TI TI-83 Plus / TI-83 Plus Silver Edition Graphing Calculator Guidebook First Steps On/Off Menus Using parentheses Graphing a function Modes Lists Creating… Tables Matrices Data and lists Split screen Beyond the Basics Inferential statistics Programming Archiving/Unarchiving Menu maps More Information Sending and receiving Formulas 10/25/02 Troubleshooting Support and service © 2001, 2002 Texas Instruments
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Chapter 1: Operating the TI-83 Plus Silver Edition Documentation Conventions In the body of this guidebook, TI-83 Plus (in silver) refers to the TI-83 Plus Silver Edition. Sometimes, as in Chapter 19, the full name TI-83 Plus Silver Edition is used to distinguish it from the TI-83 Plus. All the instructions and examples in this guidebook also work for the TI-83 Plus. All the functions of the TI-83 Plus Silver Edition and the TI-83 Plus are the same.
TI-83 Plus Keyboard Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys. Keyboard Zones Graphing — Graphing keys access the interactive graphing features. Editing — Editing keys allow you to edit expressions and values. Advanced — Advanced function keys display menus that access the advanced functions. Scientific — Scientific calculator keys access the capabilities of a standard scientific calculator.
TI-83 Plus Graphing Keys Editing Keys Advanced Function Keys Scientific Calculator Keys Colors may vary in actual product.
Using the Color.Coded Keyboard The keys on the TI-83 Plus are color-coded to help you easily locate the key you need. The light gray keys are the number keys. The blue keys along the right side of the keyboard are the common math functions. The blue keys across the top set up and display graphs. The blue Πkey provides access to applications such as the Finance application. The primary function of each key is printed on the keys. For example, when you press , the MATH menu is displayed.
The alpha function of each key is printed in green above the key. When you press the green ƒ key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press ƒ and then , the letter A is entered. This guidebook describes this keystroke combination as ƒ [A]. The y key accesses the second function printed in yellow above each key. The ƒ key accesses the alpha function printed in green above each key.
Turning On and Turning Off the TI-83 Plus Turning On the Calculator To turn on the TI-83 Plus, press É. • If you previously had turned off the calculator by pressing y M, the TI-83 Plus displays the home screen as it was when you last used it and clears any error. • If Automatic Power Down™ (APDé) had previously turned off the calculator, the TI-83 Plus will return exactly as you left it, including the display, cursor, and any error.
Turning Off the Calculator To turn off the TI-83 Plus manually, press y M. • All settings and memory contents are retained by Constant Memory TM. • Any error condition is cleared. Batteries The TI-83 Plus uses four AAA alkaline batteries and has a userreplaceable backup lithium battery (CR1616 or CR1620). To replace batteries without losing any information stored in memory, follow the steps in Appendix B.
Setting the Display Contrast Adjusting the Display Contrast You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark. Note: The TI-83 Plus has 40 contrast settings, so each number 0 through 9 represents four settings.
Note: If you adjust the contrast setting to 0, the display may become completely blank. To restore the screen, press and release y, and then press and hold } until the display reappears. When to Replace Batteries When the batteries are low, a low-battery message is displayed when you: • Turn on the calculator. • Download a new application. • Attempt to upgrade to new software. To replace the batteries without losing any information in memory, follow the steps in Appendix B.
The Display Types of Displays The TI-83 Plus displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI-83 Plus can display a horizontally or vertically split screen to show graphs and text simultaneously. Home Screen The home screen is the primary screen of the TI-83 Plus. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen.
When an entry is executed on the home screen, the answer is displayed on the right side of the next line. Entry Answer The mode settings control the way the TI-83 Plus interprets expressions and displays answers. If an answer, such as a list or matrix, is too long to display entirely on one line, an ellipsis (...) is displayed to the right or left. Press ~ and | to display the answer. Entry Answer Returning to the Home Screen To return to the home screen from any other screen, press y 5.
Display Cursors In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.
Entering Expressions and Instructions What Is an Expression? An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI-83 Plus, you enter an expression in the same order as you would write it on paper. For example, pR2 is an expression. You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value.
Most TI-83 Plus functions and operations are symbols comprising several characters. You must enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you must press « 45. Do not enter the letters L, O, and G. If you enter LOG, the TI-83 Plus interprets the entry as implied multiplication of the variables L, O, and G. Calculate 3.76 ÷ (L7.9 + ‡5) + 2 log 45.
1. Enter the part of the number that precedes the exponent. This value can be an expression. 2. Press y D. å is pasted to the cursor location. 3. If the exponent is negative, press Ì, and then enter the exponent, which can be one or two digits. When you enter a number in scientific notation, the TI-83 Plus does not automatically display answers in scientific or engineering notation. The mode settings and the size of the number determine the display format. Functions A function returns a value.
Instructions An instruction initiates an action. For example, ClrDraw is an instruction that clears any drawn elements from a graph. Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase. Some instructions take more than one argument, as indicated by an open parenthesis ( ( ) at the end of the name. For example, Circle( requires three arguments, Circle(X,Y,radius).
TI-83 Plus Edit Keys Keystrokes Result ~ or | Moves the cursor within an expression; these keys repeat. } or † Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat. On the top line of an expression on the home screen, } moves the cursor to the beginning of the expression. On the bottom line of an expression on the home screen, † moves the cursor to the end of the expression. y| Moves the cursor to the beginning of an expression.
Keystrokes Result y Changes the cursor to Þ; the next keystroke performs a 2nd operation (an operation in yellow above a key and to the left); to cancel 2nd, press y again. ƒ Changes the cursor to Ø; the next keystroke pastes an alpha character (a character in green above a key and to the right) or executes SOLVE (Chapters 10 and 11); to cancel ƒ, press ƒ or press |, }, ~, or †.
Setting Modes Checking Mode Settings Mode settings control how the TI-83 Plus displays and interprets numbers and graphs. Mode settings are retained by the Constant Memory feature when the TI-83 Plus is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings. To display the mode settings, press z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.
Changing Mode Settings To change mode settings, follow these steps. 1. Press † or } to move the cursor to the line of the setting that you want to change. 2. Press ~ or | to move the cursor to the setting you want. 3. Press Í. Setting a Mode from a Program You can set a mode from a program by entering the name of the mode as an instruction; for example, Func or Float. From a blank program command line, select the mode setting from the mode screen; the instruction is pasted to the cursor location.
Normal notation mode is the usual way we express numbers, with digits to the left and right of the decimal, as in 12345.67. Sci (scientific) notation mode expresses numbers in two parts. The significant digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of E, as in 1.234567E4. Eng (engineering) notation mode is similar to scientific notation.
The decimal setting applies to these numbers: • An answer displayed on the home screen • Coordinates on a graph (Chapters 3, 4, 5, and 6) • The Tangent( DRAW instruction equation of the line, x, and dy/dx values (Chapter 8) • Results of CALCULATE operations (Chapters 3, 4, 5, and 6) • The regression equation stored after the execution of a regression model (Chapter 12) Radian, Degree Angle modes control how the TI-83 Plus interprets angle values in trigonometric functions and polar/rectangular con
Func, Par, Pol, Seq Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these modes in detail. Func (function) graphing mode plots functions, where Y is a function of X (Chapter 3). Par (parametric) graphing mode plots relations, where X and Y are functions of T (Chapter 4). Pol (polar) graphing mode plots functions, where r is a function of q (Chapter 5). Seq (sequence) graphing mode plots sequences (Chapter 6).
Sequential, Simul Sequential graphing-order mode evaluates and plots one function completely before the next function is evaluated and plotted. Simul (simultaneous) graphing-order mode evaluates and plots all selected functions for a single value of X and then evaluates and plots them for the next value of X. Note: Regardless of which graphing mode is selected, the TI-83 Plus will sequentially graph all stat plots before it graphs any functions.
Full, Horiz, G.T Full screen mode uses the entire screen to display a graph or edit screen. Each split-screen mode displays two screens simultaneously. • Horiz (horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9). • G.T (graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9).
Using TI-83 Plus Variable Names Variables and Defined Items On the TI-83 Plus you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings. The TI-83 Plus uses assigned names for variables and other items saved in memory. For lists, you also can create your own five-character names. Variable Type Names Real numbers A, B, ... , Z Complex numbers A, B, ... , Z Matrices ãAä, ãBä, ãCä, ...
Variable Type Names Graph pictures Pic1, Pic2, ... , Pic9, Pic0 Strings Str1, Str2, ... , Str9, Str0 Apps Applications AppVars Application variables Groups Grouped variables System variables Xmin, Xmax, and others Notes about Variables • You can create as many list names as memory will allow (Chapter 11). • Programs have user-defined names and share memory with variables (Chapter 16).
• You can use DRAW STO menu items to store and recall graph databases and pictures (Chapter 8). • Although most variables can be archived, system variables including r, t, x, y, and q cannot be archived (Chapter 18) • Apps are independent applications.which are stored in Flash ROM. AppVars is a variable holder used to store variables created by independent applications. You cannot edit or change variables in AppVars unless you do so through the application which created them.
Storing Variable Values Storing Values in a Variable Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used. To store a value to a variable from the home screen or a program using the ¿ key, begin on a blank line and follow these steps. 1. Enter the value you want to store. The value can be an expression. 2. Press ¿. ! is copied to the cursor location. 3.
Displaying a Variable Value To display the value of a variable, enter the name on a blank line on the home screen, and then press Í. Archiving Variables (Archive, Unarchive) You can archive data, programs, or other variables in a section of memory called user data archive where they cannot be edited or deleted inadvertently. Archived variables are indicated by asterisks (*) to the left of the variable names. Archived variables cannot be edited or executed. They can only be seen and unarchived.
Recalling Variable Values Using Recall (RCL) To recall and copy variable contents to the current cursor location, follow these steps. To leave RCL, press ‘. 1. Press y ãRCLä. RCL and the edit cursor are displayed on the bottom line of the screen. 2. Enter the name of the variable in any of five ways. • Press ƒ and then the letter of the variable. • Press y ãLISTä, and then select the name of the list, or press y [Ln]. • Press y >, and then select the name of the matrix.
The variable name you selected is displayed on the bottom line and the cursor disappears. 3. Press Í. The variable contents are inserted where the cursor was located before you began these steps. Note: You can edit the characters pasted to the expression without affecting the value in memory.
ENTRY (Last Entry) Storage Area Using ENTRY (Last Entry) When you press Í on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI-83 Plus, ENTRY is retained in memory. To recall ENTRY, press y [. The last entry is pasted to the current cursor location, where you can edit and execute it.
Accessing a Previous Entry The TI-83 Plus retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To scroll those entries, press y [ repeatedly. If a single entry is more than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage area. 1¿ƒA Í 2¿ƒB Í y[ If you press y [ after displaying the oldest stored entry, the newest stored entry is displayed again, then the next-newest entry, and so on.
To reexecute the displayed entry, press Í again. Each reexecution displays an answer on the right side of the next line; the entry itself is not redisplayed. 0¿ƒN Í ƒNÃ1¿ƒNƒ ã:ä ƒ N ¡ Í Í Í Multiple Entry Values on a Line To store to ENTRY two or more expressions or instructions, separate each expression or instruction with a colon, then press Í. All expressions and instructions separated by colons are stored in ENTRY.
For the equation A=pr 2, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess. 8 ¿ ƒ R ƒ [:] y B ƒR¡Íy[ y | 7 y 6 Ë 95 Í Continue until the answer is as accurate as you want. Clearing ENTRY Clear Entries (Chapter 18) clears all data that the TI-83 Plus is holding in the ENTRY storage area.
You can use the variable Ans to represent the last answer in most places. Press y Z to copy the variable name Ans to the cursor location. When the expression is evaluated, the TI-83 Plus uses the value of Ans in the calculation. Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.
Storing Answers To store an answer, store Ans to a variable before you evaluate another expression. Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V.
TI-83 Plus Menus Using a TI-83 Plus Menu You can access most TI-83 Plus operations using menus. When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen. • The menu name on the left side of the top line is highlighted. Up to seven items in that menu are displayed, beginning with item 1, which also is highlighted. • A number or letter identifies each menu item’s place in the menu. The order is 1 through 9, then 0, then A, B, C, and so on.
To display any other menu listed on the top line, press ~ or | until that menu name is highlighted. The cursor location within the initial menu is irrelevant. The menu is displayed with the cursor on the first item. Note: The Menu Map in Appendix A shows each menu, each operation under each menu, and the key or key combination you press to display each menu. Displaying a Menu While using your TI-83 Plus, you often will need to access items from its menus.
Moving from One Menu to Another Some keys access more than one menu. When you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed. Press ~ and | to highlight each menu name. Scrolling a Menu To scroll down the menu items, press †. To scroll up the menu items, press }. To page down six menu items at a time, press ƒ †. To page up six menu items at a time, press ƒ }.
• Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen. • Press † or } to move the cursor to the item you want, and then press Í. After you select an item from a menu, the TI-83 Plus typically displays the previous screen. Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1 through 9 and 0 are labeled in such a way that you can select them by pressing the appropriate number key.
Leaving a Menu without Making a Selection You can leave a menu without making a selection in any of four ways. • Press y 5 to return to the home screen. • Press ‘ to return to the previous screen. • Press a key or key combination for a different menu, such as or y 9. • Press a key or key combination for a different screen, such as o or y 0.
