a program.
Where Is the Output Displayed? Depending on the commands in the program, the TI-89 / TI-92 Plus 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.) ¦ Graph-related commands typically use the Graph screen. After the program stops, the TI-89 / TI-92 Plus shows the last screen that was displayed.
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 7: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.
Resuming the Current Program You can leave the Program Editor and go to another application at any time. To return to the program or function that was displayed when you left the Program Editor, press O 7 and select 1:Current. 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.
Overview of Entering a Program A program is a series of commands executed in sequential order (although some commands alter the program flow). In general, anything that can be executed from the Home screen can be included in a program. Program execution continues until it reaches the end of the program or a Stop command. 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.
Controlling the Flow of a Program When you run a program, the program lines are executed in sequential order. However, some commands alter the program flow. For example: Tip: For information, refer to pages 295 and 297. ¦ 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.
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. ¦ Note: In this example, you cannot use circle as the program name because it conflicts with a command name.
Overview of Entering a Function A function created in the Program Editor is very similar to the functions and instructions that you typically use from the Home screen. Why Create a UserDefined Function? Functions (as well as programs) are ideal for repetitive calculations or tasks. You only need to write the function once. Then you can reuse it as many times as necessary. Functions, however, have some advantages over programs.
Entering a Function When you create a new function in the Program Editor, the TI-89 / TI-92 Plus displays a blank “template”. Function name, which you specify when you create a new function. Note: Use the cursor pad to scroll through the function for entering or editing commands. 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. Enter your commands between Func and 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). Subroutines are useful when a program needs to repeat the same group of commands at several different places. Calling a Separate Program To call a separate program, use the same syntax used to run the program from the Home screen.
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 of Variables Note: For information about folders, refer to Chapter 5. Scope Description System (Global) Variables Variables with reserved names that are created automatically to store data about the state of the TI-89 / TI-92 Plus. For example, Window variables (xmin, xmax, ymin, ymax, etc.
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. However, to avoid Circular definition errors, you must assign a value for x or i variables that are used in evaluating the function or running the program.
Using Local Variables in Functions or Programs A local variable is a temporary variable that exists only while a user-defined function is being evaluated or a user-defined program is running. Example of a Local Variable The following program segment shows a For...EndFor loop (which is discussed later in this chapter). The variable i is the loop counter. In most cases, the variable i is used only while the program is running.
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.
String Operations Strings are used to enter and display text characters. You can type a string directly, or you can store a string to a variable. 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.
String Commands Note: See Appendix A for syntax for all TI-89 / TI-92 Plus 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.
Conditional Tests Conditional tests let programs make decisions. For example, depending on whether a test is true or false, a program can decide which of two actions to perform. Conditional tests are used with control structures such as If...EndIf and loops such as While...EndWhile (described later in this chapter). Entering a Test Operator ¦ ¦ ¦ Relational Tests Type the operator directly from the keyboard. — or — Press 2 I and select 8:Test. Then select the operator from the menu.
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. „ 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...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: Executed only if x>5. Executed only if x5. Displays value of: • 2x if x>5. • 5x if x5. If...Then...ElseIf... EndIf Structures :If x>5 Then : Disp "x is greater than 5" : 2ù x! x :Else : Disp "x is less than or equal to 5" : 5ù x! x :EndIf :Disp x A more complex form of the If command lets you test a series of conditions.
Using Loops to Repeat a Group of Commands To repeat the same group of commands successively, use a loop. Several types of loops are available. Each type gives you a different way to exit the loop, based on a conditional test. „ Control Toolbar Menu Note: A loop command marks the start of the loop. The corresponding End command marks the end of the loop. To enter most of the loop-related commands, use the Program Editor’s „ Control toolbar menu.
For example: Tip: You can declare the counter variable as local (pages 288 and 290) if it does not need to be saved after the program stops. While...EndWhile Loops Displays 0, 1, 2, 3, 4, and 5. Displays 6. When variable increments to 6, the loop is not executed. :For i,0,5,1 : Disp i :EndFor :Disp i 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.
Loop...EndLoop Loops A Loop...EndLoop creates an infinite loop, which is repeated endlessly. The Loop command does not have any arguments. :Loop : -------: -------:EndLoop :-------- 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: An If command checks the condition. Note: The Exit command exits from the current loop. Exits the loop and jumps to here when x increments to 6.
Configuring the TI-89 / TI-92 Plus Programs can contain commands that change the configuration of the TI-89 / TI-92 Plus. Because mode changes are particularly useful, the Program Editor’s Mode toolbar menu makes it easy to enter the correct syntax for the setMode command. Configuration Commands Command Description getConfg Returns a list of calculator characteristics. Note: The parameter/mode strings used in the getFold Returns the name of the current folder.
Getting Input from the User and Displaying Output Although values can be built into a program (or stored to variables in advance), a program can prompt the user to enter information while the program is running. Likewise, a program can display information such as the result of a calculation. … I/O Toolbar Menu To enter most of the commonly used input/output commands, use the Program Editor’s … I/O toolbar menu. To see a submenu that lists additional commands, select 1:Dialog.
Output Commands Note: In a program, simply performing a calculation does not display the result. You must use an output command. Tip: After Disp and Output, the program immediately continues. You may want to add a Pause command. Graphical User Interface Commands Tip: When you run a program that sets up a custom toolbar, that toolbar is still available even after the program has stopped.
Creating a Custom Menu The TI-89 / TI-92 Plus custom menu feature lets you create your own toolbar menu. A custom menu can contain any available function, instruction, or set of characters. The TI-89 / TI-92 Plus has a default custom menu that you can modify or redefine. Turning the Custom Menu On and Off Note: When the custom menu is turned on, it replaces the normal toolbar menu. Unless a different custom menu has been created, the default custom menu is displayed.
Note: The following may be slightly different than the default custom menu on your calculator.
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 Graphing Commands Note: For more information about using setMode, refer to page 300. Command Description DispTbl Displays the current contents of the Table screen. setTable Sets the Graph <–> Table or Independent table parameters.
Graph Picture and Database Commands Note: For information about graph pictures and databases, also refer to Chapter 12. 306 Command Description AndPic Displays the Graph screen and superimposes a stored graph picture by using AND logic. 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.
Drawing on the Graph Screen To create a drawing object on the Graph screen, use the commands listed in this section. Pixel vs. Point Coordinates Tip: For information about pixel coordinates in split screens, refer to Chapter 14. When drawing an object, you can use either of two coordinate systems to specify a location on the screen. ¦ Pixel coordinates — Refer to the pixels that physically make up the screen. These are independent of the viewing window because the screen is always: TI.
Drawing Lines and Circles Drawing Expressions 308 Command Description Circle or PxlCrcl Draws, erases, or inverts a circle with a specified center and radius. DrawSlp Draws a line with a specified slope through a specified point. Line or PxlLine Draws, erases, or inverts a line between two sets of coordinates. 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.
Accessing Another TI-89/TI-92 Plus, a CBL 2/CBL, or a CBR If you link two TI-89 / TI-92 Plus calculators (described in Chapter 22), programs on both units can transmit variables between them. If you link a TI-89 / TI-92 Plus to a CalculatorBased Laboratoryé (CBL 2é/CBL™) or a Calculator-Based Ranger™ (CBRé), a program on the TI-89 / TI-92 Plus can access the CBL 2/CBL or CBR. … 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.
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 TI-89 / TI-92 Plus automatically checks each executed command for syntax errors. If there is an error, a message indicates the nature of the error. ¦ To display the program in the Program Editor, press ¸.
Example: Using Alternative Approaches The preview at the beginning of this chapter 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 is the program given in the preview at the beginning of the chapter. Refer to the preview for detailed information. Prompts for input in a dialog box.
Example 4 This example uses Dialog...EndDlog to create dialog boxes for input and output. It uses Loop...EndLoop to calculate the result. Defines a dialog box for input. Converts string entered with Request to an expression. Loop calculation. Defines a dialog box for output.
Assembly-Language Programs You can run programs written for the TI-89 / TI-92 Plus 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 education.ti.
Shortcuts to Run a Program On the Home screen, you can use keyboard shortcuts to run up to nine user-defined or assembly-language programs. However, the programs must have the following names. On Home screen, press: ¥1 © ¥9 Note: The programs must be stored in the MAIN folder. Also, you cannot use a shortcut to run a program that requires an argument.
Chapter 18: Text Editor 18 Preview of Text Operations .................................................................. 316 Starting a Text Editor Session.............................................................. 317 Entering and Editing Text..................................................................... 319 Entering Special Characters.................................................................. 324 Entering and Executing a Command Script .......................................
Preview of 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. ³ TI.89 Keystrokes Steps › TI.92 Plus Keystrokes 1. Start a new session on the Text Editor. O83 O83 2. Create a text variable called TEST, which will automatically store any text you enter in the new session.
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 8:Text Editor. 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 Type Automatically set as Text and cannot be changed.
Resuming the Current Session You can leave the Text Editor and go to another application at any time. To return to the session that was displayed when you left the Text Editor, press O 8 and select 1:Current. 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.
Entering and Editing Text After beginning a Text Editor session, you can enter and edit text. In general, use the same techniques that you have already used to enter and edit information on the Home screen’s entry line. Typing Text Note: Use the cursor pad to scroll through a session or position the text cursor. Tip: Press 2 C or 2 D to scroll up or down one screen at a time, and ¥ C or ¥ D to go to the top or bottom of the text session.
Typing Alphabetic Characters (continued) Deleting Characters On the TI-89, 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 alpha-lock off. After you type the character, alphalock remains on.
Cutting, Copying, and Pasting Text Cutting and copying both place highlighted text into the clipboard of the TI-89 / TI-92 Plus. 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. Tip: You can press: TI.89: ¥ 5, ¥ 6, ¥ 7 TI.92 Plus: ¥X, ¥C, ¥V to cut, copy, and paste without having to use the ƒ toolbar menu. 2. Press ƒ. 3. Select the applicable menu item. ¦ ¦ To move the text, select 4:Cut.
Inserting or Overtyping a Character By default, the TI-89 / TI-92 Plus is in insert mode. To toggle between insert and overtype mode, press 2 /. If the TI.89 / TI.92 Plus is in: The next character you type: Will be inserted at the cursor. Tip: Look at the shape of the cursor to see if you’re in insert or overtype mode. Thin cursor between characters Cursor highlights a character Will replace the highlighted character.
2. Use the TI-GRAPH LINKé software to send the file from the computer to the TI-89 / TI-92 Plus. a. Use the TI-GRAPH LINK cable to connect the computer and the calculator. b. Be sure the TI-89 / TI-92 Plus is on the Home screen. c. In the software, select Send from the Link menu. Select the text file and click Add to add it to the Files Selected list. Then click OK. d. When notified that the sending process is complete, click OK. 3. On the TI-89 / TI-92 Plus, use the Text Editor to open the text variable.
Entering Special Characters You can use the CHAR menu to select any special character from a list. You can also type certain commonly used characters from the keyboard. To see which characters are available from the keyboard, you can display a map that shows the characters and their corresponding keys. Selecting Characters from the CHAR Menu 1. Press 2 ¿. 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.
TI.89 keyboard map feature shortcuts: TI.92 Plus keyboard map feature shortcuts: GREEK (¥ c) — Accesses the GREEK (2 G) — Accesses the Greek character set (described later in this section). Greek character set (described later in this section). SYSDATA (¥ b) — Copies the CAPS (2 ¢)— Turns Caps current graph coordinates to the Lock on and off. system variable sysdata. Accent marks — (é, ü, ô, à, ç, and ~) FMT (¥ Í) — Displays the are added to the next letter you FORMATS dialog box.
Typing Accent Marks from the TI.92 Plus Keyboard Pressing an accent mark key does not display an accented letter. The accent mark will be added to the next letter you press. 1. Press 2 and then the key for the accent mark. Note: To help you find the applicable keys, this map shows only the accent mark keys. 2. Press the key for the letter you want to accent. ¦ You can accent lowercase and uppercase letters. ¦ An accent mark can be added to only those letters that are valid for that mark.
Several keys let you access lowercase and uppercase Greek letters. For example: On the TI.89: On the TI.92 Plus: 1. Press ¥ c to access the Greek character set. 1. Press 2 G to access the Greek character set. 2. Press ¥ c j + letter to access lowercase Greek letters. Example: ¥ c j [W] displays ω 2. Press 2 G + letter to access lowercase Greek letters. Example: 2 G W displays ω 3. Press ¥ c ¤ + letter to access uppercase Greek letters. Example: ¥ c ¤ [W] displays Ω 3.