VARS and VARS Y.VARS Menus VARS Menu You can enter the names of functions and system variables in an expression or store to them directly. To display the VARS menu, press . All VARS menu items display secondary menus, which show the names of the system variables. 1:Window, 2:Zoom, and 5:Statistics each access more than one secondary menu. VARS Y-VARS 1: Window... X/Y, T/q, 2: Zoom... 3: GDB... 4: Picture... 5: Statistics... 6: Table... 7: String...
Selecting a Variable from the VARS Menu or VARS Y.VARS Menu To display the VARS Y.VARS menu, press ~. 1:Function, 2:Parametric, and 3:Polar display secondary menus of the Y= function variables. VARS Y-VARS 1: Function... 2: Parametric... 3: Polar... 4: On/Off... Yn functions XnT, YnT functions rn functions Lets you select/deselect functions Note: The sequence variables (u, v, w) are located on the keyboard as the second functions of ¬, −, and ®. To select a variable from the VARS or VARS Y.
3. If you selected 1:Window, 2:Zoom, or 5:Statistics from the VARS menu, you can press ~ or | to display other secondary menus. 4. Select a variable name from the menu. It is pasted to the cursor location.
Equation Operating System (EOS) Order of Evaluation The Equation Operating System (EOS) defines the order in which functions in expressions are entered and evaluated on the TI-83 Plus. EOS lets you enter numbers and functions in a simple, straightforward sequence. EOS evaluates the functions in an expression in this order.
Note: Within a priority level, EOS evaluates functions from left to right. Calculations within parentheses are evaluated first. Implied Multiplication The TI-83 Plus recognizes implied multiplication, so you need not press ¯ to express multiplication in all cases. For example, the TI-83 Plus interprets 2p, 4sin(46), 5(1+2), and (2ä5)7 as implied multiplication. Note: TI-83 Plus implied multiplication rules, although like theTI.83, differ from those of the TI.82.
Note: An open parenthesis following a list name, matrix name, or Y= function name does not indicate implied multiplication. It specifies elements in the list (Chapter 11) or matrix (Chapter 10) and specifies a value for which to solve the Y= function. Negation To enter a negative number, use the negation key. Press Ì and then enter the number. On the TI-83 Plus, negation is in the third level in the EOS hierarchy. Functions in the first level, such as squaring, are evaluated before negation.
Special Features of the TI-83 Plus Flash – Electronic Upgradability The TI-83 Plus uses Flash technology, which lets you upgrade to future software versions without buying a new calculator. For details, refer to: Chapter 19 As new functionality becomes available, you can electronically upgrade your TI-83 Plus from the Internet.
be edited or deleted inadvertently. You can also free up RAM by archiving variables to user data Applications Applications can be installed to customize the TI-83 Plus to your classroom needs. The big 1.54 M archive space lets you store up to 94 applications at one time. Applications can also be stored on a computer for later use or linked unit-to-unit.
Calculator-Based Laboratoryé (CBL 2é, CBLé) and Calculator-Based Rangeré (CBRé) The TI-83 Plus comes with the CBL/CBR application already installed. When coupled with the (optional) CBL 2/CBL or CBR accessories, you can use the TI-83 Plus to analyze real world data. For details, refer to: Chapter 14 CBL 2/CBL and CBR let you explore mathematical and scientific relationships among distance, velocity, acceleration, and time using data collected from activities you perform.
Other TI-83 Plus Features Getting Started has introduced you to basic TI-83 Plus operations. This guidebook covers the other features and capabilities of the TI-83 Plus in greater detail. Graphing You can store, graph, and analyze up to 10 functions, up to six parametric functions, up to six polar functions, and up to three sequences. You can use DRAW instructions to annotate graphs.
Tables You can create function evaluation tables to analyze many functions simultaneously. For details, refer to: Chapter 7 Split Screen You can split the screen horizontally to display both a graph and a related editor (such as the Y= editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously.
Lists You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves. For details, refer to: Chapter 11 Statistics You can perform one- and two-variable, listbased statistical analyses, including logistic and sine regression analysis.
Applications You can use such applications as Finance or For details, refer to: the CBL/CBR. With the Finance application you Chapter 14 can use time-value-of-money (TVM) functions to analyze financial instruments such as annuities, loans, mortgages, leases, and savings. You can analyze the value of money over equal time periods using cash flow functions. You can amortize loans with the amortization functions.
Programming You can enter and store programs that include extensive control and input/output instructions. For details, refer to: Chapter 16 Archiving Archiving allows you to store data, programs, or other variables to user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory. For details, refer to: Chapter 16 Archived variables are indicated by asterisks (*) to the left of the variable names.
With the TI™ Connect or TI-GRAPH LINK™ software and a TI-GRAPH LINK cable, you can also link the TI-83 Plus to a personal computer. As future software upgrades become available on the TI web site, you can download the software to your PC and then use the TI Connect or TI-GRAPH LINK software and a TI-GRAPH LINK cable to upgrade your TI-83 Plus.
Error Conditions Diagnosing an Error The TI-83 Plus detects errors while performing these tasks. • Evaluating an expression • Executing an instruction • Plotting a graph • Storing a value When the TI-83 Plus detects an error, it returns an error message as a menu title, such as ERR:SYNTAX or ERR:DOMAIN. Appendix B describes each error type and possible reasons for the error. • If you select 1:Quit (or press y 5 or ‘), then the home screen is displayed.
Correcting an Error To correct an error, follow these steps. 1. Note the error type (ERR:error type). 2. Select 2:Goto, if it is available. The previous screen is displayed with the cursor at or near the error location. 3. Determine the error. If you cannot recognize the error, refer to Appendix B. 4. Correct the expression.
Chapter 2: Math, Angle, and Test Operations Getting Started: Coin Flip Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is 0.5. 1. Begin on the home screen.
2. Press Í to evaluate the expression. A list of 40 elements is generated with the first 7 displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has 40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on. 3. Press ~ or | to view the additional counts in the list. Ellipses (...
Keyboard Math Operations Using Lists with Math Operations Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length. + (Addition), N (Subtraction), ä (Multiplication), à (Division) You can use + (addition, Ã), N (subtraction, ¹), ä (multiplication, ¯), and à (division, ¥) with real and complex numbers, expressions, lists, and matrices. You cannot use à with matrices.
sin(value) cos(value) tan(value) You can use the inverse trig functions (arcsine, y ?; arccosine, y @; and arctangent, y A) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. sinL1(value) cosL1(value) tanL1(value) Note: The trig functions do not operate on complex numbers. ^ (Power), 2 (Square), ‡( (Square Root) You can use ^ (power, ›), 2 (square, ¡), and ‡( (square root, y C) with real and complex numbers, expressions, lists, and matrices.
log(, 10^(, ln( You can use log( (logarithm, «), 10^( (power of 10, y G), and ln( (natural log, µ) with real or complex numbers, expressions, and lists. log(value) 10^(power) ln(value) e^( (Exponential) e^( (exponential, y J) returns the constant e raised to a power. You can use e^( with real or complex numbers, expressions, and lists. e^(power) e (Constant) e (constant, y [e]) is stored as a constant on the TI-83 Plus. Press y [e] to copy e to the cursor location.
L (Negation) M (negation, Ì) returns the negative of value. You can use M with real or complex numbers, expressions, lists, and matrices. Mvalue EOS™ rules (Chapter 1) determine when negation is evaluated. For example, LA2 returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in (LA)2. Note: On the TI-83 Plus, the negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press ¹.
MATH Operations MATH Menu To display the MATH menu, press . MATH NUM CPX PRB 1: 4Frac Displays the answer as a fraction. Displays the answer as a decimal. Calculates the cube. Calculates the cube root. Calculates the xth root. Finds the minimum of a function. Finds the maximum of a function. Computes the numerical derivative. Computes the function integral. Displays the equation solver. 2: 4Dec 3: 3 4: 3‡( 5: x‡ 6: fMin( 7: fMax( 8: nDeriv( 9: fnInt( 0: Solver...
value 4Frac 4Dec (display as a decimal) displays an answer in decimal form. You can use 4Dec with real or complex numbers, expressions, lists, and matrices. You can only use 4Dec following value. value 4Dec 3(Cube), 3‡( (Cube Root) 3 (cube) returns the cube of value. You can use 3 with real or complex numbers, expressions, lists, and square matrices. value3 3‡( (cube root) returns the cube root of value. You can use 3‡( with real or complex numbers, expressions, and lists.
x‡ (Root) x‡ (xth root) returns the xth root of value. You can use x‡ with real or complex numbers, expressions, and lists. xthrootx‡value fMin(, fMax( fMin( (function minimum) and fMax( (function maximum) return the value at which the local minimum or local maximum value of expression with respect to variable occurs, between lower and upper values for variable. fMin( and fMax( are not valid in expression. The accuracy is controlled by tolerance (if not specified, the default is 1âL5).
nDeriv( nDeriv( (numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1âL3). nDeriv( is valid only for real numbers. nDeriv(expression,variable,value[,H]) nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.
fnInt( fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of expression with respect to variable, given lower limit, upper limit, and a tolerance (if not specified, the default is 1âL5). fnInt( is valid only for real numbers. fnInt(expression,variable,lower,upper[,tolerance]) Tip: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press s.
Using the Equation Solver Solver Solver displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero. Solver is valid only for real numbers. When you select Solver, one of two screens is displayed. • The equation editor (see step 1 picture below) is displayed when the equation variable eqn is empty. • The interactive solver editor is displayed when an equation is stored in eqn.
• Enter the expression directly into the equation solver. • Paste a Y= variable name from the VARS Y.VARS menu to the equation solver. • Press y K, paste a Y= variable name from the VARS Y.VARS menu, and press Í. The expression is pasted to the equation solver. The expression is stored to the variable eqn as you enter it. 3. Press Í or †. The interactive solver editor is displayed. • The equation stored in eqn is set equal to zero and displayed on the top line.
• A $ is displayed in the first column of the bottom line if the editor continues beyond the screen. Tip: To use the solver to solve an equation such as K=.5MV2, enter eqn:0=KN.5MV2 in the equation editor. Entering and Editing Variable Values When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable. You can enter an expression for a variable value. It is evaluated when you move to the next variable.
Solving for a Variable in the Equation Solver To solve for a variable using the equation solver after an equation has been stored to eqn, follow these steps. 1. Select 0:Solver from the MATH menu to display the interactive solver editor, if not already displayed. 2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press Í or †. 3. Enter an initial guess for the variable for which you are solving.
The default guess is calculated as (upper+lower) . 2 4. Edit bound={lower,upper}. lower and upper are the bounds between which the TI-83 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is bound={L1å99,1å99}. 5. Move the cursor to the variable for which you want to solve and press ƒ \ (above the Í key). • The solution is displayed next to the variable for which you solved.
• leftNrt=diff is displayed in the last line of the editor. diff is the difference between the left and right sides of the equation. A solid square in the first column next to leftNrt= indicates that the equation has been evaluated at the new value of the variable for which you solved. Editing an Equation Stored to eqn To edit or replace an equation stored to eqn when the interactive equation solver is displayed, press } until the equation editor is displayed. Then edit the equation.
Controlling the Solution for Solver or solve( The TI-83 Plus solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions. Using solve( on the Home Screen or from a Program The function solve( is available only from CATALOG or from within a program.
MATH NUM (Number) Operations MATH NUM Menu To display the MATH NUM menu, press ~. MATH NUM 1: abs( 2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: lcm( 9: gcd( CPX PRB Absolute value Round Integer part Fractional part Greatest integer Minimum value Maximum value Least common multiple Greatest common divisor abs( abs( (absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices. abs(value) Note: abs( is also available on the MATH CPX menu.
round( round( returns a number, expression, list, or matrix rounded to #decimals (9). If #decimals is omitted, value is rounded to the digits that are displayed, up to 10 digits. round(value[,#decimals]) iPart(, fPart( iPart( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices. iPart(value) fPart( (fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices.
int( int( (greatest integer) returns the largest integer real or complex numbers, expressions, lists, and matrices. int(value) Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative numbers and negative integers, but one integer less than the result of iPart( for negative noninteger numbers. min(, max( min( (minimum value) returns the smaller of valueA and valueB or the smallest element in list.
max( (maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared, max( returns a list of the larger of each pair of elements. If list and value are compared, max( compares each element in list with value. min(valueA,valueB) min(list) min(listA,listB) min(list,value) max(valueA,valueB) max(list) max(listA,listB) max(list,value) Note: min( and max( also are available on the LIST MATH menu.
lcm(valueA,valueB) lcm(listA,listB) lcm(list,value) TI-83 Plus gcd(valueA,valueB) gcd(listA,listB) gcd(list,value) Math, Angle, and Test Operations 83
Entering and Using Complex Numbers Complex-Number Modes The TI-83 Plus displays complex numbers in rectangular form and polar form. To select a complex-number mode, press z, and then select either of the two modes. • • a+bi (rectangular-complex mode) re^qi (polar-complex mode) On the TI-83 Plus, complex numbers can be stored to variables. Also, complex numbers are valid list elements. In Real mode, complex-number results return an error, unless you entered a complex number as input.
Real mode a+bi mode $ $ Entering Complex Numbers Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting. The components of complex numbers can be real numbers or expressions that evaluate to real numbers; expressions are evaluated when the command is executed. Note about Radian Versus Degree Mode Radian mode is recommended for complex number calculations.
Interpreting Complex Results Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction. In the example below, polar-complex (re^qi) and Radian modes are set. Rectangular-Complex Mode Rectangular-complex mode recognizes and displays a complex number in the form a+bi, where a is the real component, b is the imaginary component, and i is a constant equal to -1.
real component(+ or N)imaginary component i Polar-Complex Mode Polar-complex mode recognizes and displays a complex number in the form re^qi, where r is the magnitude, e is the base of the natural log, q is the angle, and i is a constant equal to -1. To enter a complex number in polar form, enter the value of r (magnitude), press y J (exponential function), enter the value of q (angle), press y V (constant), and then press ¤.
MATH CPX (Complex) Operations MATH CPX Menu To display the MATH CPX menu, press ~ ~. MATH NUM CPX PRB 1: conj( 2: real( 3: imag( 4: angle( 5: abs( 6: 4Rect 7: 4Polar Returns the complex conjugate. Returns the real part. Returns the imaginary part. Returns the polar angle. Returns the magnitude (modulus). Displays the result in rectangular form. Displays the result in polar form. conj( conj( (conjugate) returns the complex conjugate of a complex number or list of complex numbers.
real( real( (real part) returns the real part of a complex number or list of complex numbers. real(a+bi) returns a. real(re^(qi)) returns räcos(q). imag( imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers. imag(a+bi) returns b. imag(re^(qi)) returns räsin(q).
angle( angle( returns the polar angle of a complex number or list of complex numbers, calculated as tanL1 (b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant. angle(a+bi) returns tanL1(b/a). angle(re^(qi)) returns q, where Lp
4Rect 4Rect (display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Rect returns a+bi. 4Polar 4Polar (display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Polar returns re^(qi).
MATH PRB (Probability) Operations MATH PRB Menu To display the MATH PRB menu, press |. MATH NUM CPX PRB 1: rand Random-number generator Number of permutations Number of combinations Factorial Random-integer generator Random # from Normal distribution Random # from Binomial distribution 2: nPr 3: nCr 4: ! 5: randInt( 6: randNorm( 7: randBin( rand rand (random number) generates and returns one or more random numbers > 0 and < 1.
With each rand execution, the TI-83 Plus generates the same randomnumber sequence for a given seed value. The TI-83 Plus factory-set seed value for rand is 0. To generate a different random-number sequence, store any nonzero seed value to rand. To restore the factoryset seed value, store 0 to rand or reset the defaults (Chapter 18). Note: The seed value also affects randInt(, randNorm(, and randBin( instructions.
items nCr number ! (Factorial) ! (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. value must be ‚L.5 and 69. value! Note: The factorial is computed recursively using the relationship (n+1)! = nän!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is used to complete the calculation. Hence: n!=nä(nN1)ä(nN2)ä ...
randInt( randInt( (random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer >1 for numtrials (number of trials); if not specified, the default is 1. randInt(lower,upper[,numtrials]) randNorm( randNorm( (random Normal) generates and displays a random real number from a specified Normal distribution.
randBin( randBin( (random Binomial) generates and displays a random integer from a specified Binomial distribution. numtrials (number of trials) must be ‚ 1. prob (probability of success) must be ‚ 0 and 1. To generate a list of random numbers, specify an integer > 1 for numsimulations (number of simulations); if not specified, the default is 1. randBin(numtrials,prob[,numsimulations]) Note: The seed value stored to rand also affects randInt(, randNorm(, and randBin( instructions.
ANGLE Operations ANGLE Menu To display the ANGLE menu, press y [ANGLE]. The ANGLE menu displays angle indicators and instructions. The Radian/Degree mode setting affects the TI-83 Plus’s interpretation of ANGLE menu entries.
For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to Degree, you must use ¡ so that the TI-83 Plus can interpret the argument as degrees, minutes, and seconds. Degree mode Radian mode ¡ (Degree) ¡ (degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian mode, you can use ¡ to convert degrees to radians. value¡ {value1,value2,value3,value4,...,value n}¡ ¡ also designates degrees (D) in DMS format.
r (Radians) (radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In Degree mode, you can use r to convert radians to degrees. r valuer Degree mode 8DMS 8DMS (degree/minute/second) displays answer in DMS format. The mode setting must be Degree for answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid only at the end of a line.
R8Pr (, R8Pq(, P8Rx(, P8Ry( R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq( converts rectangular coordinates to polar coordinates and returns q. x and y can be lists. R8Pr(x,y), R8Pq(x,y) Note: Radian mode is set. P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry( converts polar coordinates to rectangular coordinates and returns y. r and q can be lists. P8Rx(r,q), P8Ry(r,q) Note: Radian mode is set.
TEST (Relational) Operations TEST Menu To display the TEST menu, press y :. This operator... TEST Returns 1 (true) if... LOGIC 1: = 2: ƒ 3: > 4: ‚ 5: < 6: Equal Not equal to Greater than Greater than or equal to Less than Less than or equal to =, ƒ, >, ‚, <, Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false. valueA and valueB can be real numbers, expressions, or lists.
valueA=valueB valueA>valueB valueA
TEST LOGIC (Boolean) Operations TEST LOGIC Menu To display the TEST LOGIC menu, press y ãTESTä ~. This operator... Returns a 1 (true) if... TEST LOGIC 1: and Both values are nonzero (true). At least one value is nonzero (true). Only one value is zero (false). The value is zero (false). 2: or 3: xor 4: not( Boolean Operators Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values.
valueA and valueB valueA or valueB valueA xor valueB valueA valueB and or xor ƒ0 ƒ0 returns 1 1 0 ƒ0 0 returns 0 1 1 0 ƒ0 returns 0 1 1 0 0 returns 0 0 0 not( not( returns 1 if value (which can be an expression) is 0. not(value) Using Boolean Operations Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C.
Chapter 3: Function Graphing Getting Started: Graphing a Circle Getting Started is a fast-paced introduction. Read the chapter for details. Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSquare (zoom square) to adjust the display and make the functions appear as a circle. 1. In Func mode, press o to display the Y= editor.
2. Press q 6 to select 6:ZStandard. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press s. Notice that the functions appear as an ellipse in the standard viewing window. 3. To adjust the display so that each pixel represents an equal width and height, press q 5 to select 5:ZSquare. The functions are replotted and now appear as a circle on the display. 4.
Defining Graphs TI-83 Plus—Graphing Mode Similarities Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-83 Plus graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing. Defining a Graph To define a graph in any graphing mode, follow these steps. Some steps are not always necessary. 1. Press z and set the appropriate graph mode. 2.
Displaying and Exploring a Graph After you have defined a graph, press s to display it. Explore the behavior of the function or functions using the TI-83 Plus tools described in this chapter. Saving a Graph for Later Use You can store the elements that define the current graph to any of 10 graph database variables (GDB1 through GDB9, and GDB0; Chapter 8). To recreate the current graph later, simply recall the graph database to which you stored the original graph.
Setting the Graph Modes Checking and Changing the Graphing Mode To display the mode screen, press z. The default settings are highlighted below. To graph functions, you must select Func mode before you enter values for the window variables and before you enter the functions. The TI-83 Plus has four graphing modes. • Func (function graphing) • Par (parametric graphing; Chapter 4) • Pol (polar graphing; Chapter 5) • Seq (sequence graphing; Chapter 6) Other mode settings affect graphing results.
• Float or 0123456789 (fixed) decimal mode affects displayed graph coordinates. • Radian or Degree angle mode affects interpretation of some functions. • Connected or Dot plotting mode affects plotting of selected functions. • Sequential or Simul graphing-order mode affects function plotting when more than one function is selected. Setting Modes from a Program To set the graphing mode and other modes from a program, begin on a blank line in the program editor and follow these steps. 1.
Defining Functions Displaying Functions in the Y= Editor To display the Y= editor, press o. You can store up to 10 functions to the function variables Y1 through Y9, and Y0. You can graph one or more defined functions at once. In this example, functions Y1 and Y2 are defined and selected. Defining or Editing a Function To define or edit a function, follow these steps. 1. Press o to display the Y= editor. 2. Press † to move the cursor to the function you want to define or edit. To erase a function, press ‘.
• You may use functions and variables (including matrices and lists) in the expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned. • The independent variable in the function is X. Func mode defines „ as X. To enter X, press „ or press ƒ [X]. • When you enter the first character, the = is highlighted, indicating that the function is selected. As you enter the expression, it is stored to the variable Yn as a userdefined function in the Y= editor.
4. Select the function name, which pastes the name to the cursor location on the home screen or program editor. 5. Press Í to complete the instruction. "expression"!Yn When the instruction is executed, the TI-83 Plus stores the expression to the designated variable Yn, selects the function, and displays the message Done. Evaluating Y= Functions in Expressions You can calculate the value of a Y= function Yn at a specified value of X. A list of values returns a list. Yn(value) Yn({value1,value2,value3, . . .
Selecting and Deselecting Functions Selecting and Deselecting a Function You can select and deselect (turn on and turn off) a function in the Y= editor. A function is selected when the = sign is highlighted. The TI-83 Plus graphs only the selected functions. You can select any or all functions Y1 through Y9, and Y0. To select or deselect a function in the Y= editor, follow these steps. 1. Press o to display the Y= editor. 2. Move the cursor to the function you want to select or deselect. 3.
Turning On or Turning Off a Stat Plot in the Y= Editor To view and change the on/off status of a stat plot in the Y= editor, use Plot1 Plot2 Plot3 (the top line of the Y= editor). When a plot is on, its name is highlighted on this line. To change the on/off status of a stat plot from the Y= editor, press } and ~ to place the cursor on Plot1, Plot2, or Plot3, and then press Í. Plot1 Plot2 is turned on. and Plot3 are turned off.
3. Select 1:FnOn to turn on one or more functions or 2:FnOff to turn off one or more functions. The instruction you select is copied to the cursor location. 4. Enter the number (1 through 9, or 0; not the variable Yn) of each function you want to turn on or turn off. • • If you enter two or more numbers, separate them with commas. To turn on or turn off all functions, do not enter a number after FnOn or FnOff. FnOn[function#,function#, . . .,function n] FnOff[function#,function#, . . .,function n] 5.
Setting Graph Styles for Functions Graph Style Icons in the Y= Editor This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set Y1 as a solid line, Y2 as a dotted line, and Y3 as a thick line.
Setting the Graph Style To set the graph style for a function, follow these steps. 1. Press o to display the Y= editor. 2. Press † and } to move the cursor to the function. 3. Press | | to move the cursor left, past the = sign, to the graph style icon in the first column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.) 4. Press Í repeatedly to rotate through the graph styles. The seven styles rotate in the same order in which they are listed in the table above. 5.
Shading Above and Below When you select é or ê for two or more functions, the TI-83 Plus rotates through four shading patterns. • Vertical lines shade the first function with a é or ê graph style. • Horizontal lines shade the second. • Negatively sloping diagonal lines shade the third. • Positively sloping diagonal lines shade the fourth. • The rotation returns to vertical lines for the fifth é or ê function, repeating the order described above. When shaded areas intersect, the patterns overlap.
Setting a Graph Style from a Program To set the graph style from a program, select H:GraphStyle( from the PRGM CTL menu. To display this menu, press while in the program editor. function# is the number of the Y= function name in the current graphing mode. graphstyle# is an integer from 1 to 7 that corresponds to the graph style, as shown below.
Setting the Viewing Window Variables The TI-83 Plus Viewing Window The viewing window is the portion of the coordinate plane defined by Xmin, Xmax, Ymin, and Ymax. Xscl (X scale) defines the distance between tick marks on the x-axis. Yscl (Y scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set Xscl=0 and Yscl=0. Ymax Xscl Xmin Xmax Yscl Ymin Displaying the Window Variables To display the current window variable values, press p.
• At Xres=8, functions are evaluated and graphed at every eighth pixel along the x-axis. Tip: Small Xres values improve graph resolution but may cause the TI-83 Plus to draw graphs more slowly. Changing a Window Variable Value To change a window variable value from the window editor, follow these steps. 1. Press † or } to move the cursor to the window variable you want to change. 2. Edit the value, which can be an expression. • Enter a new value, which clears the original value.
Storing to a Window Variable from the Home Screen or a Program To store a value, which can be an expression, to a window variable, begin on a blank line and follow these steps. 1. Enter the value you want to store. 2. Press ¿. 3. Press to display the VARS menu. 4. Select 1:Window to display the Func window variables (X/Y secondary menu). • Press ~ to display the Par and Pol window variables (T/q secondary menu). • Press ~ ~ to display the Seq window variables (U/V/W secondary menu). 5.
When the instruction is executed, the TI-83 Plus stores the value to the window variable and displays the value. @X and @Y The variables @X and @Y (items 8 and 9 on the VARS (1:Window) X/Y secondary menu) define the distance from the center of one pixel to the center of any adjacent pixel on a graph (graphing accuracy). @X and @Y are calculated from Xmin, Xmax, Ymin, and Ymax when you display a graph. @X = (Xmax N Xmin) 94 @Y = (Ymax N Ymin) 62 You can store values to @X and @Y.
Setting the Graph Format Displaying the Format Settings To display the format settings, press y .. The default settings are highlighted below. RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn ExprOff Sets cursor coordinates. Sets coordinates display on or off. Sets grid off or on. Sets axes on or off. Sets axes label off or on. Sets expression display on or off. Format settings define a graph’s appearance on the display.
RectGC, PolarGC RectGC (rectangular graphing coordinates) displays the cursor location as rectangular coordinates X and Y. PolarGC (polar graphing coordinates) displays the cursor location as polar coordinates R and q. The RectGC/PolarGC setting determines which variables are updated when you plot the graph, move the free-moving cursor, or trace. • RectGC updates X and Y; if CoordOn format is selected, X and Y are displayed.