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 Note: This does not insert a new line for the command, it simply marks an existing line as a command line.
Splitting the Text Editor/ Home Screen With a split screen, you can view your command script and see the result of an executed command at the same time. To: Press: Split the screen … and select 1:Script view. Return to a full screen Text Editor … and select 2:Clear split. You can also use 3 to set up a split screen manually. However, … sets up a Text Editor/Home screen split much easier than 3. Creating a Script from Your Home Screen Entries ¦ The active application is indicated by a thick border.
Creating a Lab Report If you have a TI-GRAPH LINKé cable, an optional accessory that lets the TI-89 / TI-92 Plus communicate with a personal computer, you can create lab reports. Use the Text Editor to write a report, which can include print objects. Then use the TI-GRAPH LINK software to print the report on the printer attached to the computer. Print Objects In the Text Editor, you can specify a variable name as a print object.
Printing the Report General Steps For Detailed Information 1. Connect the Refer to the manual that came with your TI-GRAPH LINK. TI-89 / TI-92 Plus to your computer via the TI-GRAPH LINK cable. 2. Use the TI-GRAPH LINK software to get the lab report from the calculator, and then print the report. Example Assume you have stored: ¦ A function as y1(x) (specify y1, not y1(x)). ¦ A graph picture as pic1. ¦ Applicable information in variables der and sol.
332 Chapter 18: Text Editor 18TXTED.
Chapter 19: Numeric Solver 19 Preview of the Numeric Solver ............................................................ 334 Displaying the Solver and Entering an Equation ............................... 335 Defining the Known Variables .............................................................. 337 Solving for the Unknown Variable ....................................................... 339 Graphing the Solution............................................................................
Preview of the Numeric Solver Consider the equation a=(m2ì m1)/(m2+m1)ù 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 ³ TI-89 Keystrokes › TI-92 Plus Keystrokes 1. Display the Numeric Solver. O9 O9 2. Enter the equation. jAÁc jM2| jM1dec jM2« jM1dp jG¸ AÁc M2| M1dec M2« M1dp G¸ D10DD 9.8CCC jGe3 D10DD 9.8CCC Ge3 When you press ¸ or D, the screen lists the variables used in the equation. 3.
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 9. The Numeric Solver screen shows the last entered equation, if any. Entering an Equation Tips: In your equation: • Do not use system function names (such as y1(x) or r1(q)) as simple variables (y1 or r1). • Be careful with implied multiplication.
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 ‡. A dialog box displays the most recently entered equation. Tip: You can specify how many equations are retained. From the Numeric Solver, press ƒ and select 9:Format (or use TI-89: ¥ Í TI-92 Plus: ¥ F). Then select a number from 1 through 11. 2. Select an equation.
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 Note: If an existing variable is locked or archived, you cannot edit its value. After typing your equation on the eqn: line, press ¸ or D. The screen lists the variables in the order they appear in the equation. If a variable is already defined, its value is shown. You can edit these variable values.
Note: You cannot solve for a system variable other than exp. Also, if the equation contains a system variable, you cannot use … to graph. Note: This error occurs if you use a reserved name incorrectly or refer to an undefined system function as a simple variable without parentheses. ¦ If the equation contains a system variable (xmin, xmax, etc.), that variable is not listed. The solver uses the system variable’s existing value. In the standard viewing window, xmax=10.
Solving for the Unknown Variable After you type an equation in the Numeric Solver and enter values for the known variables, you are ready to solve for the unknown variable. Finding the Solution With all known variables defined: 1. Move the cursor to the unknown variable. Note: To stop (break) a calculation, press ´. The unknown variable shows the value being tested when the break occurred. Put the cursor on the variable you want to solve for. 2. Press „ Solve. A é marks the solution and leftì rt.
Graphing the Solution You can graph an equation’s solutions any time after defining the known variables, either before or after you solve for the unknown variable. By graphing the solutions, you can 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 Graph View uses the current Window variable values.
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. Note: Cursor coordinate xc is the unknown variable value, and yc is the leftì rt value. Returning to a Full Screen 3. Make sure the cursor is on the unknown variable, and press †. 4. Press „ to re-solve the equation.
342 Chapter 19: Numeric Solver 19SOLVER.
Chapter 20: Number Bases 20 Preview of Number Bases..................................................................... 344 Entering and Converting Number Bases............................................. 345 Performing Math Operations with Hex or Bin Numbers .................. 346 Comparing or Manipulating Bits .......................................................... 347 Wherever you enter an integer in a TI-89 / TI-92 Plus calculation, you can enter it in decimal, binary, or hexadecimal form.
Preview of 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 ³ TI.89 Keystrokes › TI.92 Plus Keystrokes Display 3„ 3„ 1. Display the MODE dialog box, (use D to move (use D to move Page 2. For Base mode, select DEC as the default number base.
Entering and Converting Number Bases Regardless of the Base mode, you must always use the appropriate prefix when entering a binary or hexadecimal number. Entering a Binary or Hexadecimal Number To enter a binary number, use the form: (for example: 0b11100110) 0b binaryNumber Binary number with up to 32 digits Zero, not the letter O, and the letter b Note: You can type the b or h in the prefix, as well as hex characters A – F, in uppercase or lowercase.
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. Scroll to the Base mode, press B, and select the applicable setting. 3. Press ¸ to close the MODE screen.
Comparing or Manipulating Bits The following operators and functions let you compare or manipulate bits in a binary number. You can enter an integer in any number base. Your entries are converted to binary automatically for the bitwise operation, and results are displayed according to the Base mode. Boolean Operations Note: You can select these operators from the MATH/Base menu. For an example using each operator, refer to Appendix A in this book.
Rotating and Shifting Bits Function with syntax Description rotate(integer) If #ofRotations is: – or – rotate(integer,#ofRotations) Note: You can select these functions from the MATH/Base menu. For an example using each function, refer to Appendix A in this book. ¦ omitted — bits rotate once to the right (default is ë 1). ¦ negative — bits rotate the specified number of times to the right. ¦ positive — bits rotate the specified number of times to the left.
Chapter 21: Memory and Variable Management 21 Preview of Memory and Variable Management ................................. 350 Checking and Resetting Memory ......................................................... 353 Displaying the VAR-LINK Screen ......................................................... 355 Manipulating Variables and Folders with VAR-LINK ........................ 357 Pasting a Variable Name to an Application ........................................
Preview of 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. (Archived variables are locked automatically.) Finally, unarchive the variable and delete the unused variables so that they will not take up memory. Steps 1.
Steps ³ TI-89 Keystrokes › TI-92 Plus Keystrokes D2ˆ Dˆ 6. Close the Contents window. N N 7. With the f variable still highlighted, close VAR-LINK and paste the variable name to the entry line. ¸ ¸ 8. Complete the operation. 2d¸ 2d¸ 2° (use D to highlight x1) 2° (use D to highlight x1) 5. Highlight the f function variable, and view its contents. Display Notice that the function was assigned using f(x) but is listed as f on the screen. 5ù f( Notice that “ ( ” is pasted.
³ TI-89 Keystrokes Steps › TI-92 Plus Keystrokes 14. Use VAR-LINK to unarchive the variable. 2° (use D to highlight x1) ƒ9 2° (use D to highlight x1) ƒ9 15. Return to the Home screen and store a different value to the unarchived variable. " ¸ ¥" ¸ 2° ‡1 2° ‡1 ƒ1 ƒ1 ¸ ¸ ¸ 19. Because ‡ 1 also selected the MAIN folder, an error message states that you cannot delete the MAIN folder. Acknowledge the message. ¸ Display Deleting variables: 16.
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 ¯. Size of history pairs saved in the Home screen’s history area Tip: To display the size of individual variables and determine if they are in the user data archive, use the VAR-LINK screen.
Flash ROM free on the MEMORY Screen Note: For TI-92 Plus Modules and some TI-89 users, their maximum archive space is about 384-KB regardless of how much free Flash ROM is available. The Flash ROM free displayed on the Memory screen 2 ¯ is shared by archive and Flash applications. This Flash ROM is divided into sectors of 64-KB memory. Each individual sector can contain either archive or Flash applications, but not both.
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 as described later in this chapter. Displaying the VAR-LINK Screen Note: For information about using folders, refer to Chapter 5. Press 2 °. By default, the VAR-LINK screen lists all userdefined variables in all folders and with all data types.
Listing Only a Specified Folder and/or Variable Type, or Flash application Tip: To cancel a menu, press N. Tip: To list system variables (window variables, etc.), select 3:System. If you have a lot of variables and/or folders, or Flash applications, it may be difficult to locate a particular variable. By changing VARLINK’s view, you can specify the information you want to see. From the VAR-LINK screen: 1. Press „ View. 2. Highlight the setting you want to change, and press B.
Manipulating Variables and Folders with VAR-LINK On the VAR-LINK screen, you can show the contents of a variable. You can also select one or more listed items and manipulate them by using the operations in this section. Showing the Contents of a Variable Note: You cannot edit the contents from this screen. Selecting Items from the List Note: If you use † to Ÿ one or more items and then highlight a different item, the following operations affect only the Ÿ’ed items.
Creating a New Folder For information about using folders, refer to Chapter 5. 1. On VAR-LINK, press ƒ Manage and select 5:Create Folder. 2. Type a unique name, and press ¸ twice. 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.
Pasting a Variable Name to an Application Suppose you are typing an expression on the Home screen and can’t remember which variable to use. You can display the VAR-LINK screen, select a variable from the list, and paste that variable name directly onto the Home screen’s entry line. Which Applications Can You Use? Procedure From the following applications, you can paste a variable name to the current cursor location.
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. Why Would You Want to Archive a Variable? Note: You cannot archive variables with reserved names or system variables. The user data archive lets you: ¦ Store data, programs, or any other variables to a safe location where they cannot be edited or deleted inadvertently.
From the VAR-LINK Screen To archive or unarchive: Tip: To select a single variable, highlight it. To select multiple variables, highlight each variable and press † Ÿ. 2. Select one or more variables, which can be in different folders. (You can select an entire folder by selecting the folder name.) 1. Press 2 ° to display the VAR-LINK screen. 3. Press ƒ and select either: 8:Archive Variable – or – 9:Unarchive Variable Note: If you get a Garbage Collection message, refer to page 362.
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 / TI-92 Plus will attempt to rearrange the archived variables to make additional room. Responding to the Garbage Collection Message When you see the message to the right: ¦ ¦ To continue archiving, press ¸. – or – To cancel, press N.
How Unarchiving a Variable Affects the Process When you unarchive a variable, it is copied to RAM but is not actually deleted from the user data archive memory. variable A After you unarchive variables B and C, they continue to take up space. Unarchived variables are “marked for deletion,” meaning they will be deleted during the next garbage collection.
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. What Causes the Memory Error? The Memory Error message is displayed if there is not enough free RAM to access the archived variable.
Chapter 22: Linking and Upgrading 22 Linking Two Units .................................................................................. 366 Transmitting Variables, Flash Applications, and Folders................. 367 Transmitting Variables under Program Control................................. 371 Upgrading Product Software (Base Code) ......................................... 373 Collecting and Transmitting ID Lists................................................... 378 Compatibility between a TI.
Linking Two Units The TI-89 and the TI-92 Plus each come with a cable that lets you link two units. Once connected, you can transmit information between two units. Connecting before Sending or Receiving Using firm pressure, insert one end of the cable into the I/O port of each unit. Either unit can send or receive, depending on how you set them up from the VAR-LINK screen.
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 and folders. Setting Up the Units Most Flash applications will transfer only from a TI-89 to a TI-89 or from a TI-92 Plus to a TI-92 Plus. You cannot send Flash applications to a TI-92 unless it contains a Plus module and Advanced Mathematics 2.x product software (base code).
Rules for Transmitting Variables, Flash Applications, or Folders Unlocked and unarchived variables having the same name on both the sending and receiving units will be overwritten from the sending unit. Locked and archived variables having the same name on both the sending and receiving units must be unlocked or unarchived on the receiving unit before they can be overwritten from the sending unit. You can lock, but you cannot archive a Flash application or a folder.
Common Error and Notification Messages Shown on: Message and Description: Sending unit This is displayed after several seconds if: Note: The sending unit may not always display this message. Instead, it may remain BUSY until you cancel the transmission. ¦ A cable is not attached to the sending unit’s I/O 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.
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 or Flash application, move the cursor to highlight it. Note: You cannot delete the Main folder. ¦ To select a single folder, highlight it and press † to place a checkmark (Ÿ) beside it. This selects the folder and its contents. Note: Use † to select multiple variables, Flash applications, or folders.