GridOff, GridOn Grid points cover the viewing window in rows that correspond to the tick marks on each axis. GridOff does not display grid points. GridOn displays grid points. AxesOn, AxesOff AxesOn displays the axes. AxesOff does not display the axes. This overrides the LabelOff/ LabelOn format setting. LabelOff, LabelOn LabelOff and LabelOn determine whether to display labels for the axes (X and Y), if AxesOn format is also selected.
ExprOn, ExprOff ExprOn and ExprOff determine whether to display the Y= expression when the trace cursor is active. This format setting also applies to stat plots. When ExprOn is selected, the expression is displayed in the top-left corner of the graph screen. When ExprOff and CoordOn both are selected, the number in the top-right corner specifies which function is being traced.
Displaying Graphs Displaying a New Graph To display the graph of the selected function or functions, press s. TRACE, ZOOM instructions, and CALC operations display the graph automatically. As the TI-83 Plus plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated. Pausing or Stopping a Graph While plotting a graph, you can pause or stop graphing. • Press Í to pause; then press Í to resume. • Press É to stop; then press s to redraw.
If you performed any of these actions since the graph was last displayed, the TI-83 Plus will replot the graph based on new values when you press s.
Graphing a Family of Curves If you enter a list (Chapter 11) as an element in an expression, the TI-83 Plus plots the function for each value in the list, thereby graphing a family of curves. In Simul graphing-order mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on. {2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and 6 sin(X). {2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X).
Exploring Graphs with the Free-Moving Cursor Free-Moving Cursor When a graph is displayed, press |, ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or †, the cursor moves from the center of the viewing window. As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if CoordOn format is selected.
value displayed at the bottom of the screen actually may not be a point on the function. To move the cursor along a function, use r. The coordinate values displayed as you move the cursor approximate actual math coordinates, *accurate to within the width and height of the pixel. As Xmin, Xmax, Ymin, and Ymax get closer together (as in a Zoom In) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates.
Exploring Graphs with TRACE Beginning a Trace Use TRACE to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the Y= editor, at the middle X value on the screen. The cursor coordinates are displayed at the bottom of the screen if CoordOn format is selected.
When the trace cursor moves along a function, the Y value is calculated from the X value; that is, Y=Yn(X). If the function is undefined at an X value, the Y value is blank. Trace cursor on the curve If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately. Moving the Trace Cursor from Function to Function To move the trace cursor from function to function, press † and }.
be valid for the current viewing window. When you have completed the entry, press Í to move the cursor. Note: This feature does not apply to stat plots. Panning to the Left or Right If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right. Xmin and Xmax are updated to correspond to the new viewing window.
Leaving and Returning to TRACE When you leave and return to TRACE, the trace cursor is displayed in the same location it was in when you left TRACE, unless Smart Graph has replotted the graph. Using TRACE in a Program On a blank line in the program editor, press r. The instruction Trace is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function.
Exploring Graphs with the ZOOM Instructions ZOOM Menu To display the ZOOM menu, press q. You can adjust the viewing window of the graph quickly in several ways. All ZOOM instructions are accessible from programs. ZOOM MEMORY 1:ZBox 2:Zoom In 3:Zoom Out 4:ZDecimal 5:ZSquare 6:ZStandard 7:ZTrig 8:ZInteger 9:ZoomStat 0:ZoomFit TI-83 Plus Draws a box to define the viewing window. Magnifies the graph around the cursor. Views more of a graph around the cursor. Sets @X and @Y to 0.1.
Zoom Cursor When you select 1:ZBox, 2:Zoom In, or 3:Zoom Out, the cursor on the graph becomes the zoom cursor (+), a smaller version of the free-moving cursor (+). ZBox To define a new viewing window using ZBox, follow these steps. 1. Select 1:ZBox from the ZOOM menu. The zoom cursor is displayed at the center of the screen. 2. Move the zoom cursor to any spot you want to define as a corner of the box, and then press Í.
To use ZBox to define another box within the new graph, repeat steps 2 through 4. To cancel ZBox, press ‘. Zoom In, Zoom Out Zoom In magnifies the part of the graph that surrounds the cursor location. Zoom Out displays a greater portion of the graph, centered on the cursor location. The XFact and YFact settings determine the extent of the zoom. To zoom in on a graph, follow these steps. 1. Check XFact and YFact; change as needed. 2. Select 2:Zoom In from the ZOOM menu. The zoom cursor is displayed. 3.
4. Press Í. The TI-83 Plus adjusts the viewing window by XFact and YFact; updates the window variables; and replots the selected functions, centered on the cursor location. 5. Zoom in on the graph again in either of two ways. • To zoom in at the same point, press Í. • To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press Í. To zoom out on a graph, select 3:Zoom Out and repeat steps 3 through 5.
ZSquare ZSquare replots the functions immediately. It redefines the viewing window based on the current values of the window variables. It adjusts in only one direction so that @X=@Y, which makes the graph of a circle look like a circle. Xscl and Yscl remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph. ZStandard ZStandard replots the functions immediately. It updates the window variables to the standard values shown below.
ZInteger ZInteger redefines the viewing window to the dimensions shown below. To use ZInteger, move the cursor to the point that you want to be the center of the new window, and then press Í; ZInteger replots the functions. @X=1 @Y=1 Xscl=10 Yscl=10 ZoomStat ZoomStat redefines the viewing window so that all statistical data points are displayed. For regular and modified box plots, only Xmin and Xmax are adjusted. ZoomFit ZoomFit replots the functions immediately.
Using ZOOM MEMORY ZOOM MEMORY Menu To display the ZOOM MEMORY menu, press q ~. ZOOM MEMORY 1: ZPrevious 2: ZoomSto 3: ZoomRcl 4: SetFactors... Uses the previous viewing window. Stores the user-defined window. Recalls the user-defined window. Changes Zoom In and Zoom Out factors. ZPrevious ZPrevious replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction. ZoomSto ZoomSto immediately stores the current viewing window.
ZoomRcl ZoomRcl graphs the selected functions in a user-defined viewing window. The user-defined viewing window is determined by the values stored with the ZoomSto instruction. The window variables are updated with the user-defined values, and the graph is plotted. ZOOM FACTORS The zoom factors, XFact and YFact, are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to Zoom In or Zoom Out around a point.
Changing XFact and YFact You can change XFact and YFact in either of two ways. • Enter a new value. The original value is cleared automatically when you enter the first digit. • Place the cursor on the digit you want to change, and then enter a value or press { to delete it. Using ZOOM MEMORY Menu Items from the Home Screen or a Program From the home screen or a program, you can store directly to any of the user-defined ZOOM variables.
Using the CALC (Calculate) Operations CALCULATE Menu To display the CALCULATE menu, press y ãCALCä. Use the items on this menu to analyze the current graph functions. CALCULATE 1:value 2:zero 3:minimum 4:maximum 5:intersect 6:dy/dx 7:‰f(x)dx Calculates a function Y value for a given X. Finds a zero (x-intercept) of a function. Finds a minimum of a function. Finds a maximum of a function. Finds an intersection of two functions. Finds a numeric derivative of a function.
To evaluate a selected function at X, follow these steps. 1. Select 1:value from the CALCULATE menu. The graph is displayed with X= in the bottom-left corner. 2. Enter a real value, which can be an expression, for X between Xmin and Xmax. 3. Press Í. The cursor is on the first selected function in the Y= editor at the X value you entered, and the coordinates are displayed, even if CoordOff format is selected. To move the cursor from function to function at the entered X value, press } or †.
The time zero spends to find the correct zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess. To find a zero of a function, follow these steps. 1. Select 2:zero from the CALCULATE menu. The current graph is displayed with Left Bound? in the bottom-left corner. 2. Press } or † to move the cursor onto the function for which you want to find a zero. 3.
4. Press | or ~ (or enter a value) to select a point near the zero of the function, between the bounds, and then press Í. The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. To move to the same x-value for other selected functions, press } or †. To restore the free-moving cursor, press | or ~. minimum, maximum minimum and maximum find a minimum or maximum of a function within a specified interval to a tolerance of 1âL5.
The cursor is on the solution, and the coordinates are displayed, even if you have selected CoordOff format; Minimum or Maximum is displayed in the bottom-left corner. To move to the same x-value for other selected functions, press } or †. To restore the free-moving cursor, press | or ~. intersect intersect finds the coordinates of a point at which two or more functions intersect using solve(. The intersection must appear on the display to use intersect. To find an intersection, follow these steps. 1.
3. Press † or }, if necessary, to move the cursor to the second function, and then press Í. 4. Press ~ or | to move the cursor to the point that is your guess as to location of the intersection, and then press Í. The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. Intersection is displayed in the bottom-left corner. To restore the free-moving cursor, press |, }, ~, or †.
To move to the same x-value for other selected functions, press } or †. To restore the free-moving cursor, press | or ~. ‰f(x)dx ‰f(x)dx (numerical integral) finds the numerical integral of a function in a specified interval. It uses the fnInt( function, with a tolerance of H=1âL3. To find the numerical derivative of a function, follow these steps. 1. Select 7:‰f(x)dx from the CALCULATE menu. The current graph is displayed with Lower Limit? in the bottom-left corner. 2.
Chapter 4: Parametric Graphing Getting Started: Path of a Ball Getting Started is a fast-paced introduction. Read the chapter for details. Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How far does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity.
1. Press z. Press † † † ~ Í to select Par mode. Press † † ~ Í to select Simul for simultaneous graphing of all three parametric equations in this example. 2. Press o. Press 30 „ ™ 25 y ; 1 (to select ¡) ¤ Í to define X1T in terms of T. 3. Press 30 „ ˜ 25 y ; 1 ¤ ¹ 9.8 ¥ 2 „ ¡ Í to define Y1T. The vertical component vector is defined by X2T and Y2T. 4. Press 0 Í to define X2T. 5. Press ~ to display the VARS Y.VARS menu. Press 2 to display the PARAMETRIC secondary menu. Press 2 Í to define Y2T.
The horizontal component vector is defined by X3T and Y3T. 6. Press ~ 2, and then press 1 Í to define X3T. Press 0 Í to define Y3T. 7. Press | | } Í to change the graph style to è for X3T and Y3T. Press } Í Í to change the graph style to ë for X2T and Y2T. Press } Í Í to change the graph style to ë for X1T and Y1T. (These keystrokes assume that all graph styles were set to ç originally.) 8. Press p. Enter these values for the window variables. Tmin=0 Tmax=5 Tstep=.
10. Press s. The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion. Tip: To simulate the ball flying through the air, set graph style to ì (animate) for X1T and Y1T. 11. Press r to obtain numerical results and answer the questions at the beginning of this section. Tracing begins at Tmin on the first parametric equation (X1T and Y1T). As you press ~ to trace the curve, the cursor follows the path of the ball over time.
Defining and Displaying Parametric Graphs TI-83 Plus Graphing Mode Similarities The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing. Setting Parametric Graphing Mode To display the mode screen, press z.
In this editor, you can display and enter both the X and Y components of up to six equations, X1T and Y1T through X6T and Y6T. Each is defined in terms of the independent variable T. A common application of parametric graphs is graphing equations over time. Selecting a Graph Style The icons to the left of X1T through X6T represent the graph style of each parametric equation (Chapter 3). The default in Par mode is ç (line), which connects plotted points.
Selecting and Deselecting Parametric Equations The TI-83 Plus graphs only the selected parametric equations. In the Y= editor, a parametric equation is selected when the = signs of both the X and Y components are highlighted. You may select any or all of the equations X1T and Y1T through X6T and Y6T. To change the selection status, move the cursor onto the = sign of either the X or Y component and press Í. The status of both the X and Y components is changed.
Setting the Graph Format To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings; Seq graphing mode has an additional axes format setting. Displaying a Graph When you press s, the TI-83 Plus plots the selected parametric equations. It evaluates the X and Y components for each value of T (from Tmin to Tmax in intervals of Tstep), and then plots each point defined by X and Y.
• Store parametric equations. • Select or deselect parametric equations. • Store values directly to window variables.
Exploring Parametric Graphs Free-Moving Cursor The free-moving cursor in Par graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. TRACE To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one Tstep at a time.
To move five plotted points at a time on a function, press y | or y ~. If you move the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately. Quick Zoom is available in Par graphing; panning is not (Chapter 3). Moving the Trace Cursor to Any Valid T Value To move the trace cursor to any valid T value on the current function, enter the number.
ZOOM operations in Par graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. ZOOM The T window variables (Tmin, Tmax, and Tstep) are only affected when you select ZStandard. The VARS ZOOM secondary menu ZT/Zq items 1:ZTmin, 2:ZTmax, and 3:ZTstep are the zoom memory variables for Par graphing. CALC operations in Par graphing work the same as in Func graphing.
Chapter 5: Polar Graphing Getting Started: Polar Rose Getting Started is a fast-paced introduction. Read the chapter for details. The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B. 1. Press z to display the mode screen. Press † † † ~ ~ Í to select Pol graphing mode. Select the defaults (the options on the left) for the other mode settings. 2. Press o to display the polar Y= editor. Press 8 ˜ 2.
3. Press q 6 to select 6:ZStandard and graph the equation in the standard viewing window. The graph shows only five petals of the rose, and the rose does not appear to be symmetrical. This is because the standard window sets qmax=2p and defines the window, rather than the pixels, as square. 4. Press p to display the window variables. Press † 4 y B to increase the value of qmax to 4p. 5. Press q 5 to select 5:ZSquare and plot the graph. 6.