Transmitting Variables under Program Control You can use a program containing GetCalc and SendCalc or SendChat to transmit a variable from one calculator to another. Overview of Commands SendCalc sends a variable to the link port, where a linked calculator can receive the variable value. The linked calculator must be on the Home screen or must execute GetCalc from a program. If you send to a TI-92, however, an error occurs if the TI-92 executes GetCalc from a program.
Running the Program Note: For information about using the Program Editor, refer to Chapter 17. This procedure assumes that: ¦ The two calculators are linked with the connecting cable as described on page 366. ¦ The Chat program is loaded on both calculators. (A program loaded on a TI-92 must use SendCalc instead of SendChat.) − Use each calculator’ s Program Editor to enter the program.
Upgrading Product Software (Base Code) You can upgrade the product software (base code) on your TI-89 / TI-92 Plus. You can also transfer product software (base code) from one TI-89 or TI-92 Plus to another, provided that the receiving unit has the correct certification that allows it to run that software. Product Software (Base Code) Upgrades The term product software includes these two types of base code upgrades: ¦ Maintenance upgrades (which are released free of charge).
Backing Up Your Unit Before a Product Software (Base Code) Installation Important: Before installation, install new batteries. When you install a product software (base code) upgrade, the installation process: ¦ Deletes all user-defined variables (in both RAM and the user data archive), functions, programs, and folders. ¦ Could delete all Flash applications. ¦ Resets all system variables and modes to their original factory settings. This is equivalent to using the MEMORY screen to reset all memory.
Transferring Product Software (Base Code) If the sending TI-89 or TI-92 Plus has its original product software (base code) or a free maintenance upgrade, the receiving TI-89 or TI-92 Plus does not need a new certificate. Its current certificate is valid, and the maintenance upgrade can be transferred. If the sending TI-89 or TI-92 Plus has a purchased feature upgrade, the upgrade must be purchased for the receiving unit. A certificate can then be downloaded and installed on the receiving unit.
Transferring Product Software (continued) During the transfer, the receiving unit shows how the transfer is progressing. When the transfer is complete: ¦ The sending unit returns to the VAR-LINK screen. ¦ The receiving unit returns to the Home screen. You may need to use ¥ | (lighten) or ¥ « (darken) to adjust the contrast. Do Not Attempt to Cancel a Product Software (Base Code) Transfer After the transfer starts, the receiving unit’s existing base code is effectively deleted.
Error Messages Most error messages are displayed on the sending unit. Depending on when the error occurs during the transfer process, you may see an error message on the receiving unit. Error Message Description The sending and receiving units are not connected properly, or the receiving unit is not set up to receive. The certificate on the receiving unit is not valid for the product software (base code) on the sending unit. You must obtain and install a valid certificate.
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 / TI-92 Plus calculators. ID Lists and Group Certificates The ID list feature provides a convenient way to collect calculator IDs for group purchase of commercial applications. After the IDs are collected, transmit them to Texas Instruments so a group certificate can be issued.
Transmitting the ID List to a Computer After all the IDs are collected onto one calculator, use the TI-GRAPH LINKé software and a computer-to-calculator cable (available separately) to store the ID list on a computer. The ID list can then be sent as an e-mail attachment, or it can be printed and faxed or mailed to Texas Instruments. For complete instructions on how to transmit an ID list from a TI-89 / TI-92 Plus to a computer, refer to the TI-GRAPH LINK guidebook. The general steps are: 1.
Compatibility between a TI-89, TI-92 Plus, and TI-92 In general, TI-89 and TI-92 Plus data and programs are compatible, with some differences. However, both calculators have incompatibilities with the TI-92. Where possible, data transfer with a TI-92 is allowed. Main Types of Incompatibilities All data is compatible between a TI-89 and TI-92 Plus, but some programs written for one may not run the same on the other because of differences in the calculators’ screen sizes and keyboards.
TI-92 to TI-89 or TI-92 Plus TI-89 or TI-92 Plus to TI-92 All user-defined variables, including functions and programs, can be sent from a TI-92 to a TI-89 or TI-92 Plus. However, they may behave differently. Examples are: ¦ Conflicts between TI-89 / TI-92 Plus system variable, function, and instruction names and TI-92 user-defined names. ¦ Programs or functions that use symbolic local variables.
382 Chapter 22: Linking and Upgrading 22LINK.
Chapter 23: Activities 23 Analyzing the Pole-Corner Problem .................................................... 384 Deriving the Quadratic Formula .......................................................... 386 Exploring a Matrix ................................................................................. 388 Exploring cos(x) = sin(x)...................................................................... 389 Finding Minimum Surface Area of a Parallelepiped..........................
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. Hint: Use proportional sides and the Pythagorean theorem to find the length c with respect to w.
5. Compute the exact maximum length of the pole. Enter: c ( 2 ± ) Hint: Use the auto-paste feature to copy the result from step 4 to the entry line inside the parentheses of c( ) and press ¥ ¸. 6. Compute the approximate maximum length of the pole. Result: Approximately 20.8097 feet. Chapter 23: Activities 23ACTS.
Deriving the Quadratic Formula This activity shows you how to derive the quadratic formula: ë b „ bñ -4ac x= 2a Detailed information about using the functions in this example can be found in Chapter 3: 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.
7. Factor the result using the factor() function. 8. Multiply both sides of the equation by 4añ. 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. Chapter 23: Activities 23ACTS.
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.
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. In the Y= Editor, set y1(x)=cos(x) and 2(x)=sin(x). 2. In the Window Editor, set xmin=0 and xmax=3p. 3. Press „ and select A:ZoomFit. Hint: Press ‡ and select 5:Intersection.
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 Chapter 3: Symbolic Manipulation and Chapter 10: 3D Graphing.
Finding the Minimum Surface Area Analytically Perform the following steps to solve the problem analytically on the Home screen. Hint: Press ¸ to obtain the exact result in symbolic form. Press ¥ ¸ to obtain the approximate result in decimal form. 2. Find the minimum surface area when the value of v equals 300. 1. Solve for x and y in terms of v. Enter: solve(d(sa(x,y,v),x)=0 and d(sa(x,y,v),y)=0,{x,y}) Enter: 300! v Enter: sa(v^(1/3), v^(1/3),v) Chapter 23: Activities 23ACTS.
Running a Tutorial Script Using the Text Editor This activity shows you how to use the Text Editor to run a tutorial script. Detailed information about text operations can be found in Chapter 18: Text Editor. Running a Tutorial Script Perform the following steps to write a script using the Text Editor, test each line, and observe the results in the history area on the Home screen. 1. Open the Text Editor, and create a new variable named demo1.
Note: Press … and select 2:Clear split to go back to a full-sized Text Editor screen. 4. Press † repeatedly to execute each line in the script one at a time. Tip: Press 2 K twice to display the Home screen. 5. To see the results of the script on a full-sized screen, go to the Home screen. Chapter 23: Activities 23ACTS.
Decomposing a Rational Function This activity examines what happens when a rational function is decomposed into a quotient and remainder. Detailed information about the steps used in this example can be found in Chapter 6: Basic Function Graphing and Chapter 3: Symbolic Manipulation. Decomposing a Rational Function To examine the decomposition of the rational function f(x)=(xò ì 10xñ ì x+50)/(xì 2) on a graph: Note: Actual entries are displayed in reverse type in the example screens. 1.
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= y= Note: Be sure the Graph mode is set to Function. [ë 10,15,10] [ë 100,100,10] 8. Draw the graph. 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.
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. Detailed information about using the commands in this example can be found in Chapter 15: Data/Matrix Editor, and Chapter 16: Statistics and Data Plots. 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).
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. Note: Set up several box plots to compare different subsets of the entire data set. 3. Open the „ Plot Setup toolbar menu. 4. Define the plot and filter parameters for Plot 1 as shown in this screen. 5. Copy Plot 1 to Plot 2. 6.
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) Note: Only Plot 1 through Plot 5 should be selected. 8. In the Y= Editor, deselect any functions that may be selected from a previous activity. 9. Display the plots by pressing „ and selecting 9:Zoomdata. 10.
CBL 2/CBL Program for the TI-89 / TI-92 Plus This activity provides a program that can be used when the TI-89 / TI-92 Plus is connected to a Calculator-Based Laboratoryé (CBL 2é/CBL™) unit. This program works with the “Newton’s Law of Cooling” experiment, and is similar to the “Coffee To Go” experiment in the CBL System Experiment Workbook. You can use your computer keyboard to type lengthy text and then use TI-GRAPH LINK to send it to the TI-89 / TI-92 Plus.
Studying the Flight of a Hit Baseball This activity uses the split screen settings to show a parametric graph and a table at the same time to study the flight of a hit baseball. 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.
5. Set the Window variables to: t values= x values= y values= [0,4,.1] [0,300,50] [0,100,10] Hint: Press 2 a. 6. Switch to the right side and display the graph. Hint: Press ¥ &. 7. Display the TABLE SETUP dialog box, and change tblStart to 0 and @tbl to 0.1. Hint: Press ¥ '. 8. Display the table in the left side and press D to highlight t=2. Note: As you move the trace cursor from tc=0.0 to tc=3.1, you will see the position of the ball at time tc. 9. Switch to the right side.
Visualizing Complex Zeros of a Cubic Polynomial This activity describes graphing the complex zeros of a cubic polynomial. Detailed information about the steps used in this example can be found in Chapter 3: Symbolic Manipulation and Chapter 10: 3D Graphing. Visualizing Complex Roots Perform the following steps to expand the cubic polynomial (xì 1)(xì i)(x+i), find the absolute value of the function, graph the modulus surface, and use the Trace tool to explore the modulus surface. 1.
Note: Calculating and drawing the graph takes about three minutes. 6. In the Y=Editor, press: TI-89: ¥ Í TI-92 Plus: ¥ F and set the Graph Format variables to: Axes= ON Labels= ON Style= HIDDEN SURFACE 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.
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.
Computing the Time-Value-of-Money This activity creates a function that can be used to find the cost of financing an item. Detailed information about the steps used in this example can be found in Chapter 17: Programming.
Finding Rational, Real, and Complex Factors This activity shows how to find rational, real, or complex factors of expressions. Detailed information about the steps used in this example can be found in Chapter 3: Symbolic Manipulation. Finding Factors Enter the expressions shown below on the Home screen. 1. factor(x^3ì 5x) ¸ displays a rational result. 2. factor(x^3+5x) ¸ displays a rational result. 3. factor(x^3ì 5x,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 Chapter 17: Programming. Sampling-withoutReplacement 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.
408 Chapter 23: Activities 23ACTS.
Appendix A: Functions and Instructions Quick-Find Locator ................................................................................ 410 Alphabetical Listing of Operations ...................................................... 414 A This appendix describes the syntax and the action of each TI-89 / TI-92 Plus function and instruction. Name of the function or instruction. Key or menu for entering the name. You can also type the name.
Quick-Find Locator This section lists the TI-89 / TI-92 Plus functions and instructions in functional groups along with the page numbers where they are described in this appendix.
Math Matrices + (add) à (divide) ! (factorial) ¡ (degree) 526 527 531 535 _ (underscore) 536 539 0b, 0h 432 4DD 456 4Hex 506 4Sphere 415 angle() 422 conj() 424 cosh() 441 e^() 451 fpart() 458 int() 459 isPrime() 465 log() 469 mod() 476 P4Rx() 487 R4Pq() 490 remain() 499 shift() 501 sinê() 510 tan() 511 tanhê() 538 xê ì (subtract) ë (negate) ‡() (sqr.
Programming = ≤ # (indirection) and ClrErr ClrIO CustmOff Cycle DelVar DispG DropDown EndCustm EndFunc EndPrgm EndWhile Exit Func getConfg() getMode() Goto InputStr left() Loop NewProb Output Pause Prompt Return SendCalc setGraph() setUnits() switch() Then Try when() 529 530 534 414 420 421 428 429 434 438 440 443 443 443 443 444 451 452 453 455 458 460 466 472 476 479 482 491 494 495 497 509 513 515 517 ≠ > ! (store) ans() ClrGraph ClrTable CustmOn Define Dialog DispHome Else EndDlog EndIf EndTBar entry
Strings & (append) dim() inString() ord() shift() 532 437 458 476 499 # (indirection) expr() left() right() string() 534 446 460 491 508 char() format() mid() rotate() Appendix A: Functions and Instructions 419 450 468 491 413 8992APPA.
Alphabetical Listing of Operations Operations whose names are not alphabetic (such as +, !, and >) are listed at the end of this appendix, starting on page 526. 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 TI-89: 2 ˆ Style = 3:Square TI-92 Plus: 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) ⇒ approx(p) ¸ value 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) ⇒ matrix augment(matrix1; matrix2) ⇒ matrix 1 2 [3 4] 5 [6] [1,2;3,4]!M1 ¸ 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.
BldData CATALOG BldData [dataVar] Creates data variable dataVar based on the information used to plot the current graph. BldData is valid in all graphing modes. 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(a^3ùx^2+aùx^2+a^3+a) ¸ aø(a + ëi)ø(a + i)ø(x + ëi)ø(x + i) 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.
Circle CATALOG Circle x, y, r [, drawMode] Draws a circle with its center at window coordinates (x, y) and with a radius of r. In a ZoomSqr viewing window: ZoomSqr:Circle 1,2,3 ¸ 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.
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. For functions such as solve() that return arbitrary constants or integers (@1, @2, etc.), ClrHome resets the suffix to 1. ClrIO CATALOG ClrIO Clears the Program I/O screen. ClrTable CATALOG ClrTable Clears all table values.
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() TI-89: 2 X key cos(expression1) ⇒ cos(list1) ⇒ list TI-92 Plus: X key In Degree angle mode: expression 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 either a degree or radian angle, according to the current angle mode setting. You can use ó or ô to override the angle mode temporarily.
cosê () TI-89: ¥ R key cosê (expression1) ⇒ cosê (list1) ⇒ list TI-92 Plus: 2 R key expression In Degree angle mode: cosê (1) ¸ cosê (expression1) returns the angle whose cosine is expression1 as an expression. cosê (list1) returns a list of the inverse cosines of each element of list1. In Radian angle mode: cosê ({0,.2,.5}) ¸ p {2 Note: The result is returned as either a degree or radian angle, according to the current angle mode setting.
⇒ coshê(squareMatrix1) squareMatrix Returns the matrix inverse hyperbolic cosine of squareMatrix1. This is not the same as calculating the inverse hyperbolic cosine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. crossP() In Radian angle mode and Rectangular complex format mode: coshê([1,5,3;4,2,1;6,ë 2,1]) ¸ .486…ì.725…øi ë.322…ì 2.083…øi 2.525…+1.734…øi ë.009…ì 1.
cSolve() starts with exact symbolic methods. Except in EXACT mode, cSolve() also uses iterative approximate complex polynomial factoring, if necessary. Display Digits mode in Fix 2: exact(cSolve(x^5+4x^4+5x ^3ì6xì3=0,x)) ¸ cSolve(ans(1),x) ¸ Note: See also cZeros(), solve(), and zeros(). Note: If equation is non-polynomial with functions such as abs(), angle(), conj(), real(), or imag(), you should place an underscore _ (TI-89: ¥ TI-92 Plus: 2 ) at the end of var.
Simultaneous polynomial equations can have extra variables that have no values, but represent given numeric values that could be substituted later. cSolve(u_ù v_ì u_=c_ù v_ and v_^2=ë u_,{u_,v_}) ¸ 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. The suffix resets to 1 when you use ClrHome or ƒ 8:Clear Home.
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.
Custom 2 ¾ key Program listing: Custom block EndCustm Sets up a toolbar that is activated when you press 2 ¾. It is very similar to the ToolBar instruction except that Title and Item statements cannot have labels. block can be either a single statement or a series of statements separated with the “:” character. Note: 2 ¾ acts as a toggle. The first instance invokes the menu, and the second instance removes the menu. The menu is removed also when you change applications.
cZeros() MATH/Algebra/Complex menu cZeros(expression, var) ⇒ Display Digits mode in Fix 3: list Returns a list of candidate real and non-real values of var that make expression=0. cZeros() does this by computing exp8list(cSolve(expression=0,var),var). Otherwise, cZeros() is similar to zeros(). cZeros(x^5+4x^4+5x^3ì 6xì 3,x) ¸ {ë 2.125 ë.612 .965 ë 1.114 ì 1.073ø i ë 1.114 + 1.073ø i} Note: See also cSolve(), solve(), and zeros().
Simultaneous polynomials can have extra variables that have no values, but represent given numeric values that could be substituted later. cZeros({u_ùv_ìu_ì(c_ùv_), v_^2+u_},{u_,v_}) ¸ You can also include unknown variables that do not appear in the expressions. These zeros show how families of zeros might contain arbitrary constants of the form @k, where k is an integer suffix from 1 through 255. The suffix resets to 1 when you use ClrHome or ƒ 8:Clear Home.
d() 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. If the order is less than zero, the result will be an anti-derivative.
Zero, not the letter O, followed by b or h. 0b binaryNumber 0h hexadecimalNumber A binary number can have up to 32 digits. A hexadecimal number can have up to 8. Without a prefix, integer1 is treated as decimal. The result is displayed in decimal, regardless of the Base mode. 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.
Define progName(arg1Name, arg2Name, ...) = Prgm block EndPrgm Creates progName as a program or subprogram, but cannot return a result using Return. Can execute a block of multiple statements. block can be either a single statement or a series of statements separated with the “:” character. block also can include expressions and instructions (such as If, Then, Else, and For) without restrictions. Define listinpt()=prgm:Local n,i,str1,num:InputStr "Enter name of list",str1:Input "No.
Apply solve() to an implicit solution if you want to try to convert it to one or more equivalent explicit solutions. deSolve(y'=(cos(y))^2ù x,x,y) ¸ xñ tan(y)= +@3 2 When comparing your results with textbook or manual solutions, be aware that different methods introduce arbitrary constants at different points in the calculation, which may produce different general solutions.
deSolve(2ndOrderOde and boundaryCondition1 and boundaryCondition2, independentVar, dependentVar) ⇒ a particular solution deSolve(w''ì 2w'/x+(9+2/x^2)w= xù e^(x) and w(p/6)=0 and w(p/3)=0,x,w) ¸ Returns a particular solution that satisfies 2ndOrderOde and has specified values at two different points. p e 3øxøcos(3øx) w= 10 p 6 e øxøsin(3øx) ì det() + 10 x⋅e x 10 MATH/Matrix menu det([a,b;c,d]) ¸ aø d ì bø c Returns the determinant of squareMatrix.
Dialog CATALOG Program listing: Dialog block EndDlog Generates a dialog box when the program is executed. block can be either a single statement or a series of statements separated with the “:” character. Valid block options in the … I/O, 1:Dialog menu item in the Program Editor are 1:Text, 2:Request, 4:DropDown, and 7:Title.
DispG CATALOG In function graphing mode: DispG Displays the current contents of the Graph screen. DispHome © :5ù cos(x)! y1(x) :ë 10! xmin :10! xmax :ë 5! ymin :5! ymax :DispG © CATALOG DispHome Displays the current contents of the Home screen. DispTbl Program segment: Program segment: © :Disp "The result is: ",xx :Pause "Press Enter to quit" :DispHome :EndPrgm CATALOG DispTbl Displays the current contents of the Table screen.
dotP() MATH/Matrix/Vector ops menu dotP(list1, list2) ⇒ dotP({a,b,c},{d,e,f}) ¸ aø d + bø e + cø f expression Returns the “dot” product of two lists. dotP({1,2},{5,6}) ¸ dotP(vector1, vector2) ⇒ expression Returns the “dot” product of two vectors. Both must be row vectors, or both must be column vectors. DrawFunc 17 dotP([a,b,c],[d,e,f]) ¸ aø d + bø e + cø f dotP([1,2,3],[4,5,6]) ¸ 32 CATALOG DrawFunc expression Draws expression as a function, using x as the independent variable.
DrawPol CATALOG DrawPol expression[, qmin] [, qmax] [, qstep] Draws the polar graph of expression, using q as the independent variable. Defaults for qmin, qmax, and qstep are the current settings for the Window variables qmin, qmax, and qstep. Specifying values does not alter the window settings. If the current graphing mode is not polar, these three arguments are required. In function graphing mode and ZoomStd window: DrawPol 5ù cos(3ù q),0,3.5,.1 ¸ Note: Regraphing erases all drawn items.
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.
e^(squareMatrix1) ⇒ squareMatrix e^([1,5,3;4,2,1;6,ë 2,1]) ¸ Returns the matrix exponential of squareMatrix1. This is not the same as calculating e raised to the power of each element. For information about the calculation method, refer to cos(). 782.209 680.546 524.929 559.617 488.795 371.222 456.509 396.521 307.879 squareMatrix1 must be diagonalizable. The result always contains floating-point numbers.
EndCustm See Custom, page 429. EndDlog See Dialog, page 437. EndFor See For, page 450. EndFunc See Func, page 451. EndIf See If, page 456. EndLoop See Loop, page 466. EndPrgm See Prgm, page 481. EndTBar See ToolBar, page 515. EndTry See Try, page 515. EndWhile See While, page 518. entry() CATALOG entry() ⇒ expression entry(integer) ⇒ expression On the Home screen: Returns a previous entry-line entry from the Home screen history area.
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: education.ti.com Warning: Exec gives you access to the full power of the microprocessor.
expand() MATH/Algebra menu expand((x+y+1)^2) ¸ xñ + 2ø xø y + 2ø x + yñ + 2ø y + 1 expand(expression1 [, var]) ⇒ expression expand(list1 [,var]) ⇒ list expand(matrix1 [,var]) ⇒ matrix expand(expression1) returns expression1 expanded with respect to all its variables. The expansion is polynomial expansion for polynomials and partial fraction expansion for rational expressions.
expand(expression1,[var]) also distributes logarithms and fractional powers regardless of var. For increased distribution of logarithms and fractional powers, inequality constraints might be necessary to guarantee that some factors are nonnegative. expand(expression1, [var]) also distributes absolute values, sign(), and exponentials, regardless of var. Note: See also tExpand() for trigonometric angle-sum and multiple-angle expansion.
factor() MATH/Algebra menu factor(expression1[, var]) ⇒ expression factor(list1[,var]) ⇒ list factor(matrix1[,var]) ⇒ matrix factor(a^3ù x^2ì aù x^2ì a^3+a) ¸ aø(a ì1)ø(a + 1)ø(x ì1)ø(x + 1) factor(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 without introducing new non-real subexpressions.
factor(rationalNumber) returns the rational number factored into primes. For composite numbers, the computing time grows exponentially with the number of digits in the second-largest factor. For example, factoring a 30-digit integer could take more than a day, and factoring a 100-digit number could take more than a century. factor(152417172689) ¸ 123457ø1234577 isPrime(152417172689) ¸false Note: To stop (break) a computation, press ´.
Use the “|” operator to restrict the solution interval and/or specify the sign of other undefined variables. fMax(.5x^3ì xì 2,x)|x1 ¸ For the APPROX setting of the Exact/Approx mode, fMax() iteratively searches for one approximate local maximum. This is often faster, particularly if you use the “|” operator to constrain the search to a relatively small interval that contains exactly one local maximum. fMax(aù x^2,x) ¸ x = ˆ or x = ë ˆ or x = 0 or a = 0 x = ë.816...
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. For CATALOG Program segment: For var, low, high [, step] block EndFor Executes the statements in block iteratively for each value of var, from low to high, in increments of step.
fpart() MATH/Number menu fpart(ë 1.234) ¸ fpart(expression1) ⇒ expression fpart(list1) ⇒ list fpart(matrix1) ⇒ matrix Returns the fractional part of the argument. ë.234 fpart({1, ë 2.3, 7.003}) ¸ {0 ë.3 .003} For a list or matrix, returns the fractional parts of the elements. The argument can be a real or a complex number. Func CATALOG In function graphing mode, define a piecewise function: Func block EndFunc Required as the first statement in a multistatement function definition.
GetCalc 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. Note: To get a variable to the link port from another unit, use 2 ° on the other unit to select and send a variable, or do a SendCalc on the other unit. getConfg() © :Disp "Press Enter when ready" :Pause :GetCalc L1 :Disp "List L1 received" © CATALOG getConfg() ⇒ ListPairs TI-89: Returns a list of calculator attributes.
getFold() CATALOG getFold() ⇒ nameString Returns the name of the current folder as a string. getKey() "main" getFold()! oldfoldr ¸ "main" oldfoldr ¸ "main" CATALOG getKey() ⇒ Program listing: integer Returns the key code of the key pressed. Returns 0 if no key is pressed. The prefix keys (shift ¤, second function 2, option ¥, alpha j, and drag ‚) are not recognized by themselves; however, they modify the keycodes of the key that follows them. For example: ¥ Ù ƒ Ù ƒ 2 Ù.
getType() CATALOG getType(var) ⇒ string Returns a string indicating the data type of variable var. If var has not been defined, returns the string "NONE".