Defining and Displaying Polar Graphs TI-83 Plus Graphing Mode Similarities The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing. Setting Polar Graphing Mode To display the mode screen, press z.
In this editor, you can enter and display up to six polar equations, r1 through r6. Each is defined in terms of the independent variable q. Selecting Graph Styles The icons to the left of r1 through r6 represent the graph style of each polar equation (Chapter 3). The default in Pol graphing mode is ç (line), which connects plotted points. Line, è (thick), ë (path), ì (animate), and í (dot) styles are available for polar graphing.
To change the selection status, move the cursor onto the = sign, and then press Í. Setting Window Variables To display the window variable values, press p. These variables define the viewing window. The values below are defaults for Pol graphing in Radian angle mode. qmin=0 qmax=6.2831853... qstep=.1308996...
Setting the Graph Format To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. Displaying a Graph When you press s, the TI-83 Plus plots the selected polar equations. It evaluates R for each value of q (from qmin to qmax in intervals of qstep) and then plots each point. The window variables define the viewing window. As the graph is plotted, X, Y, R, and q are updated.
• Store polar equations. • Select or deselect polar equations. • Store values directly to window variables.
Exploring Polar Graphs Free-Moving Cursor The free-moving cursor in Pol graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. TRACE To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one qstep at a time.
screen, the coordinate values at the bottom of the screen continue to change appropriately. Quick Zoom is available in Pol graphing mode; panning is not (Chapter 3). Moving the Trace Cursor to Any Valid q Value To move the trace cursor to any valid q value on the current function, enter the number. When you enter the first digit, a q= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the q= prompt.
CALC operations in Pol graphing work the same as in Func graphing. The CALCULATE menu items available in Pol graphing are 1:value, 2:dy/dx, and 3:dr/dq.
Chapter 6: Sequence Graphing Getting Started: Forest and Trees Getting Started is a fast-paced introduction. Read the chapter for details. A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees? 1. Press z. Press † † † ~ ~ ~ Í to select Seq graphing mode. 2. Press y .
3. Press o. If the graph-style icon is not í (dot), press | |, press Í until í is displayed, and then press ~ ~. 4. Press ~ 3 to select iPart( (integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain. Press Ë 8 y [u] £ „ ¹ 1 ¤ to define the number of trees after each harvest. Press à 1000 ¤ to define the new trees. Press † 4000 to define the number of trees at the beginning of the program. 5. Press p 0 to set nMin=0. Press † 50 to set nMax=50.
6. Press r. Tracing begins at nMin (the start of the forestry plan). Press ~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for n (number of years), X (X=n, because n is plotted on the x-axis), and Y (tree count) are displayed at the bottom.
Defining and Displaying Sequence Graphs TI-83 Plus Graphing Mode Similarities The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing. Setting Sequence Graphing Mode To display the mode screen, press z.
You can define sequence functions in terms of: • The independent variable n • The previous term in the sequence function, such as u(nN1) • The term that precedes the previous term in the sequence function, such as u(nN2) • The previous term or the term that precedes the previous term in another sequence function, such as u(nN1) or u(nN2) referenced in the sequence v(n).
The sequence Y= editor displays the nMin value because of its relevance to u(nMin), v(nMin), and w(nMin), which are the initial values for the sequence equations u(n), v(n), and w(n), respectively. nMin in the Y= editor is the same as nMin in the window editor. If you enter a new value for nMin in one editor, the new value for nMin is updated in both editors. Note: Use u(nMin), v(nMin), or w(nMin) only with a recursive sequence, which requires an initial value.
Defining and Editing a Sequence Function To define or edit a sequence function, follow the steps in Chapter 3 for defining a function. The independent variable in a sequence is n. In Seq graphing mode, you can enter the sequence variable in either of two ways. • Press „. • Press y N [N]. You can enter the function name from the keyboard. • To enter the function name u, press y [u] (above ¬). • To enter the function name v, press y [v] (above −).
For example, in the nonrecursive sequence below, you can calculate u(5) directly, without first calculating u(1) or any previous term. The sequence equation above returns the sequence 2, 4, 6, 8, 10, …for n = 1, 2, 3, 4, 5, … . Note: You may leave blank the initial value u(nMin) when calculating nonrecursive sequences.
Using an initial value u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, . . . Tip: On the TI-83 Plus, you must type each character of the terms. For example, to enter u(nN1), press y [u] £ „ ¹ À ¤. Recursive sequences require an initial value or values, since they reference undefined terms. • If each term in the sequence is defined in relation to the previous term, as in u(nN1), you must specify an initial value for the first term.
Setting Window Variables To display the window variables, press p. These variables define the viewing window. The values below are defaults for Seq graphing in both Radian and Degree angle modes.
PlotStart is the first term to be plotted. PlotStart=1 begins plotting on the first term in the sequence. If you want plotting to begin with the fifth term in a sequence, for example, set PlotStart=5. The first four terms are evaluated but are not plotted on the graph. PlotStep is the incremental n value for graphing only. PlotStep does not affect sequence evaluation; it only designates which points are plotted on the graph.
Selecting Axes Combinations Setting the Graph Format To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in Seq mode.
Axes Setting x-axis y-axis Time n u(n), v(n), w(n) Web u(nN1), v(nN1), w(nN1) u(n), v(n), w(n) uv u(n) v(n) vw v(n) w(n) uw u(n) w(n) Displaying a Sequence Graph To plot the selected sequence functions, press s. As a graph is plotted, the TI-83 Plus updates X, Y, and n. Smart Graph applies to sequence graphs (Chapter 3).
Exploring Sequence Graphs Free-Moving Cursor The free-moving cursor in Seq graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. TRACE The axes format setting affects TRACE. When Time, uv, vw, or uw axes format is selected, TRACE moves the cursor along the sequence one PlotStep increment at a time.
In Web format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the x-axis at the initial value of the first selected function. Tip: To move the cursor to a specified n during a trace, enter a value for n, and press Í. For example, to quickly return the cursor to the beginning of the sequence, paste nMin to the n= prompt and press Í.
ZOOM operations in Seq graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. ZOOM PlotStart, PlotStep, nMin, and nMax are only affected when you select ZStandard. The VARS Zoom secondary menu ZU items 1 through 7 are the ZOOM MEMORY variables for Seq graphing. CALC The only CALC operation available in Seq graphing is value. • When Time axes format is selected, value displays Y (the u(n) value) for a specified n value.
Evaluating u, v, and w To enter the sequence names u, v, or w, press y [u], [v], or [w]. You can evaluate these names in any of three ways. • Calculate the nth value in a sequence. • Calculate a list of values in a sequence. • Generate a sequence with u(nstart,nstop[,nstep]). nstep is optional; default is 1.
Graphing Web Plots Graphing a Web Plot To select Web axes format, press y . ~ Í. A web plot graphs u(n) versus u(nN1), which you can use to study long-term behavior (convergence, divergence, or oscillation) of a recursive sequence. You can see how the sequence may change behavior as its initial value changes. Valid Functions for Web Plots When Web axes format is selected, a sequence will not graph properly or will generate an error.
Displaying the Graph Screen In Web format, press s to display the graph screen. The TI-83 Plus: • Draws a y=x reference line in AxesOn format. • Plots the selected sequences with u(nN1) as the independent variable. Note: A potential convergence point occurs whenever a sequence intersects the y=x reference line. However, the sequence may or may not actually converge at that point, depending on the sequence’s initial value. Drawing the Web To activate the trace cursor, press r.
Using Web Plots to Illustrate Convergence Example: Convergence 1. Press o in Seq mode to display the sequence Y= editor. Make sure the graph style is set to í (dot), and then define nMin, u(n) and u(nMin) as shown below. 2. Press y . Í to set Time axes format. 3. Press p and set the variables as shown below.
4. Press s to graph the sequence. 5. Press y . and select the Web axes setting. 6. Press p and change the variables below. Xmin=L10 Xmax=10 7. Press s to graph the sequence. 8. Press r, and then press ~ to draw the web. The displayed cursor coordinates n, X (u(nN1)), and Y (u(n)) change accordingly. When you press ~, a new n value is displayed, and the trace cursor is on the sequence. When you press ~ again, the n value remains the same, and the cursor moves to the y=x reference line.
Graphing Phase Plots Graphing with uv, vw, and uw The phase-plot axes settings uv, vw, and uw show relationships between two sequences. To select a phase-plot axes setting, press y ., press ~ until the cursor is on uv, vw, or uw, and then press Í. Axes Setting x-axis y-axis uv u(n) v(n) vw v(n) w(n) uw u(n) w(n) Example: Predator-Prey Model Use the predator-prey model to determine the regional populations of a predator and its prey that would maintain population equilibrium for the two species.
These are the variables (given values are in parentheses): R = M = K = W = G = D = n = Rn = Wn = number of rabbits rabbit population growth rate without foxes rabbit population death rate with foxes number of foxes fox population growth rate with rabbits fox population death rate without rabbits time (in months) R n N1 (1+MNKW n N1 ) W n N1 (1+GR n N1 ND) (.05) (.001) (.0002) (.03) 1. Press o in Seq mode to display the sequence Y= editor.
3. Press p and set the variables as shown below. nMin=0 nMax=400 PlotStart=1 PlotStep=1 Xmin=0 Xmax=400 Xscl=100 Ymin=0 Ymax=300 Yscl=100 4. Press s to graph the sequence. 5. Press r ~ to individually trace the number of rabbits (u(n)) and foxes (v(n)) over time (n). Tip: Press a number, and then press Í to jump to a specific n value (month) while in TRACE. 6. Press y . ~ ~ Í to select uv axes format.
7. Press p and change these variables as shown below. Xmin=84 Xmax=237 Xscl=50 Ymin=25 Ymax=75 Yscl=10 8. Press r. Trace both the number of rabbits (X) and the number of foxes (Y) through 400 generations. Note: When you press r, the equation for u is displayed in the top-left corner. Press } or † to see the equation for v.
Comparing TI-83 Plus and TI-82 Sequence Variables Sequences and Window Variables Refer to the table if you are familiar with the TI-82. It shows TI-83 Plus sequences and sequence window variables, as well as their TI-82 counterparts. TI-83 Plus TI.
Keystroke Differences Between TI-83 Plus and TI-82 Sequence Keystroke Changes Refer to the table if you are familiar with the TI-82. It compares TI-83 Plus sequence-name syntax and variable syntax with TI.82 sequence-name syntax and variable syntax.
Chapter 7: Tables Getting Started: Roots of a Function Getting Started is a fast-paced introduction. Read the chapter for details. Evaluate the function Y = X3 N 2X at each integer between L10 and 10. How many sign changes occur, and at what X values? 1. Press z † † † Í to set Func graphing mode. 2. Press o. Press „ 3 to select 3. Then press ¹ 2 „ to enter the function Y1=X3N2X. 3. Press y - to display the TABLE SETUP screen. Press Ì 10 Í to set TblStart=L10. Press 1 Í to set @Tbl=1.
Press Í to select Indpnt: Auto (automatically generated independent values). Press † Í to select Depend: Auto (automatically generated dependent values). 4. Press y 0 to display the table screen. 5. Press † until you see the sign changes in the value of Y1.
Setting Up the Table TABLE SETUP Screen To display the TABLE SETUP screen, press y -. TblStart, @Tbl TblStart (table start) defines the initial value for the independent variable. TblStart applies only when the independent variable is generated automatically (when Indpnt: Auto is selected). @Tbl (table step) defines the increment for the independent variable. Note: In Seq mode, both TblStart and @Tbl must be integers.
Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask Selections Table Characteristics Indpnt: Auto Depend: Auto Values are displayed automatically in both the independent-variable column and in all dependentvariable columns. Indpnt: Ask Depend: Auto The table is empty; when you enter a value for the independent variable, all corresponding dependentvariable values are calculated and displayed automatically.
Defining the Dependent Variables Defining Dependent Variables from the Y= Editor In the Y= editor, enter the functions that define the dependent variables. Only functions that are selected in the Y= editor are displayed in the table. The current graphing mode is used. In Par mode, you must define both components of each parametric equation (Chapter 4). Editing Dependent Variables from the Table Editor To edit a selected Y= function from the table editor, follow these steps. 1.
3. Press Í. The cursor moves to the bottom line. Edit the function. 4. Press Í or †. The new values are calculated. The table and the Y= function are updated automatically. Note: You also can use this feature to view the function that defines a dependent variable without having to leave the table.
Displaying the Table The Table To display the table, press y 0. Current cell Dependent-variable values in the second and third columns Independent-variable values in the first column Current cell’s full value Note: The table abbreviates the values, if necessary. Independent and Dependent Variables The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1).
Graphing Mode Independent Variable Dependent Variable Func (function) X Y1 through Y9, and Y0 Par (parametric) T X1T/Y1T through X6T/Y6T Pol (polar) q r1 through r6 Seq (sequence) n u(n), v(n), and w(n) Clearing the Table from the Home Screen or a Program From the home screen, select the ClrTable instruction from the CATALOG. To clear the table, press Í. From a program, select 9:ClrTable from the PRGM I/O menu or from the The table is cleared upon execution.
Note: You can scroll back from the value entered for TblStart. As you scroll, TblStart is updated automatically to the value shown on the top line of the table. In the example above, TblStart=0 and @Tbl=1 generates and displays values of X=0, …, 6; but you can press } to scroll back and display the table for X=M1, …, 5. Displaying Other Dependent Variables If you have defined more than two dependent variables, the first two selected Y= functions are displayed initially.