Goto CATALOG Program segment: Goto labelName © :0! temp :1! i :Lbl TOP : temp+i! temp : If i<10 Then : i+1! i : Goto TOP : EndIf :Disp temp © Transfers program control to the label labelName. labelName must be defined in the same program using a Lbl instruction. Graph CATALOG Graph expression1[, expression2] [, var1] [, var2] The Smart Graph feature graphs the requested expressions/ functions using the current graphing mode.
4Hex MATH/Base menu integer1 4Hex ⇒ integer Converts integer1 to a hexadecimal number. Binary or hexadecimal numbers always have a 0b or 0h prefix, respectively. 256 4Hex ¸ 0h100 0b111100001111 4Hex ¸ 0hF0F Zero, not the letter O, followed by b or h. 0b binaryNumber 0h hexadecimalNumber A binary number can have up to 32 digits. A hexadecimal number can have up to 8. Without a prefix, integer1 is treated as decimal (base 10). The result is displayed in hexadecimal, regardless of the Base mode.
Program segment: If Boolean expression1 Then block1 ElseIf Boolean expression2 Then block2 © ElseIf Boolean expressionN Then blockN EndIf Allows for program branching. If Boolean expression1 evaluates to true, executes block1. If Boolean expression1 evaluates to false, evaluates Boolean expression2, etc.
InputStr CATALOG Program segment: InputStr [promptString,] var Pauses the program, displays promptString on the Program I/O screen, waits for you to enter a response, and stores your response as a string in variable var. © :InputStr "Enter Your Name",str1 © If you omit promptString, “?” is displayed as a prompt. Note: The difference between Input and InputStr is that InputStr always stores the result as a string so that “ ” are not required.
iPart() MATH/Number menu iPart(ë 1.234) ¸ iPart(number) ⇒ integer iPart(list1) ⇒ list iPart(matrix1) ⇒ matrix Returns the integer part of the argument. ë 1. iPart({3/2,ë 2.3,7.003}) ¸ {1 ë 2. 7.} For lists and matrices, returns the integer part of each element. The argument can be a real or a complex number. 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 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 floating-point numbers is their product. lcm(6,9) ¸ 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 LineTan expression1, expression2 Displays the Graph screen and draws a line tangent to expression1 at the point specified. expression1 is an expression or the name of a function, where x is assumed to be the independent variable, and expression2 is the x value of the point that is tangent. In function graphing mode and a ZoomTrig window: Graph cos(x) TI-89: " TI-92 Plus: ¥ " LineTan cos(x),p/4 ¸ Note: In the example shown, expression1 is graphed separately.
list4mat() MATH/List menu list4mat(list [, elementsPerRow]) ⇒ list4mat({1,2,3}) ¸ matrix Returns a matrix filled row-by-row with the elements from list. [1 2 3] list4mat({1,2,3,4,5},2) ¸ 1 2 3 4 5 0 elementsPerRow, if included, specifies the number of elements per row. Default is the number of elements in list (one row). If list does not fill the resulting matrix, zeros are added.
LnReg MATH/Statistics/Regressions menu LnReg list1, list2[, [list3] [, list4, list5]] Calculates the logarithmic 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.
log() CATALOG log(expression1) ⇒ log(list1) ⇒ list log(2.0) ¸ expression .301... If complex format mode is REAL: Returns the base-10 logarithm of the argument. For a list, returns the base-10 logs of the elements. log({ë 3,1.2,5}) ¸ Error: Non-real result If complex format mode is RECTANGULAR: log({ë 3,1.2,5}) ¸ p ln(3) ln(5) {ln(10) + ln(10) øi .079... ln(10)} log(squareMatrix1) ⇒ squareMatrix Returns the matrix base-10 logarithm of squareMatrix1.
Loop CATALOG Program segment: Loop block EndLoop Repeatedly executes the statements in block. Note that the loop will be executed endlessly, unless a Goto or Exit instruction is executed within block. block is a sequence of statements separated with the “:” character.
mat4list() MATH/List menu ⇒ mat4list(matrix) mat4list([1,2,3]) ¸ list 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 MedMed list1, list2[, [list3] [, list4, list5]] In function graphing mode: 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 1 2 ...} {0,2,3,4,3,4,6}! L2 ¸ {0 2 3 ... MedMed L1,L2 ¸ Done ShowStat ¸ list1 represents xlist. list2 represents ylist. list3 represents frequency. list4 represents category codes. list5 represents category include list.
min() MATH/List menu min(2.3,1.4) ¸ min(expression1, expression2) ⇒ expression min(list1, list2) ⇒ list min(matrix1, matrix2) ⇒ matrix min({1,2},{ë 4,3}) ¸ 1.4 {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) ⇒ min({0,1,ë 7,1.3,.5}) ¸ expression ë7 Returns the minimum element of list.
mRowAdd() MATH/Matrix/Row ops menu mRowAdd(expression, matrix1, index1, index2) ⇒ matrix Returns a copy of matrix1 with each element in row index2 of matrix1 replaced with: expression × row index1 + row index2 nCr() mRowAdd(ë 3,[1,2;3,4],1,2) ¸ 1 2 [0 L2] mRowAdd(n,[a,b;c,d],1,2) ¸ a b [aø n+c bø n+d] 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 tak
NewData CATALOG NewData dataVar, list1[, list2] [, list3]... Creates data variable dataVar, where the columns are the lists in order. Must have at least one list. list1, list2, ..., listn can be lists as shown, NewData mydata,{1,2,3},{4,5,6} ¸ Done (Go to the Data/Matrix Editor and open the var mydata to display the data variable below.) expressions that resolve to lists, or list variable names. NewData makes the new variable current in the Data/Matrix Editor.
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 ¸ PlotsOff ¸ {1 2 {1,2,3,4}! L1 ¸ {2 3 {2,3,4,5}! L2 ¸ NewPlot 1,1,L1,L2,,,,4 ¸ Done Done 3 4} 4 5} Done Press ¥ % to display: mark specifies the display type of the mark.
The goal is six significant digits. The adaptive algorithm terminates when it seems likely that the goal has been achieved, or when it seems unlikely that additional samples will yield a worthwhile improvement. A warning is displayed (“Questionable accuracy”) when it seems that the goal has not been achieved. Nest nInt() to do multiple numeric integration. Integration limits can depend on integration variables outside them. nInt(cos(x),x,ë p,p+1í ë 12) ¸ ë 1.041...
nPr() MATH/Probability menu nPr(expression1, expression2) ⇒ expression For integer expression1 and expression2 with expression1 ‚ expression2 ‚ 0, nPr() is the number of permutations of expression1 things taken expression2 at a time. Both arguments can be integers or symbolic expressions. nPr(expression, 0) ⇒ nPr(z,3) ¸ zø (zì 2)ø (zì 1) ans(1)|z=5 ¸ 1 nPr(z,ë 3) ¸(z+1)ø (z+2)ø (z+3) nPr(z,c) ¸ 1 nPr(expression, negInteger) ⇒ 1/((expression+1)ø (expression+2)...
OneVar MATH/Statistics menu OneVar list1 [[, list2] [, list3] [, list4]] Calculates 1-variable statistics and updates all the system statistics variables. {0,2,3,4,3,4,6}! L1 ¸ OneVar L1 ¸ ShowStat ¸ Done x‚3 or x‚4 ¸ x‚3 All the lists must have equal dimensions except for list4. list1 represents xlist. list2 represents frequency. list3 represents category codes. list4 represents category include list.
ord() MATH/String menu ord(string) ⇒ integer ord(list1) ⇒ list Returns the numeric code of the first character in character string string, or a list of the first characters of each list element. See Appendix B for a complete listing of character codes.
part() CATALOG part(expression1[ ,nonNegativeInteger]) This advanced programming function lets you identify and extract all of the subexpressions in the simplified result of expression1. For example, if expression1 simplifies to cos(pù x+3): • The cos() function has one argument: (pù x+3). • The sum of (pù x+3) has two operands: pù x and 3. • The number 3 has no arguments or operands. • The product pù x has two operands: p and x. • The variable x and the symbolic constant p have no arguments or operands.
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 sub-expressions. Note: When using part(), do not rely on any particular order in sums and products.
The example Program Editor function to the right uses getType() and part() to partially implement symbolic differentiation. Studying and completing this function can help teach you how to differentiate manually. You could even include functions that the TI-89 / TI-92 Plus cannot differentiate, such as Bessel functions.
PlotsOff CATALOG PlotsOff [1] [, 2] [, 3] ... [, 9] Turns off the specified plots for graphing. When in 2-graph mode, only affects the active graph. PlotsOff 1,2,5 ¸ Done PlotsOff ¸ Done PlotsOn 2,4,5 ¸ Done PlotsOn ¸ Done If no parameters, then turns off all plots. PlotsOn CATALOG PlotsOn [1] [, 2] [, 3] ... [, 9] Turns on the specified plots for graphing. When in 2-graph mode, only affects the active graph. If you do not include any arguments, turns on all plots.
PopUp CATALOG PopUp itemList, var Displays a pop-up menu containing the character strings from itemList, waits for you to select an item, and stores the number of your selection in var. PopUp {"1990","1991","1992"},var1 ¸ The elements of itemList must be character strings: {item1String, item2String, item3String, ...} If var already exists and has a valid item number, that item is displayed as the default choice. itemList must contain at least one choice.
product() MATH/List menu product(list[, start[, end]]) ⇒ expression Returns the product of the elements contained in list. Start and end are optional. They specify a range of elements. product(matrix1[, start[, end]]) ⇒ matrix Returns a row vector containing the products of the elements in the columns of matrix1. Start and end are optional. They specify a range of rows.
PtOff CATALOG PtOff 2,4 ¸ PtOff x, y PtOff xList, yList Displays the Graph screen and turns off the screen pixel nearest to window coordinates (x, y). PtOn CATALOG PtOn 3,5 ¸ PtOn x, y PtOn xList, yList Displays the Graph screen and turns on the screen pixel nearest to window coordinates (x, y). ptTest() CATALOG ptTest (x, y) ⇒ Boolean constant expression ptTest (xList, yList) ⇒ Boolean constant expression ptTest(3,5) ¸ true Returns true or false.
PxlHorz CATALOG PxlHorz row [, drawMode] PxlHorz 25,1 ¸ Displays the Graph screen and draws a horizontal line at pixel position row. If drawMode = 1, draws the line (default). If drawMode = 0, turns off the line. If drawMode = -1, turns a line that is on to off or off to on (inverts pixels along the line). Note: Regraphing erases all drawn items. See also LineHorz.
PxlText CATALOG PxlText string, row, col TI-89: PxlText "sample Displays the Graph screen and places character string string on the screen, starting at pixel coordinates (row, col). text",20,10 ¸ TI-92 Plus: PxlText "sample text",20,50 ¸ string is positioned with the upper-left corner of its first character at the coordinates. Note: Regraphing erases all drawn items. PxlVert CATALOG PxlVert 50,1 ¸ PxlVert col [, drawMode] Draws a vertical line down the screen at pixel position col.
The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using Gram-Schmidt. The columns in qMatName are the orthonormal basis vectors that span the space defined by matrix.
QuartReg 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. 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.
rand() MATH/Probability menu rand([n]) ⇒ RandSeed 1147 ¸ expression n is an integer ƒ zero. (Sets the random-number seed.) With no parameter, returns the next random number between 0 and 1 in the sequence. When an argument is positive, returns a random integer in the interval [1, n]. When an argument is negative, returns a random integer in the interval [ë n,ë 1]. randMat() Done rand() ¸ rand(6) ¸ rand(ë 100) ¸ .158...
RclPic CATALOG RclPic picVar [, row, column] Displays the Graph screen and adds the picture stored in picVar at the upper left-hand corner pixel coordinates (row, column) using OR logic. picVar must be a picture data type. Default coordinates are (0, 0). real() MATH/Complex menu ⇒ real(2+3i) ¸ 2 Returns the real part of the argument. real(z) ¸ z Note: All undefined variables are treated as real variables. See also imag().
ref() MATH/Matrix menu ref(matrix1[, tol]) ⇒ matrix Returns the row echelon form of matrix1. 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. Otherwise, tol is ignored. • If you use ¥ ¸ or set the mode to Exact/Approx=APPROXIMATE, computations are done using floating-point arithmetic.
Return CATALOG Return [expression] Returns expression as the result of the function. Use within a Func...EndFunc block, or Prgm...EndPrgm block. Note: Use Return without an argument to exit a program. Define factoral(nn)=Func :local answer,count:1! answer :For count,1,nn :answerù count! answer:EndFor :Return answer:EndFunc ¸ Done factoral(3) ¸ 6 Note: Enter the text as one long line on the Home screen (without line breaks).
⇒ rotate(list1[,#ofRotations]) In Dec base mode: list Returns a copy of list1 rotated right or left by #of Rotations elements. Does not alter list1. rotate({1,2,3,4}) ¸ 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 element). rotate({1,2,3,4},ë 2) ¸ {3 4 1 2} ⇒ rotate(string1[,#ofRotations]) string Returns a copy of string1 rotated right or left by #of Rotations characters.
rowNorm() MATH/Matrix/Norms menu rowNorm(matrix) ⇒ expression Returns the maximum of the sums of the absolute values of the elements in the rows in matrix. rowNorm([-5,6,-7;3,4,9;9,-9,-7]) 25 ¸ Note: All matrix elements must simplify to numbers. See also colNorm(). 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.
Send CATALOG Program segment: Send list CBL 2é/CBLé (Calculator-Based Laboratoryé) or CBRé (Calculator-Based Rangeré) instruction. Sends list to the link port. SendCalc © :Send {1,0} :Send {1,2,1} © CATALOG Program segment: SendCalc var Sends variable var to the link port, where another unit linked to that port can receive the variable value. The receiving unit must be on the Home screen or must execute GetCalc from a program.
setFold() CATALOG setFold(newfolderName) ⇒ oldfolderString Returns the name of the current folder as a string and sets newfolderName as the current folder. newFold chris ¸ Done setFold(main) ¸ "chris" setFold(chris)! oldfoldr ¸ "main" The folder newfolderName must exist.
setMode() CATALOG setMode(modeNameString, settingString) setMode(list) ⇒ stringList ⇒ string Sets mode modeNameString to the new setting settingString, and returns the current setting of that mode. modeNameString is a character string that specifies which mode you want to set. It must be one of the mode names from the table below. settingString is a character string that specifies the new setting for the mode. It must be one of the settings listed below for the specific mode you are setting.
setTable() CATALOG setTable(modeNameString, settingString) ⇒ string Sets the table parameter modeNameString to settingString, and returns the previous setting of the parameter. Storing the previous setting lets you restore it later. modeNameString is a character string that specifies which parameter you want to set. It must be one of the parameters from the table below. settingString is a character string that specifies the new setting for the parameter.
Shade CATALOG 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.) In the ZoomTrig viewing window: 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.
shift() CATALOG shift(integer1[,#ofShifts]) ⇒ In Bin base mode: integer Shifts the bits in a binary integer. You can enter integer1 in any number base; it is converted automatically to a signed, 32-bit binary form. If the magnitude of integer1 is too large for this form, a symmetric modulo operation brings it within the range. If #ofShifts is positive, the shift is to the left. If #ofShifts is negative, the shift is to the right. The default is ë 1 (shift right one bit).
ShowStat CATALOG ShowStat Displays a dialog box containing the last computed statistics results if they are still valid. Statistics results are cleared automatically if the data to compute them has changed. {1,2,3,4,5}! L1 ¸ {1 2 3 4 5} {0,2,6,10,25}! L2 ¸ {0 2 6 10 25} TwoVar L1,L2 ¸ ShowStat ¸ Use this instruction after a statistics calculation, such as LinReg. sign() MATH/Number menu sign(ë 3.
simult(coeffMatrix, constMatrix[, tol]) ⇒ matrix Solves multiple systems of linear equations, where each system has the same equation coefficients but different constants. Each column in constMatrix must contain the constants for a system of equations. Each column in the resulting matrix contains the solution for the corresponding system.
sinê(squareMatrix1) ⇒ squareMatrix Returns the matrix inverse sine of squareMatrix1. This is not the same as calculating the inverse sine of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. sinh() In Radian angle mode and Rectangular complex format mode: sinê([1,5,3;4,2,1;6,ë 2,1]) ¸ ë.164…ì.064…øi .725…ì 1.515…øi 2.083…ì 2.632…øi 1.490…ì 2.105…øi … .947…ì.778…øi … ë 1.790…+1.
SinReg MATH/Statistics/Regressions menu SinReg list1, list2 [ , [iterations] , [ period] [, list3, list4] ] Calculates the sinusoidal regression and updates all the system statistics variables. All the lists must have equal dimensions except for list4. list1 represents xlist. list2 represents ylist. list3 represents category codes. list4 represents category include list. In function graphing mode: seq(x,x,1,361,30)! L1 ¸ {1 31 61 …} {5.5,8,11,13.5,16.5,19,19.5,17, 14.5,12.5,8.5,6.5,5.5}! L2 ¸ {5.
For the EXACT setting of the Exact/Approx mode, portions that cannot be solved are returned as an implicit equation or inequality. exact(solve((xì a)e^(x)=ë xù (xì a),x)) ¸ e x + x = 0 or x = a Use the “|” operator to restrict the solution interval and/or other variables that occur in the equation or inequality. When you find a solution in one interval, you can use the inequality operators to exclude that interval from subsequent searches.
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. solve(e^(z)ù y=1 and ë y=sin(z),{y,z=2p}) ¸ y=.001… and z=6.281… Use guesses to seek additional solutions one by one. For convergence, a guess may have to be rather close to a solution. SortA MATH/List menu SortA listName1[, listName2] [, listName3] ... SortA vectorName1[, vectorName2] [, vectorName3] ... Sorts the elements of the first argument in ascending order.
stdDev(matrix1[, freqmatrix]) ⇒ matrix stdDev([1,2,5;-3,0,1;.5,.7,3]) ¸ [2.179... 1.014... 2] Returns a row vector of the standard deviations of the columns in matrix1. Each freqmatrix element counts the number of consecutive occurrences of the corresponding element in matrix1. stdDev([L1.2,5.3;2.5,7.3;6,L4], [4,2;3,3;1,7]) ¸ [2.7005,5.44695] Note: matrix1 must have at least two rows.
string() MATH/String menu string(expression) ⇒ string Simplifies expression and returns the result as a character string. string(1.2345) ¸ string(1+2) ¸ "1.2345" "3" string(cos(x)+‡(3)) ¸ "cos(x) + ‡(3)" 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.
sum(matrix1[, start[, end]]) ⇒ sum([1,2,3;4,5,6]) ¸[5 matrix 7 9] Returns a row vector containing the sums of the elements in the columns in matrix1. sum([1,2,3;4,5,6;7,8,9]) ¸ [12 15 18] Start and end are optional. They specify a sum([1,2,3;4,5,6;7,8,9],2,3) range of rows. ¸ [11,13,15] 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.
Table CATALOG Table expression1[, expression2] [, var1] 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. The currently selected functions in the Y= Editor are temporarily ignored.
tanê () TI-89: ¥ S key tanê (expression1) ⇒ tanê (list1) ⇒ list TI-92 Plus: 2 S key In Degree angle mode: expression tanê (1) ¸ tanê (expression1) returns the angle whose tangent is expression1 as an expression. tanê (list1) returns a list of the inverse tangents of each element of list1. 45 In Radian angle mode: tanê ({0,.2,.5}) ¸ {0 .197... .463...} Note: The result is returned as either a degree or radian angle, according to the current angle mode setting.
tanhê(squareMatrix1) ⇒ squareMatrix Returns the matrix inverse hyperbolic tangent of squareMatrix1. This is not the same as calculating the inverse hyperbolic tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. taylor() In Radian angle mode and Rectangular complex format mode: tanhê([1,5,3;4,2,1;6,ë 2,1]) ¸ ë.099…+.164…øi ë.087…ì.725…øi .511…ì 2.083…øi .267…ì 1.490…øi … .
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(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 tmpCnv(100_¡c,_¡f) ¸ 212.ø_¡F tmpCnv(32_¡f,_¡c) ¸ 0.ø_¡C tmpCnv(0_¡c,_¡k) ¸ 273.15ø_¡K tmpCnv(0_¡f,_¡r) ¸ 459.67ø_¡R Celsius Fahrenheit Kelvin Rankine Note: To select temperature units from a menu, press: For ¡, press 2 “. TI-89: For _ , press ¥ . TI-92 Plus: For _ , press 2 .
Toolbar CATALOG Program segment: 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 TwoVar list1, list2[, [list3] [, list4, list5]] Calculates the TwoVar statistics 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 1 2 ...} {0,2,3,4,3,4,6}! L2 ¸ {0 2 3 ...} TwoVar L1,L2 ¸ Done ShowStat ¸ 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]) ⇒ variance({a,b,c}) ¸ añ -aø (b+c)+bñ -bø c+cñ expression Returns the variance of list. 3 Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Note: list must contain at least two elements. variance(matrix1[, freqmatrix]) ⇒ matrix variance({1,2,5,ë 6,3,ë 2}) ¸ 31/2 variance({1,3,5},{4,6,2}) ¸ 68/33 variance([1,2,5;ë 3,0,1; .5,.7,3]) ¸ [4.75 1.
Nest when() to define expressions that have more than two pieces. TI-89: " TI-92 Plus: ¥ " ClrGraph ¸ Done Graph when(x<0,when(x<ë p, 4ù sin(x),2x+3),5ì x^2) ¸ when() is helpful for defining recursive functions. when(n>0,nù factoral(nì 1),1) Done ! factoral(n) ¸ factoral(3) ¸ 6 3! ¸ While 6 CATALOG 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.
integer1 xor integer2 ⇒ In Hex base mode: integer Compares two real integers bit-by-bit using an xor operation. Internally, both integers are converted to signed, 32-bit binary numbers. When corresponding bits are compared, the result is 1 if either bit (but not both) is 1; the result is 0 if both bits are 0 or both bits are 1. The returned value represents the bit results, and is displayed according to the Base mode. You can enter the integers in any number base.
zeros({expression1, expression2}, {varOrGuess1, varOrGuess2 [, … ]}) ⇒ matrix Returns candidate real zeros of the simultaneous algebraic expressions, where each varOrGuess specifies an unknown whose value you seek. 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.
For polynomial systems, computation time or memory exhaustion may depend strongly on the order in which you list unknowns. If your initial choice exhausts memory or your patience, try rearranging the variables in the expressions and/or varOrGuess list. If you do not include any guesses and if any expression is non-polynomial in any variable but all expressions are linear in the unknowns, zeros() uses Gaussian elimination to attempt to determine all real zeros.
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 ¸ {1 2 3 4} {2 3 4 5} {2,3,4,5}! L2 ¸ newPlot 1,1,L1,L2 ¸ Done ZoomStd ¸ Note: Does not adjust ymin and ymax for histograms. TI-89: " TI-92 Plus: ¥ " 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 TI-89: " TI-92 Plus: ¥ " 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.
+ (add) « key expression1 + expression2 ⇒ expression Returns the sum of expression1 and expression2. 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.
⇒ ⇒ expression - matrix1 matrix1 - expression 20ì [1,2;3,4] ¸ matrix matrix 19 [ë 3 expression ì matrix1 returns a matrix of expression times the identity matrix minus matrix1. matrix1 must be square. ë2 16] matrix1 ì expression returns a matrix of expression times the identity matrix subtracted from matrix1. matrix1 must be square. Note: Use .. (dot minus) to subtract an expression from each element.
expression à list1 ⇒ list list1 à expression ⇒ list a/{3,a,‡(a)} ¸ Returns a list containing the quotients of expression divided by list1 or list1 divided by a { 3 1 ‡a} {a,b,c}/(aù bù c) ¸ expression. 1 {bø c matrix1 à expression ⇒ matrix 1 aø c 1 aø b} 1 aø c 1 aø b] [a,b,c]/(aù bù c) ¸ Returns a matrix containing the quotients of matrix1àexpression. 1 [bø c Note: Use . / (dot divide) to divide an expression by each element.
= (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.
.. (dot subt.) ¶ | keys [a,2;b,3].ì [c,4;d,5] ¸ x.ì [c,4;d,5] ¸ matrix1 .ì matrix2 ⇒ matrix expression .ì matrix1 ⇒ matrix matrix1 .ì matrix2 returns a matrix that is the difference between each pair of corresponding elements in matrix1 and matrix2. expression .ì matrix1 returns a matrix that is the difference of expression and each element in matrix1. .ù (dot mult.) ¶ p keys [a,2;b,3].ù [c,4;5,d] ¸ matrix1 .ù matrix2 ⇒ matrix expression .ù matrix1 ⇒ matrix x.ù [a,b;c,d] ¸ matrix1 .