Chapter 8: Draw Instructions Getting Started: Drawing a Tangent Line Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to find the equation of the tangent line at X = ‡2/2 for the function Y = sin(X). Before you begin, select Radian and Func mode from the mode screen, if necessary. 1. Press o to display the Y= editor. Press ˜ „ ¤ to store sin(X) in Y1. 2. Press q 7 to select 7:ZTrig, which graphs the equation in the Zoom Trig window.
3. Press y < 5 to select 5:Tangent(. The tangent instruction is initiated. 4. Press y C 2 ¤ ¥ 2. 5. Press Í. The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph.
Using the DRAW Menu DRAW Menu To display the DRAW menu, press y <. The TI-83 Plus’s interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph. DRAW POINTS STO 1:ClrDraw 2:Line( 3:Horizontal 4:Vertical 5:Tangent( 6:DrawF 7:Shade( 8:DrawInv 9:Circle( 0:Text( A:Pen TI-83 Plus Clears all drawn elements. Draws a line segment between 2 points. Draws a horizontal line. Draws a vertical line.
Before Drawing on a Graph The DRAW instructions draw on top of graphs. Therefore, before you use the DRAW instructions, consider whether you want to perform one or more of the following actions. • Change the mode settings on the mode screen. • Change the format settings on the format screen. • Enter or edit functions in the Y= editor. • Select or deselect functions in the Y= editor. • Change the window variable values. • Turn stat plots on or off. • Clear existing drawings with ClrDraw.
You can use most DRAW menu and DRAW POINTS menu instructions to draw directly on a graph, using the cursor to identify the coordinates. You also can execute these instructions from the home screen or from within a program. If a graph is not displayed when you select a DRAW menu instruction, the home screen is displayed.
Clearing Drawings Clearing Drawings When a Graph Is Displayed All points, lines, and shading drawn on a graph with DRAW instructions are temporary. To clear drawings from the currently displayed graph, select 1:ClrDraw from the DRAW menu. The current graph is replotted and displayed with no drawn elements. Clearing Drawings from the Home Screen or a Program To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor.
Drawing Line Segments Drawing a Line Segment Directly on a Graph To draw a line segment when a graph is displayed, follow these steps. 1. Select 2:Line( from the DRAW menu. 2. Place the cursor on the point where you want the line segment to begin, and then press Í. 3. Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press Í. To continue drawing line segments, repeat steps 2 and 3. To cancel Line(, press ‘.
Drawing a Line Segment from the Home Screen or a Program Line( also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The values may be entered as expressions.
Drawing Horizontal and Vertical Lines Drawing a Line Directly on a Graph To draw a horizontal or vertical line when a graph is displayed, follow these steps. 1. Select 3:Horizontal or 4:Vertical from the DRAW menu. A line is displayed that moves as you move the cursor. 2. Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical lines) through which you want the drawn line to pass. 3. Press Í to draw the line on the graph. To continue drawing lines, repeat steps 2 and 3.
Drawing a Line from the Home Screen or a Program Horizontal (horizontal line) draws a horizontal line at Y=y. y can be an expression but not a list. Horizontal y Vertical (vertical line) draws a vertical line at X=x. x can be an expression but not a list. Vertical x To instruct the TI-83 Plus to draw more than one horizontal or vertical line, separate each instruction with a colon ( : ).
Drawing Tangent Lines Drawing a Tangent Line Directly on a Graph To draw a tangent line when a graph is displayed, follow these steps. 1. Select 5:Tangent( from the DRAW menu. 2. Press † and } to move the cursor to the function for which you want to draw the tangent line. The current graph’s Y= function is displayed in the top-left corner, if ExprOn is selected. 3. Press ~ and | or enter a number to select the point on the function at which you want to draw the tangent line. 4. Press Í.
Tip: Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for X and the equation for Y. Drawing a Tangent Line from the Home Screen or a Program Tangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X2, at point X=value. X can be an expression. expression is interpreted as being in Func mode.
Drawing Functions and Inverses Drawing a Function DrawF (draw function) draws expression as a function in terms of X on the current graph. When you select 6:DrawF from the DRAW menu, the TI-83 Plus returns to the home screen or the program editor. DrawF is not interactive. DrawF expression Note: You cannot use a list in expression to draw a family of curves.
DrawInv expression Note: You cannot use a list in expression to draw a family of curves.
Shading Areas on a Graph Shading a Graph To shade an area on a graph, select 7:Shade( from the DRAW menu. The instruction is pasted to the home screen or to the program editor. Shade( draws lowerfunc and upperfunc in terms of X on the current graph and shades the area that is specifically above lowerfunc and below upperfunc. Only the areas where lowerfunc < upperfunc are shaded. Xleft and Xright, if included, specify left and right boundaries for the shading.
patres specifies one of eight shading resolutions.
Drawing Circles Drawing a Circle Directly on a Graph To draw a circle directly on a displayed graph using the cursor, follow these steps. 1. Select 9:Circle( from the DRAW menu. 2. Place the cursor at the center of the circle you want to draw. Press Í. 3. Move the cursor to a point on the circumference. Press Í to draw the circle on the graph. Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display.
To continue drawing circles, repeat steps 2 and 3. To cancel Circle(, press ‘. Drawing a Circle from the Home Screen or a Program Circle( draws a circle with center (X,Y) and radius. These values can be expressions. Circle(X,Y,radius) Tip: When you use Circle( on the home screen or from a program, the current window values may distort the drawn circle. Use ZSquare (Chapter 3) before drawing the circle to adjust the window variables and make the circle circular.
Placing Text on a Graph Placing Text Directly on a Graph To place text on a graph when the graph is displayed, follow these steps. 1. Select 0:Text( from the DRAW menu. 2. Place the cursor where you want the text to begin. 3. Enter the characters. Press ƒ or y 7 to enter letters and q. You may enter TI-83 Plus functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.
Text(row,column,value,value…) value can be text enclosed in quotation marks ( " ), or it can be an expression. The TI-83 Plus will evaluate an expression and display the result with up to 10 characters. Split Screen On a Horiz split screen, the maximum value for row is 25. On a G.T split screen, the maximum value for row is 45, and the maximum value for column is 46.
Using Pen to Draw on a Graph Using Pen to Draw on a Graph Pen draws directly on a graph only. You cannot execute Pen from the home screen or a program. To draw on a displayed graph, follow these steps. 1. Select A:Pen from the DRAW menu. 2. Place the cursor on the point where you want to begin drawing. Press Í to turn on the pen. 3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time. 4. Press Í to turn off the pen.
Drawing Points on a Graph DRAW POINTS Menu To display the DRAW POINTS menu, press y < ~. The TI-83 Plus’s interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph. DRAW POINTS STO 1:Pt-On( 2:Pt-Off( 3:Pt-Change( 4:Pxl-On( 5:Pxl-Off( 6:Pxl-Change( 7:pxl-Test( Turns on a point. Turns off a point. Toggles a point on or off. Turns on a pixel. Turns off a pixel. Toggles a pixel on or off.
3. Press Í to draw the point. To continue drawing points, repeat steps 2 and 3. To cancel Pt.On(, press ‘. Erasing Points with Pt.Off( To erase (turn off) a drawn point on a graph, follow these steps. 1. Select 2:Pt.Off( (point off) from the DRAW POINTS menu. 2. Move the cursor to the point you want to erase. 3. Press Í to erase the point. To continue erasing points, repeat steps 2 and 3. To cancel Pt.Off(, press ‘.
Changing Points with Pt.Change( To change (toggle on or off) a point on a graph, follow these steps. 1. Select 3:Pt.Change( (point change) from the DRAW POINTS menu. 2. Move the cursor to the point you want to change. 3. Press Í to change the point’s on/off status. To continue changing points, repeat steps 2 and 3. To cancel Pt.Change(, press ‘. Drawing Points from the Home Screen or a Program Pt.On( (point on) turns on the point at (X=x,Y=y). Pt.Off( turns the point off. Pt.
Note: If you specified mark to turn on a point with Pt.On(, you must specify mark when you turn off the point with Pt.Off(. Pt.Change( does not have the mark option.
Drawing Pixels TI-83 Plus Pixels A pixel is a square dot on the TI-83 Plus display. The Pxl. (pixel) instructions let you turn on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from the DRAW POINTS menu, the TI-83 Plus returns to the home screen or the program editor. The pixel instructions are not interactive. Turning On and Off Pixels with Pxl.On( and Pxl.Off( Pxl.
Using pxl.Test( pxl.Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is turned off on the current graph. row must be an integer between 0 and 62. column must be an integer between 0 and 94. pxl.Test(row,column) Split Screen On a Horiz split screen, the maximum value for row is 30 for Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(. On a G.T split screen, the maximum value for row is 50 and the maximum value for column is 46 for Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.
Storing Graph Pictures (Pic) DRAW STO Menu To display the DRAW STO menu, press y < |. When you select an instruction from the DRAW STO menu, the TI-83 Plus returns to the home screen or the program editor. The picture and graph database instructions are not interactive. DRAW POINTS STO 1: StorePic 2: RecallPic 3: StoreGDB 4: RecallGDB Stores the current picture. Recalls a saved picture. Stores the current graph database. Recalls a saved graph database.
A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any parts of the display hidden by these items are stored with the picture. To store a graph picture, follow these steps. 1. Select 1:StorePic from the DRAW STO menu. StorePic is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the picture variable to which you want to store the picture.
Recalling Graph Pictures (Pic) Recalling a Graph Picture To recall a graph picture, follow these steps. 1. Select 2:RecallPic from the DRAW STO menu. RecallPic is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the picture variable from which you want to recall a picture. For example, if you enter 3, the TI-83 Plus will recall the picture stored to Pic3. Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to RecallPic.
Storing Graph Databases (GDB) What Is a Graph Database? A graph database (GDB) contains the set of elements that defines a particular graph. You can recreate the graph from these elements. You can store up to 10 GDBs in variables GDB1 through GDB9, or GDB0 and recall them to recreate graphs. A GDB stores five elements of a graph.
2. Enter the number (from 1 to 9, or 0) of the GDB variable to which you want to store the graph database. For example, if you enter 7, the TI-83 Plus will store the GDB to GDB7. Note: You also can select a variable from the GDB secondary menu ( 3). The variable is pasted next to StoreGDB. 3. Press Í to store the current database to the specified GDB variable.
Recalling Graph Databases (GDB) Recalling a Graph Database CAUTION: When you recall a GDB, it replaces all existing Y= functions. Consider storing the current Y= functions to another database before recalling a stored GDB. To recall a graph database, follow these steps. 1. Select 4:RecallGDB from the DRAW STO menu. RecallGDB is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the GDB variable from which you want to recall a GDB.
Deleting a Graph Database To delete a GDB from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18).
Chapter 9: Split Screen Getting Started: Exploring the Unit Circle Getting Started is a fast-paced introduction. Read the chapter for details. Use G.T (graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0°, 30°, 45°, 60°, 90°, and so on. 1. Press z to display the mode screen. Press † † ~ Í to select Degree mode. Press † ~ Í to select Par (parametric) graphing mode. Press † † † † ~ ~ Í to select G.
3. Press o to display the Y= editor for Par graphing mode. Press ™ „ ¤ Í to store cos(T) to X1T. Press ˜ „ ¤ Í to store sin(T) to Y1T. 4. Press p to display the window editor. Enter these values for the window variables. Tmin=0 Tmax=360 Tstep=15 Xmin=L2.3 Xmax=2.3 Xscl=1 Ymin=L2.5 Ymax=2.5 Yscl=1 5. Press r. On the left, the unit circle is graphed parametrically in Degree mode and the trace cursor is activated.
Using Split Screen Setting a Split-Screen Mode To set a split-screen mode, press z, and then move the cursor to the bottom line of the mode screen. • Select Horiz (horizontal) to display the graph screen and another screen split horizontally. • Select G.T (graph-table) to display the graph screen and table screen split vertically. $ $ The split screen is activated when you press any key that applies to either half of the split screen.
Some screens are never displayed as split screens. For example, if you press z in Horiz or G.T mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns. When you press a key or key combination in either Horiz or G.T mode, the cursor is placed in the half of the display for which that key applies. For example, if you press r, the cursor is placed in the half in which the graph is displayed.
Horiz (Horizontal) Split Screen Horiz Mode In Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves. The top half displays the graph. The bottom half displays any of these editors.
Moving from Half to Half in Horiz Mode To use the top half of the split screen: • Press s or r. • Select a ZOOM or CALC operation. To use the bottom half of the split screen: • Press any key or key combination that displays the home screen. • Press o (Y= editor). • Press … Í (stat list editor). • Press p (window editor). • Press y 0 (table editor). Full Screens in Horiz Mode All other screens are displayed as full screens in Horiz split-screen mode.
G.T (Graph-Table) Split Screen G.T Mode In G.T (graph-table) split-screen mode, a vertical line splits the screen into left and right halves. The left half displays the graph. The right half displays the table. Moving from Half to Half in G.T Mode To use the left half of the split screen: • Press s or r. • Select a ZOOM or CALC operation. To use the right half of the split screen, press y 0.
Using r in G.T Mode As you move the trace cursor along a graph in the split screen’s left half in G.T mode, the table on the right half automatically scrolls to match the current cursor values. Note: When you trace in Par graphing mode, both components of an equation (XnT and YnT) are displayed in the two columns of the table. As you trace, the current value of the independent variable T is displayed on the graph. Full Screens in G.
TI-83 Plus Pixels in Horiz and G.T Modes TI-83 Plus Pixels in Horiz and G.T Modes Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on. DRAW POINTS Menu Pixel Instructions For Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(: • In Horiz mode, row must be {30; column must be {94. • In G.T mode, row must be {50; column must be {46. Pxl.