& (append) TI-89: ¥ p key string1 & string2 ⇒ TI-92 Plus: 2 H key string Returns a text string that is string2 appended to string1. "Hello " & "Nick" ¸ "Hello Nick" ‰() (integrate) 2 < key ‰(expression1, var[, lower] [,upper]) ⇒ ‰(list1,var [,order]) ⇒ list ‰(matrix1,var [,order]) ⇒ matrix expression aò 3 - 3 bò 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.
‰() can be nested to do multiple integrals. Integration limits can depend on integration variables outside them. ‰(‰(ln(x+y),y,0,x),x,0,a) ¸ Note: See also nInt(). ‡() (square root) 2 ] key ‡ (expression1) ⇒ ‡ (list1) ⇒ list ‡(4) ¸ expression Returns the square root of the argument. 2 ‡({9,a,4}) ¸ {3 ‡a 2} For a list, returns the square roots of all the elements in list1.
^ (power) Z key expression1 ^ expression2 ⇒ list1 ^ list2 ⇒ list expression 4^2 ¸ 16 {a,2,c}^{1,b,3} ¸ {a 2 b cò } Returns the first argument raised to the power of the second argument. 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.
ô (radian) MATH/Angle menu expression1ô ⇒ expression list1ô ⇒ list matrix1ô ⇒ matrix In Degree or Radian angle mode: ‡2 2 cos((p/4)ô ) ¸ In Degree angle mode, multiplies expression1 by 180/p. In Radian angle mode, returns expression1 unchanged. cos({0ô,(p/12)ô,ë pô }) ¸ This function gives you a way to use a radian angle while in Degree mode. (In Degree angle mode, sin(), cos(), tan(), and polar-torectangular conversions expect the angle argument to be in degrees.
¡, ', " 2 “ key (¡), 2 È key ('), 2 É key (") ⇒ dd¡mm'ss.ss" dd mm ss.ss expression A positive or negative number A non-negative number A non-negative number In Degree angle mode: 25°13'17.5" ¸ 25.221... 25°30' ¸ 51/2 Returns dd +(mm /60)+(ss.ss /3600). This base-60 entry format lets you: • Enter an angle in degrees/minutes/seconds without regard to the current angle mode. • Enter time as hours/minutes/seconds.
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 chapter about constants and measurement units in this book. You can press: TI-89: 2 9 TI-92 Plus: ¥ À to select units from a menu, or you can type the unit names directly.
xê CATALOG (^ -1) expression1 xê ⇒ list1 xê ⇒ list expression Returns the reciprocal of the argument. For a list, returns the reciprocals of the elements in list1. squareMatrix1 xê ⇒ squareMatrix Returns the inverse of squareMatrix1. 3.1^ë 1 ¸ .322581 {a,4,ë.1,xì 2}^ë 1 ¸ 1 1 {a 4 ë 10. 1 xì 2} [1,2;3,4]^ë 1 ¸ [1,2;a,4]^ë 1 ¸ squareMatrix1 must be a non-singular square matrix. | (“with”) TI-89: Í key TI-92 Plus: 2 Í key expression | Boolean expression1 [and Boolean expression2]...
! (store) § key expression ! var list ! var matrix ! var expression ! fun_name(parameter1,...) list ! fun_name(parameter1,...) matrix ! fun_name(parameter1,...) p 4 p/4! myvar ¸ 2cos(x)! Y1(x) ¸ {1,2,3,4}! Lst5 ¸ Done {1 2 3 4} If variable var does not exist, creates var and initializes it to expression, list, or matrix. 1 2 3 [1,2,3;4,5,6]! MatG ¸ [4 5 6] If var already exists and if it is not locked or protected, replaces its contents with expression, list, or matrix.
540 Appendix A: Functions and Instructions 8992APPA.
Appendix B: Reference Information B TI-89 / TI-92 Plus Error Messages ....................................................... 542 Modes....................................................................................................... 550 TI-89 / TI-92 Plus Character Codes ..................................................... 555 TI-89 Key Codes ..................................................................................... 556 TI-92 Plus Key Codes................................................
TI-89 / TI-92 Plus 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. If the error occurs inside a Try...EndTry block, the error number is stored in system variable errornum. Many of the error messages are selfexplanatory and do not require descriptive information. However, additional information has been added for some error messages.
Error Number 160 Description Argument must be an expression For example, zeros(2x+3=0,x) is invalid because the first argument is an equation. 161 ASAP or Exec string too long 163 Attribute (8-digit number) of object (8-digit number) not found 165 Batteries too low for sending/receiving product code Install new batteries before sending or receiving product software (base code).
Error Number 260 Description Domain error An argument must be in a specified domain. For example, ans(100) is not valid because the argument for ans() must be in the range 1–99. 270 Duplicate variable name 280 Else and ElseIf invalid outside of If..
Error Number Description 405 Invalid axes 410 Invalid command 420 Invalid folder name 430 Invalid for the current mode settings 440 Invalid implied multiply For example, x(x+1) is invalid; whereas, xù (x+1) is the correct syntax. This is to avoid confusion between implied multiplication and function calls. 450 Invalid in a function or current expression Only certain commands are valid in a user-defined function.
Error Number Description 560 Invalid outside Loop..EndLoop, For..EndFor, or While..EndWhile blocks For example, the Exit command is valid only inside these loop blocks. 570 Invalid pathname For example, \\var is invalid. 575 Invalid polar complex 580 Invalid program reference Programs cannot be referenced within functions or expressions such as 1+p(x) where p is a program. 590 Invalid syntax block A Dialog..EndDlog block is empty or has more than one title. A Custom..
Error Number Description 690 Missing ) 700 Missing " 710 Missing ] 720 Missing } 730 Missing start or end of block syntax 740 Missing Then in the If..EndIf block 750 Name is not a function or program 765 No functions selected 780 No solution found Using the interactive math features (F5:Math) in the Graph application can give this error. For example, if you attempt to find an inflection point of the parabola y1(x)=xñ , which does not exist, this error will be displayed.
Error Number 850 Description Program not found A program reference inside another program could not be found in the provided path during execution. 860 Recursion is limited to 255 calls deep 870 Reserved name or system variable 875 ROM-resident routine not available 880 Sequence setup 885 Signature error 890 Singular matrix 895 Slope fields need one selected function and are used for 1st-order equations only 900 Stat 910 Syntax The structure of the entry is incorrect.
Error Number Description Warning: ˆ^0 or undef^0 replaced by 1 Warning: 0^0 replaced by 1 Warning: 1^ˆ or 1^undef replaced by 1 Warning: cSolve may specify more zeros Warning: May produce false equation 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 ˆ or ë ˆ Warning: Questionable accuracy Warning:
Modes This section describes the modes of the TI-89 / TI-92 Plus and lists the possible settings of each mode. These mode settings are displayed when you press 3. Graph Specifies the type of graphs you can plot.
Angle Specifies the units in which angle values are interpreted and displayed in trig functions and polar/rectangular conversions. 1:RADIAN 2:DEGREE Exponential Format Specifies which notation format should be used. These formats affect only how an answer is displayed; you can enter a number in any format. Numeric answers can be displayed with up to 12 digits and a 3-digit exponent. 1:NORMAL Expresses numbers in standard format. For example, 12345.
Vector Format Determines how 2-element and 3-element vectors are displayed. You can enter vectors in any of the coordinate systems. 1:RECTANGULAR Coordinates are in terms of x, y, and z. For example, [3,5,2] represents x = 3, y = 5, and z = 2. 2:CYLINDRICAL Coordinates are in terms of r, q, and z. For example, [3,∠45,2] represents r = 3, q = 45, and z = 2. 3:SPHERICAL Pretty Print Coordinates are in terms of r, q, and f. For example, [3, ∠45, ∠90] represents r = 3, q = 45, and f = 90.
Split 1 App and Split 2 App Specifies which application is displayed on the screen. ¦ For a full screen, only Split 1 App is active. ¦ For a split screen, Split 1 App is the top or left part of the screen and Split 2 App is the bottom or right part. The available application choices are those listed when you press B from the Page 2 mode screen or when you press O. You must have different applications in each screen unless you are in 2-graph mode.
Base Lets you perform calculations by entering numbers in decimal, binary, or hexadecimal form. Unit System 1:DEC Decimal numbers use 0 - 9 in the base 10 format 2:HEX Hexadecimal numbers use 0 - 9 and A - F in the base 16 format. 3:BIN Binary numbers use 0 and 1 in the base 2 format. 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.
TI-89 / TI-92 Plus 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). You can use ord() to find the numeric code of a character. For example, ord("A") returns 65. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.
TI-89 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 ¤ None 2 ¥ j Assoc. Value Assoc. Value Assoc. Value Assoc. Value Assoc.
Table 1: Key Codes for Primary Keys (Continued) Key Modifier ¤ None 2 ¥ j Assoc. Value Assoc. Value Assoc. Value Assoc. Value Assoc. ¸ CR 13 CR 13 ENTRY 4109 APPROX 8205 CR Value 13 § STO4 258 P 80 RCL 4354 @ 64 p 112 Á = 61 A 65 ' 39 ƒ 157 a 97 ^ EE 149 K 75 ∠ 159 SYMB 8341 k 107 · - 173 SPACE 32 ANS 4372 8365 SPACE 32 ¶ .
Table 3: Greek Letters (prefixed by ¥ c) Keys Second modifier j 558 ¤ Assoc. Value Á [A] α 128 c [B] β 129 b [D] δ 133 e [E] ε 134 Í [F] φ 145 m [G] γ 131 y [L] λ 137 z [M] µ 181 § [P] π 140 © [R] ρ 141 ª [S] σ 143 Ü [T] τ 144 ¶ [W] ω 148 Ù ξ 138 Ú ψ 146 Û ζ 135 Assoc.
TI-92 Plus 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 ƒ will return a value of 268. Table 1: Key Codes for Primary Keys Key Modifier ¤ None Assoc. Value Assoc. 2 Value Assoc. ¥ Value Assoc.
Table 1: Key Codes for Primary Keys (Continued) Key Modifier ¤ None Assoc. Value Assoc. 2 Value Assoc. ¥ Value Assoc.
Table 2: Arrow Keys Arrow Keys Normal ¤ 2 ¥ ‚ C 338 16722 4434 8530 33106 E 342 16726 4438 8534 33110 B 340 16724 4436 8532 33108 F 348 16732 4444 8540 33116 D 344 16728 4440 8536 33112 G 345 16729 4441 8537 33113 A 337 16721 4433 8529 33105 H 339 16723 4435 8531 33107 Note: The Grab (‚)modifier only affects the arrow keys. Table 3: Grave Letters (prefixed by 2 A) Key Assoc.
Table 6: Greek Letters (prefixed by 2 G) Key Assoc. Normal A α 128 129 B β D δ 133 E ε 134 F φ 145 G γ 131 L λ 137 M µ 181 P π 140 R ρ 141 S σ 143 T τ 144 W ω 148 X ξ 138 Y ψ 146 Z ζ 135 ¤ 132 130 139 142 147 Table 7: Tilde Letters (prefixed by 2 N) Key Assoc. Normal ¤ N ñ 241 209 O õ 245 Table 8: Caret Letters (prefixed by 2 O) Key Assoc.
Entering Complex Numbers You can enter complex numbers in the polar form (rq), 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.
Important: Do not use the r e i q polar form in Degree angle mode. It will cause a Domain error. To enter the: Do this: Polar form re iq – or – Substitute the applicable values or variable names for r and q, where q is interpreted according to the Angle mode setting. (rq) Note: To get the e symbol, press: TI.89: ¥ s. TI.92 Plus: 2 s Do not simply type an alphabetic e. TI.89: j [R] ¥ s 2 ) ¥ Ï d – or – c j [R] 2 ’ ¥ Ï d Parentheses are required for the (rq) form. TI.
Using Complex Variables in Symbolic Calculations Regardless of the Complex Format mode setting, undefined variables are treated as real numbers. To perform complex symbolic analysis, you can use either of the following methods to set up a complex variable. Method 1: Use an underscore _ (TI.89: ¥ TI.92 Plus: 2 ) as the last character in the variable name to designate a complex variable. For example: Note: For best results in calculations such as cSolve() and cZeros(), use Method 1.
Accuracy Information To maximize accuracy, the TI-89 / TI-92 Plus 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.