• In G.T mode, row must be {45; column must be {46. Text(row,column,"text") PRGM I/O Menu Output( Instruction For the Output( instruction: • In Horiz mode, row must be {4; column must be {16. • In G.T mode, row must be {8; column must be {16. Output(row,column,"text") Setting a Split-Screen Mode from the Home Screen or a Program To set Horiz or G.T from a program, follow these steps. 1. Press z while the cursor is on a blank line in the program editor. 2. Select Horiz or G.T.
Chapter 10: Matrices Getting Started: Systems of Linear Equations Getting Started is a fast-paced introduction. Read the chapter for details. Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83 Plus, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form. 1. Press y >. Press ~ ~ to display the MATRX EDIT menu. Press 1 to select 1: [A]¸ 2. Press 2 Í 4 Í to define a 2×4 matrix.
4. Press 2 Í 3 Í 3 Í to complete the first row for X + 2Y + 3Z = 3. 5. Press 2 Í 3 Í 4 Í 3 Í to enter the second row for 2X + 3Y + 4Z = 3. 6. Press y 5 to return to the home screen. If necessary, press ‘ to clear the home screen. Press y > ~ to display the MATRX MATH menu. Press } to wrap to the end of the menu. Select B:rref( to copy rref( to the home screen. 7. Press y > 1 to select 1: [A] from the MATRX NAMES menu. Press ¤ Í. The reduced row-echelon form of the matrix is displayed and stored in Ans.
Defining a Matrix What Is a Matrix? A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor. The TI-83 Plus has 10 matrix variables, [A] through [J]. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI-83 Plus matrices. Selecting a Matrix Before you can define or display a matrix in the editor, you first must select the matrix name.
2. Select the matrix you want to define. The MATRX EDIT screen is displayed. Accepting or Changing Matrix Dimensions The dimensions of the matrix (row × column) are displayed on the top line. The dimensions of a new matrix are 1 ×1. You must accept or change the dimensions each time you edit a matrix. When you select a matrix to define, the cursor highlights the row dimension. • To accept the row dimension, press Í. • To change the row dimension, enter the number of rows (up to 99), and then press Í.
Viewing and Editing Matrix Elements Displaying Matrix Elements After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero. Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three columns of a matrix, showing the values of the elements in abbreviated form if necessary.
Deleting a Matrix To delete matrices from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Viewing a Matrix The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line. Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions.
Viewing-Context Keys Key Function | or ~ Moves the rectangular cursor within the current row † or } Moves the rectangular cursor within the current column; on the top row, } moves the cursor to the column dimension; on the column dimension, } moves the cursor to the row dimension Í Switches to editing context; activates the edit cursor on the bottom line ‘ Switches to editing context; clears the value on the bottom line Any entry character Switches to editing context; clears the value on the bott
2. Press |, }, ~, and † to move the cursor to the matrix element you want to change. 3. Switch to editing context by pressing Í, ‘, or an entry key. 4. Change the value of the matrix element using the editing-context keys described below. You may enter an expression, which is evaluated when you leave editing context. Note: You can press ‘ Í to restore the value at the rectangular cursor if you make a mistake. 5. Press Í, }, or † to move to another element.
Editing-Context Keys Key Function | or ~ Moves the edit cursor within the value † or } Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor within the column Í Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor to the next row element ‘ Clears the value on the bottom line Any entry character Copies the character to the location of the edit cur
Using Matrices with Expressions Using a Matrix in an Expression To use a matrix in an expression, you can do any of the following. • Copy the name from the MATRX NAMES menu. • Recall the contents of the matrix into the expression with y K (Chapter 1). • Enter the matrix directly (see below). Entering a Matrix in an Expression You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression. To enter a matrix in an expression, follow these steps. 1.
5. Repeat steps 2 through 4 to enter all of the rows. 6. Press y [ ] ] to indicate the end of the matrix. Note: The closing ]] are not necessary at the end of an expression or preceding !. The resulting matrix is displayed in the form: [[element1,1,...,element1,n],...,[elementm,1,...,elementm,n]] Any expressions are evaluated when the entry is executed. Note: The commas that you must enter to separate elements are not displayed on output.
Displaying and Copying Matrices Displaying a Matrix To display the contents of a matrix on the home screen, select the matrix from the MATRX NAMES menu, and then press Í. Ellipses in the left or right column indicate additional columns. # or $ in the right column indicate additional rows. Press ~, |, †, and } to scroll the matrix. Copying One Matrix to Another To copy a matrix, follow these steps. 1. Press y > to display the MATRX NAMES menu. 2. Select the name of the matrix you want to copy.
3. Press ¿. 4. Press y > again and select the name of the new matrix to which you want to copy the existing matrix. 5. Press Í to copy the matrix to the new matrix name. Accessing a Matrix Element On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select matrix from the MATRX NAMES menu.
Using Math Functions with Matrices Using Math Functions with Matrices You can use many of the math functions on the TI-83 Plus keyboard, the MATH menu, the MATH NUM menu, and the MATH TEST menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same. + (Add), – (Subtract), ä (Multiply) To add (Ã) or subtract (¹) matrices, the dimensions must be the same.
matrixAämatrixB Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is multiplied by value. matrixävalue valueämatrix L (Negation) Negating a matrix (Ì) returns a matrix in which the sign of every element is changed (reversed).
abs( abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of each element of matrix. abs(matrix) round( round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded to 10 digits. round(matrix[,#decimals]) M1 (Inverse) Use the L1 function (œ) to invert a matrix (^L1 is not valid). matrix must be square. The determinant cannot equal zero.
matrixL1 Powers To raise a matrix to a power, matrix must be square. You can use 2 (¡), 3 (MATH menu), or ^power (›) for integer power between 0 and 255. matrix2 matrix3 matrix^power Relational Operations To compare two matrices using the relational operations = and ƒ (TEST menu), they must have the same dimensions. = and ƒ compare matrixA and matrixB on an element-by-element basis. The other relational operations are not valid with matrices.
matrixAƒmatrixB returns 1 if at least one comparison is false; it returns 0 if no comparison is false. iPart(, fPart(, int( iPart( (integer part), fPart( (fractional part), and int( (greatest integer) are on the MATH NUM menu. iPart( returns a matrix containing the integer part of each element of matrix. fPart( returns a matrix containing the fractional part of each element of matrix. int( returns a matrix containing the greatest integer of each element of matrix.
Using the MATRX MATH Operations MATRX MATH Menu To display the MATRX MATH menu, press y > ~. NAMES MATH EDIT 1: det( 2: T 3: dim( 4: Fill( 5: identity( 6: randM( 7: augment( 8: Matr4list( 9: List4matr( 0: cumSum( A: ref( B: rref( C: rowSwap( D: row+( E: ärow( F: ärow+( TI-83 Plus Calculates the determinant. Transposes the matrix. Returns the matrix dimensions. Fills all elements with a constant. Returns the identity matrix. Returns a random matrix. Appends two matrices. Stores a matrix to a list.
det( det( (determinant) returns the determinant (a real number) of a square matrix. det(matrix) T (Transpose) (transpose) returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of matrix. T matrixT Accessing Matrix Dimensions with dim( dim( (dimension) returns a list containing the dimensions ({rows columns}) of matrix. dim(matrix) Note: dim(matrix)!Ln:Ln(1) returns the number of rows. dim(matrix)!Ln:Ln(2) returns the number of columns.
Creating a Matrix with dim( Use dim( with ¿ to create a new matrixname of dimensions rows × columns with 0 as each element. {rows,columns}!dim(matrixname) Redimensioning a Matrix with dim( Use dim( with ¿ to redimension an existing matrixname to dimensions rows × columns. The elements in the old matrixname that are within the new dimensions are not changed. Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted.
Fill(value,matrixname) identity( identity( returns the identity matrix of dimension rows × dimension columns. identity(dimension) randM( randM( (create random matrix) returns a rows × columns random matrix of integers ‚ L9 and 9. The seed value stored to the rand function controls the values (Chapter 2). randM(rows,columns) augment( augment( appends matrixA to matrixB as new columns. matrixA and matrixB both must have the same number of rows.
augment(matrixA,matrixB) Matr4list( Matr4list( (matrix stored to list) fills each listname with elements from each column in matrix. Matr4list( ignores extra listname arguments. Likewise, Matr4list( ignores extra matrix columns. Matr4list(matrix,listnameA,...,listname n) & Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with a specific column from matrix, you must enter column# after matrix.
Matr4list(matrix,column#,listname) & List4matr( List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. If dimensions of all lists are not equal, List4matr( fills each extra matrixname row with 0. Complex lists are not valid. List4matr(listA,...,list n,matrixname) & cumSum( cumSum( returns cumulative sums of the elements in matrix, starting with the first element. Each element is the cumulative sum of the column from top to bottom.
cumSum(matrix) Row Operations MATRX MATH menu items A through F are row operations. You can use a row operation in an expression. Row operations do not change matrix in memory. You can enter all row numbers and values as expressions. You can select the matrix from the MATRX NAMES menu. ref(, rref( ref( (row-echelon form) returns the row-echelon form of a real matrix. The number of columns must be greater than or equal to the number of rows.
rref(matrix) rowSwap( rowSwap( returns a matrix. It swaps rowA and rowB of matrix. rowSwap(matrix,rowA,rowB) row+( row+( (row addition) returns a matrix. It adds rowA and rowB of matrix and stores the results in rowB.
ärow( ärow( (row multiplication) returns a matrix. It multiplies row of matrix by value and stores the results in row. ärow(value,matrix,row) ärow+( ärow+( (row multiplication and addition) returns a matrix. It multiplies rowA of matrix by value, adds it to rowB, and stores the results in rowB.
Chapter 11: Lists Getting Started: Generating a Sequence Getting Started is a fast-paced introduction. Read the chapter for details. Calculate the first eight terms of the sequence 1/A2. Store the results to a usercreated list. Then display the results in fraction form. Begin this example on a blank line on the home screen. 1. Press y 9 ~ to display the LIST OPS menu. 2. Press 5 to select 5:seq(, which pastes seq( to the current cursor location. 3.
4. Press ¿, and then press y ƒ to turn on alpha-lock. Press [S] [E] [Q], and then press ƒ to turn off alpha-lock. Press 1 to complete the list name. 5. Press Í to generate the list and store it in SEQ1. The list is displayed on the home screen. An ellipsis (...) indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements. 6. Press y 9 to display the LIST NAMES menu.
7. Press to display the MATH menu. Press 1 to select 1:4Frac, which pastes 4Frac to the current cursor location. 8. Press Í to show the sequence in fraction form. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.
Naming Lists Using TI-83 Plus List Names L1 through L6 The TI-83 Plus has six list names in memory: L1, L2, L3, L4, L5, and L6. The list names L1 through L6 are on the keyboard above the numeric keys À through ¸. To paste one of these names to a valid screen, press y, and then press the appropriate key. L1 through L6 are stored in stat list editor columns 1 through 6 when you reset memory. Creating a List Name on the Home Screen To create a list name on the home screen, follow these steps. 1.
4. Enter zero to four letters, q, or numbers to complete the name. 5. Press Í. The list is displayed on the next line. The list name and its elements are stored in memory. The list name becomes an item on the LIST NAMES menu. Note: If you want to view a user-created list in the stat list editor, you must store it in the stat list editor (Chapter 12). You also can create a list name in these four places.
Storing and Displaying Lists Storing Elements to a List You can store list elements in either of two ways. • Use braces and ¿ on the home screen. • Use the stat list editor (Chapter 12). The maximum dimension of a list is 999 elements. Tip: When you store a complex number to a list, the entire list is converted to a list of complex numbers. To convert the list to a list of real numbers, display the home screen, and then enter real(listname)!listname.
Copying One List to Another To copy a list, store it to another list. Accessing a List Element You can store a value to or recall a value from a specific list element. You can store to any element within the current list dimension or one element beyond. listname(element) Deleting a List from Memory To delete lists from memory, including L1 through L6, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Resetting memory restores L1 through L6.
Using Lists in Graphing You can use lists to graph a family of curves (Chapter 3).
Entering List Names Using the LIST NAMES Menu To display the LIST NAMES menu, press y 9. Each item is a usercreated list name. LIST NAMES menu items are sorted automatically in alphanumerical order. Only the first 10 items are labeled, using 1 through 9, then 0. To jump to the first list name that begins with a particular alpha character or q, press ƒ [letter from A to Z or q]. Tip: From the top of a menu, press } to move to the bottom. From the bottom, press † to move to the top.
• The Ù symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editor’s Name= prompt or the stat plot editor’s XList: and YList: prompts. Entering a User-Created List Name Directly To enter an existing list name directly, follow these steps. 1. Press y 9 ~ to display the LIST OPS menu. 2. Select B:Ù, which pastes Ù to the current cursor location. Ù is not always necessary.
Attaching Formulas to List Names Attaching a Formula to a List Name You can attach a formula to a list name so that each list element is a result of the formula. When executed, the attached formula must resolve to a list. When anything in the attached formula changes, the list to which the formula is attached is updated automatically. • When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated.
The next screen shows another list, L4. The elements of L4 are the sum of the same formula that is attached to L3. However, quotation marks are not entered, so the formula is not attached to L4. On the next line, L6!L3(1):L3 changes the first element in L3 to L6, and then redisplays L3. The last screen shows that editing L3 updated ÙADD10, but did not change L4. This is because the formula L3+10 is attached to ÙADD10, but it is not attached to L4.