System Variables and Reserved Names This section lists the names of system variables and reserved function names that are used by the TI-89 / TI-92 Plus. Only those system variables and reserved function names that are identified by an asterisk (*) can be deleted by using DelVar var on the entry line.
EOS (Equation Operating System) Hierarchy This section describes the Equation Operating System (EOSé) that is used by the TI-89 / TI-92 Plus. 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.
Indirection The indirection operator (#) converts a string to a variable or function name. For example, #(“x”&”y”&”z”) creates the variable name xyz. Indirection also allows the creation and modification of variables from inside a program. For example, if 10!r and “r”!s1, then #s1=10. Post Operators Post operators are operators that come directly after an argument, such as 5!, 25%, or 60ó15' 45". Arguments followed by a post operator are evaluated at the fourth priority level.
Regression Formulas This section describes how the statistical regressions are calculated.
Regression Description 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.
Runge-Kutta Method For Runge-Kutta integrations of ordinary differential equations, the TI-89 / TI-92 Plus uses the Bogacki-Shampine 3(2) formula as found in the journal Applied Math Letters, 2 (1989), pp. 1–9. 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.
574 Appendix B: Reference Information 8992APPB DOC TI-89/TI-92 Plus:8992appb doc (English) Susan Gullord Revised: 02/23/01 1:54 PM Printed: 02/23/01 2:24 PM Page 574 of 34
Appendix C: Service and Warranty Information C Battery Information ............................................................................... 576 In Case of Difficulty ............................................................................... 579 Support and Service Information......................................................... 580 Warranty Information ............................................................................
Battery Information The TI-89 / TI-92 Plus 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 Note: The TI-89 uses four AAA size alkaline batteries. The TI-92 Plus uses four AA size alkaline batteries. Note: To avoid loss of information stored in memory, the TI-89 / TI-92 Plus must be off. Do not remove the alkaline batteries and the lithium battery at the same time.
Replacing the Alkaline Batteries in the TI-89 1. If the TI-89 is on, turn it off (press 2 ®) to avoid loss of information stored in memory. 2. Slide the protective cover over the keyboard. 3. Holding the calculator upright, push down on the battery cover latch, and then 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. Lithium battery AAA alkaline batteries 6.
Replacing the Alkaline Batteries in the TI-92 Plus 1. If the TI-92 Plus is on, turn it off (press 2 ®) to avoid loss of information stored in memory. 2. Holding the TI-92 Plus unit upright, slide the latch on the top of the unit to the left unlocked position; slide the rear cover down about one-eighth inch and remove it from the main unit. top Slide to open. I/O 3. Remove all four discharged AA batteries. 4.
In Case of Difficulty If you have difficulty operating the TI-89 / TI-92 Plus, the following suggestions may help you correct the problem. Suggestions 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.
Support and Service Information For additional information about TI support, service, and products, please see below. For General Information E-mail: ti-cares@ti.com Phone: 1-800-TI-CARES (1-800-842-2737) For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands only Home Page: education.ti.com For Technical Questions Phone: 1.972.917.8324 For Product (hardware) Service Customers in the U.S.
Warranty Information See the information below concerning the warranty for your TI-89 / TI-92 Plus. Customers in the U.S. and Canada Only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments (“TI”) electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage.
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.
Appendix D: Programmer’s Guide D setMode( ) and getMode( ) ................................................................... 584 setGraph( ) .............................................................................................. 587 setTable( ) ...............................................................................................
setMode( ) and getMode( ) Parameter/Mode Setting 584 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 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 Appendix D: Programmer’s Guide 8992APPD.
Parameter/Mode Setting Strings FLOAT 10 24 FLOAT 11 25 FLOAT 12 26 Angle 3 RADIAN 1 DEGREE 2 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 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 Appendix
Parameter/Mode Setting 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 2:1 3 Exact/Approx 14 AUTO 1 EXACT 2 APPROXIMATE Base 586 Strings 3 15 DEC 1 HEX 2 BIN 3 Appendix D: Programmer’s Guide 8992APPD.
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 1 ON 2 Leading Cursor 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 Appendix D: Programmer’s Guide 8992APPD.
Parameter/Mode Setting Fields 9 SLPFLD 1 DIRFLD 2 FLDOFF 3 DE Axes 10 TIME 1 Y1-VS-Y2 2 T-VS-Y' 3 Y-VS-Y' 4 Y1-VS-Y2' 5 Y1'-VS-Y2' 6 XR Style 588 Strings 11 WIRE FRAME 1 HIDDEN SRUFACE 2 CONTOUR LEVELS 3 WIRE AND CONTOUR 4 IMPLICIT PLOT 5 Appendix D: Programmer’s Guide 8992APPD.
setTable( ) Parameter/Mode Setting Graph <->Table OFF ON Strings 1 1 2 Independent 2 AUTO 1 ASK Axes 2 4 Appendix D: Programmer’s Guide 8992APPD.
590 Appendix D: Programmer’s Guide 8992APPD.
Index Commands and functions are bold. Special symbols are presented at the beginning of the index.
A (continued) angle( ), angle, 415 angle, ±, 535 angle, angle( ), 415 ans( ), last answer, 50, 416 APD (Automatic Power Down), 14 append, &, 293, 532. inside front cover, inside back cover APPLICATIONS menu, 34, 38 approx( ), approximate, 70, 416 approximate answer. inside front cover, inside back cover Approximate mode, 29, 41, 54, 62, 553 approximate, approx( ), 70, 416 arbitrary integer, @, 80.
C (continued) colDim( ), matrix column dimension, 421 colNorm( ), matrix column norm, 421 combinations, nCr( ), 470 comDenom( ), common denominator, 70, 71, 74, 421 command mark, 328 command scripts, 94, 328, 329 activity, 392 commands, 409 – 540 comment, ¦, 282, 539.
D (continued) derivatives, 10 first derivative, d ( ), 10, 66, 75, 76, 432 numeric derivative, nDeriv( ), 75, 470 Derivatives (graph math tool), 122, 124, 132, 138 deSolve( ), solution, 75, 196, 434 det( ), matrix determinant, 436 diag( ), matrix diagonal, 436 dialog boxes, 35 Dialog, define dialog box, 302, 437 differential equations DIRFLD, direction field, 180, 185, 198 first order, 186, 196 FLDOFF, field off, 180, 185, 199 graphing, 175 – 199 initial conditions, 184 second order, 187, 196 SLPFLD, slope
E (continued) entry( ), entry, 50, 443 EOS (Equation Operating System), 568 equal, =, 294, 529 Equation Operating System (EOS), 568 equations, solving, 333 – 341 errors and troubleshooting, 579, 580 Circular definition, 289 clear error, ClrErr, 310, 420 Memory error, 364 messages, 542 – 549 Out-of-memory, 79 pass error, PassErr, 310, 479 programs, 310 transmission, 369, 377 warnings, 549 Estep window variable, 182 Euler method, 180, 193 evaluate polynomial, polyEval( ), 480 exact( ), exact, 443 Exact/Approx
F (continued) field off, FLDOFF, 180, 185, 199 field picture, fldpic, 183 Fill, matrix fill, 448 Flash applications, 4, 38, 45, 79, 353, 356.
G (continued) H matrix data, 203 Maximum, 122, 123 Minimum, 11, 122, 123 modes, 41, 54, 108, 130, 136, 142, 157, 179, 550 native independent variable, 204 nested functions, 206 operations, 410 overview, 107, 129, 135, 141, 156, 178 panning, 118 parametric, 127 – 132 pausing, 115 pictures, 217, 218 piecewise functions, 206 pixels, 566 polar, 133 – 138 programs, 305 QuickCenter, 118 recall graph database, RclGDB, 306, 488 selecting functions, 111, 131, 143, 179 sequence, 139 – 151 setting, setGraph( ), 300,
K keyboard, 16, 17 j (alpha) key, 18 ¥ (diamond) key, 18 ‚ (hand) key, 18 2 (second) key, 18 ¤ (shift) key, 18 key codes, 301, 556 – 562 map, 324, 325, inside front cover, inside back cover shortcuts, 325, inside front cover, inside back cover L lab reports, 330, 331 label, Lbl, 287, 296, 299, 459 Labels graph format, 114 language, 4 Language mode, 42, 554 last answer, 20, 28, 49, 51 last entry, 20, 49, 50 Lbl, label, 287, 296, 299, 459 lcm, least common multiple, 460 Leading Cursor graph format, 114 least
M (continued) dimension, dim( ), 437 dot addition, .+, 530 dot division, .à, 531 dot multiplication, .†, 531 dot power, .^, 531 dot subtraction, .
N natural log base, e, 80 natural logarithm, ln( ), 463 ncontour window variable, 158 nCr( ), combinations, 470 ncurves window variable, 182 nDeriv( ), numeric derivative, 75, 470 negate, M, 25, 528 new data, NewData, 240, 249, 273, 289, 471 folder, NewFold, 101, 289, 471 list, newList( ), 471 matrix, newMat( ), 471 picture, NewPic, 289, 306, 471 plot, NewPlot, 266, 305, 472 problem, NewProb, 43, 472 NewData, new data, 240, 249, 273, 289, 471 NewFold, new folder, 101, 289, 471 newList( ), new list, 471 newM
P (continued) point change, PtChg, 307, 482 off, PtOff, 307, 483 on, PtOn, 307, 483 test, ptTest( ), 307, 483 text, PtText, 307, 483 polar coordinate, R4Pq( ), 487 coordinate, R4Pr( ), 487 graphing, 133 – 138 vector display, 4Polar, 480 polyEval( ), evaluate polynomial, 480 polynomials, 9, 72, 76 activity, 402 evaluate, polyEval( ), 480 random, randPoly( ), 488 PopUp, popup menu, 301, 481 power of ten, 10^( ), 537 power, ^, 534, 569 PowerReg, power regression, 262, 481, 571 pretty print, 6, 11, 23, 29 Prett
P (continued) return, Return, 286, 287, 491 running, 278.
S (continued) seq( ), sequence, 494 sequence graphing, 139 – 151 serial number, 55 service information, 580 set folder, setFold( ), 101, 300, 495 graph, setGraph( ), 300, 305, 495 mode, setMode( ), 300, 305, 496 table, setTable( ), 225, 300, 305, 497 units, setUnits( ), 300, 497 Set factors (zoom), 119, 121 setFold( ), set folder, 101, 300, 495 setGraph( ), set graph, 300, 305, 495 setMode( ), set mode, 300, 305, 496 setTable( ), set table, 225, 300, 305, 497 setUnits( ), set units, 300, 497 Shade (graph ma
S (continued) shift, shift( ), 293, 499 string to expression, expr( ), 292, 293, 301, 381, 446 within, InString, 293, 458 Style, style, 112, 305, 508 subMat( ), submatrix, 508 submenus, 35 substitutions, 67, 68, 69 subtract, N, 526 sum( ), summation, 492, 508 sum, Σ( ), 75, 533 switch( ), switch, 300, 509 symbolic manipulation, 57 – 80 sysdata, system data, 203 system variables, 567, 568 T t0 window variable, 181 TABLE SETUP, table setup, 224 Table, build table, 305, 510 table-graph, Graph<->Table, 224 tab
U (continued) W Unlock, unlock, 289, 516 upgrading product code, 373, 374 user-defined functions, 46, 77, 78, 97 – 99, 157, 205, 207, 285, 286, 433 user-defined units, 88 warranty information, 581 web plots convergence, 148 divergence, 148 oscillation, 149 WEB, 142, 146, 147 WEB, web plots, 142, 146, 147 when( ), when, 202, 206, 517 While, while, 298, 518 window variables qmax, 137 qmin, 137 qstep, 137 @x, 566 @y, 566 diftol, 182 dtime, 182 Estep, 182 eyeψ (rotation), 158, 162, 163 eyeq (x axis), 158, 16
X xgrid window variable, 158 xmax window variable, 113, 131, 137, 143, 144, 158, 182, 566 xmin window variable, 113, 131, 137, 143, 144, 158, 182, 566 xor, Boolean exclusive or, 294, 347, 518 XorPic, exclusive or picture, 306, 519 xres window variable, 113 xscl window variable, 113, 131, 137, 143, 144, 182, 566 xyline plots, 266 ZoomRcl, zoom recall, 121, 524 ZoomSqr, zoom square, 119, 524 ZoomStd, zoom standard, 119, 525 ZoomSto, zoom store, 121, 525 ZoomTrig, zoom trig, 119, 525 Y Y= editor, 106, 109, 1