1. Press ƒ [ã], enter the formula (which must resolve to a list), and press ƒ [ã] again. Note: When you include more than one list name in a formula, each list must have the same dimension. 2. Press ¿. 3. Enter the name of the list to which you want to attach the formula. • Press y, and then enter a TI-83 Plus list name L1 through L6. • Press y 9 and select a user.created list name from the LIST NAMES menu. • Enter a user.created list name directly using Ù. 4. Press Í.
Detaching a Formula from a List You can detach (clear) an attached formula from a list in several ways. For example: • Enter ""!listname on the home screen. • Edit any element of a list to which a formula is attached. • Use the stat list editor (Chapter 12). • Use ClrList or ClrAllList to detach a formula from a list (Chapter 18).
Using Lists in Expressions Using a List in an Expression You can use lists in an expression in any of three ways. When you press Í, any expression is evaluated for each list element, and a list is displayed. • Use L1–L6 or any user-created list name in an expression. • Enter the list elements directly. • Use y K to recall the contents of the list into an expression at the cursor location (Chapter 1).
Using Lists with Math Functions You can use a list to input several values for some math functions. Other chapters and Appendix A specify whether a list is valid. The function is evaluated for each list element, and a list is displayed. • When you use a list with a function, the function must be valid for every element in the list. In graphing, an invalid element, such as L1 in ‡({1,0,L1}), is ignored. This returns an error. This graphs Xä‡(1) and Xä‡(0), but skips Xä‡(L1).
LIST OPS Menu LIST OPS Menu To display the LIST OPS menu, press y 9 ~. NAMES OPS 1: SortA( MATH 2: SortD( 3: dim( 4: Fill( 5: seq( 6: cumSum( 7: @List( 8: Select( 9: augment( 0: List4matr( A: Matr4list( B: Ù Sorts lists in ascending order. Sorts lists in descending order. Sets the list dimension. Fills all elements with a constant. Creates a sequence. Returns a list of cumulative sums. Returns difference of successive elements. Selects specific data points. Concatenates two lists.
With one list, SortA( and SortD( sort the elements of listname and update the list in memory. SortA(listname) SortD(listname) With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname. All lists must have the same dimension. SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[,dependlist2,...
Using dim( to Find List Dimensions dim( (dimension) returns the length (number of elements) of list. dim(list) Using dim( to Create a List You can use dim( with ¿ to create a new listname with dimension length from 1 to 999. The elements are zeros. length!dim(listname) Using dim( to Redimension a List You can use dim with ¿ to redimension an existing listname to dimension length from 1 to 999. • The elements in the old listname that are within the new dimension are not changed.
length!dim(listname) Fill( Fill( replaces each element in listname with value. Fill(value,listname) Note: dim( and Fill( are the same as dim( and Fill( on the MATRX MATH menu (Chapter 10). seq( seq( (sequence) returns a list in which each element is the result of the evaluation of expression with regard to variable for the values ranging from begin to end at steps of increment. variable need not be defined in memory. increment can be negative; the default value for increment is 1.
seq(expression,variable,begin,end[,increment]) cumSum( cumSum( (cumulative sum) returns the cumulative sums of the elements in list, starting with the first element. list elements can be real or complex numbers. cumSum(list) @List( @List( returns a list containing the differences between consecutive elements in list. @List subtracts the first element in list from the second element, subtracts the second element from the third, and so on.
Select( Select( selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists, xlistname and ylistname. For example, you can use Select( to select and then analyze a portion of plotted CBL 2™/CBL™ or CBR™ data. Select(xlistname,ylistname) Note: Before you use Select(, you must have selected (turned on) a scatter plot or xyLine plot. Also, the plot must be displayed in the current viewing window.
Using Select( to Select Data Points from a Plot To select data points from a scatter plot or xyLine plot, follow these steps. 1. Press y 9 ~ 8 to select 8:Select( from the LIST OPS menu. Select( is pasted to the home screen. 2. Enter xlistname, press ¢, enter ylistname, and then press ¤ to designate list names into which you want the selected data to be stored. 3. Press Í. The graph screen is displayed with Left Bound? in the bottom-left corner. 4.
5. Press | and ~ to move the cursor to the stat plot data point that you want as the left bound. 6. Press Í. A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left corner. 7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press Í.
The x-values and y-values of the selected points are stored in xlistname and ylistname. A new stat plot of xlistname and ylistname replaces the stat plot from which you selected data points. The list names are updated in the stat plot editor. Note: The two new lists (xlistname and ylistname) will include the points you select as left bound and right bound. Also, left-bound x-value right-bound x-value must be true. augment( augment( concatenates the elements of listA and listB.
List4matr( List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. If the dimensions of all lists are not equal, then List4matr( fills each extra matrixname row with 0. Complex lists are not valid. List4matr(list1,list2, . . . ,list n,matrixname) & Matr4list( Matr4list( (matrix stored to lists) fills each listname with elements from each column in matrix.
& Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with a specific column from matrix, you must enter a column# after matrix. Matr4list(matrix,column#,listname) & Ù preceding one to five characters identifies those characters as a usercreated listname. listname may comprise letters, q, and numbers, but it must begin with a letter from A to Z or q.
Ù need not precede a user-created list name where a list name is the only valid input, for example, at the Name= prompt in the stat list editor or the Xlist: and Ylist: prompts in the stat plot editor. If you enter Ù where it is not necessary, the TI-83 Plus will ignore the entry.
LIST MATH Menu LIST MATH Menu To display the LIST MATH menu, press y 9 |. NAMES OPS MATH 1:min( 2:max( 3:mean( 4:median( 5:sum( 6:prod( 7:stdDev( 8:variance( Returns minimum element of a list. Returns maximum element of a list. Returns mean of a list. Returns median of a list. Returns sum of elements in a list. Returns product of elements in list. Returns standard deviation of a list. Returns the variance of a list.
min(listA[,listB]) max(listA[,listB]) Note: min( and max( are the same as min( and max( on the MATH NUM menu. mean(, median( mean( returns the mean value of list. median( returns the median value of list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid.
sum(, prod( sum( (summation) returns the sum of the elements in list. start and end are optional; they specify a range of elements. list elements can be real or complex numbers. prod( returns the product of all elements of list. start and end elements are optional; they specify a range of list elements. list elements can be real or complex numbers.
To evaluate G 2 (N–1) from N=1 to 4: stdDev(, variance( stdDev( returns the standard deviation of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid. variance( returns the variance of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list.
Chapter 12: Statistics Getting Started: Pendulum Lengths and Periods Getting Started is a fast-paced introduction. Read the chapter for details. A group of students is attempting to determine the mathematical relationship between the length of a pendulum and its period (one complete swing of a pendulum). The group makes a simple pendulum from string and washers and then suspends it from the ceiling. They record the pendulum’s period for each of 12 string lengths.* Length (cm) 6.5 11.0 13.2 15.0 18.0 23.
1. Press z † † † Í to set Func graphing mode. 2. Press … 5 to select 5:SetUpEditor. SetUpEditor is pasted to the home screen. Press Í. This removes lists from stat list editor columns 1 through 20, and then stores lists L1 through L6 in columns 1 through 6. Note: Removing lists from the stat list editor does not delete them from memory. 3. Press … 1 to select 1:Edit from the STAT EDIT menu. The stat list editor is displayed.
5. Press ~ to move the rectangular cursor to the first row in L2. Press Ë 51 Í to store the first time measurement (.51 sec) in L2. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 time values in the table. 6. Press o to display the Y= editor. If necessary, press ‘ to clear the function Y1. As necessary, press }, Í, and ~ to turn off Plot1, Plot2, and Plot3 from the top line of the Y= editor (Chapter 3). As necessary, press †, |, and Í to deselect functions. 7.
8. Press Í to select On, which turns on plot 1. Press † Í to select " (scatter plot). Press † y d to specify Xlist:L1 for plot 1. Press † y e to specify Ylist:L2 for plot 1. Press † ~ Í to select + as the Mark for each data point on the scatter plot. 9. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and plot 1 is displayed. This is a scatter plot of the time-versus-length data.
11. Press y d ¢ y e ¢. Press ~ 1 to display the VARS Y.VARS FUNCTION secondary menu, and then press 1 to select 1:Y1. L1, L2, and Y1 are pasted to the home screen as arguments to LinReg(ax+b). 12. Press Í to execute LinReg(ax+b). The linear regression for the data in L1 and L2 is calculated. Values for a and b are displayed on the home screen. The linear regression equation is stored in Y1.
14. Press … 1 to select 1:Edit. The stat list editor is displayed. Press ~ and } to move the cursor onto L3. Press y 6. An unnamed column is displayed in column 3; L3, L4, L5, and L6 shift right one column. The Name= prompt is displayed in the entry line, and alpha-lock is on. 15. Press y 9 to display the LIST NAMES menu. If necessary, press † to move the cursor onto the list name RESID. 16. Press Í to select RESID and paste it to the stat list editor’s Name= prompt.
17. Press Í. RESID is stored in column 3 of the stat list editor. Press † repeatedly to examine the residuals. Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in L1. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in L1. Plotting the residuals will show this pattern more clearly. 18. Press y , 2 to select 2:Plot2 from the STAT PLOTS menu.
20. Press o to display the Y= editor. Press | to move the cursor onto the = sign, and then press Í to deselect Y1. Press } Í to turn off plot 1. 21. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals. Notice the pattern of the residuals: a group of negative residuals, then a group of positive residuals, and then another group of negative residuals.
23. Press q 9 to select 9:ZoomStat from the ZOOM menu. The window variables are adjusted automatically, and the original scatter plot of time-versus-length data (plot 1) is displayed. 24. Press … ~ ƒ [A] to select A:PwrReg from the STAT CALC menu. PwrReg is pasted to the home screen. Press y d ¢ y e ¢. Press ~ 1 to display the VARS Y.VARS FUNCTION secondary menu, and then press 1 to select 1:Y1. L1, L2, and Y1 are pasted to the home screen as arguments to PwrReg. 25.
26. Press s. The regression line and the scatter plot are displayed. The new function y=.192x.522 appears to fit the data well. To get more information, examine a residual plot. 27. Press o to display the Y= editor. Press | Í to deselect Y1. Press } Í to turn off plot 1. Press ~ Í to turn on plot 2. Note: Step 19 defined plot 2 to plot residuals (RESID) versus string length (L1). 28. Press q 9 to select 9:ZoomStat from the ZOOM menu.
To see the magnitudes of the residuals, continue with these steps. 29. Press r. Press ~ and | to trace the data. Observe the values for Y at each point. With this model, the largest positive residual is about 0.041 and the smallest negative residual is about L0.027. All other residuals are less than 0.02 in magnitude. Now that you have a good model for the relationship between length and period, you can use the model to predict the period for a given string length.
31. Press £ 20 ¤ to enter a string length of 20 cm. Press Í to calculate the predicted time of about 0.92 seconds. Based on the residual analysis, we would expect the prediction of about 0.92 seconds to be within about 0.02 seconds of the actual value.
32. Press y [ to recall the Last Entry. Press | | | 5 to change the string length to 50 cm. 33. Press Í to calculate the predicted time of about 1.48 seconds. Since a string length of 50 cm exceeds the lengths in the data set, and since residuals appear to be increasing as string length increases, we would expect more error with this estimate. Note: You also can make predictions using the table with the TABLE SETUP settings Indpnt:Ask and Depend:Auto (Chapter 7).
Setting Up Statistical Analyses Using Lists to Store Data Data for statistical analyses is stored in lists, which you can create and edit using the stat list editor. The TI-83 Plus has six list variables in memory, L1 through L6, to which you can store data for statistical calculations. Also, you can store data to list names that you create (Chapter 11). Setting Up a Statistical Analysis To set up a statistical analysis, follow these steps. Read the chapter for details. 1.
Displaying the Stat List Editor The stat list editor is a table where you can store, edit, and view up to 20 lists that are in memory. Also, you can create list names from the stat list editor. To display the stat list editor, press …, and then select 1:Edit from the STAT EDIT menu. The top line displays list names. L1 through L6 are stored in columns 1 through 6 after a memory reset. The number of the current column is displayed in the top-right corner. The bottom line is the entry line.
Using the Stat List Editor Entering a List Name in the Stat List Editor To enter a list name in the stat list editor, follow these steps. 1. Display the Name= prompt in the entry line in either of two ways. • Move the cursor onto the list name in the column where you want to insert a list, and then press y 6. An unnamed column is displayed and the remaining lists shift right one column. • Press } until the cursor is on the top line, and then press ~ until you reach the unnamed column.
2. Enter a valid list name in any of four ways. • Select a name from the LIST NAMES menu (Chapter 11). • Enter L1, L2, L3, L4, L5, or L6 from the keyboard. • Enter an existing user-created list name directly from the keyboard. • Enter a new user-created list name. 3. Press Í or † to store the list name and its elements, if any, in the current column of the stat list editor. To begin entering, scrolling, or editing list elements, press †. The rectangular cursor is displayed.
Creating a Name in the Stat List Editor To create a name in the stat list editor, follow these steps. 1. Display the Name= prompt. 2. Press [letter from A to Z or q] to enter the first letter of the name. The first character cannot be a number. 3. Enter zero to four letters, q, or numbers to complete the new usercreated list name. List names can be one to five characters long. 4. Press Í or † to store the list name in the current column of the stat list editor.
Removing All Lists and Restoring L1 through L6 You can remove all user-created lists from the stat list editor and restore list names L1 through L6 to columns 1 through 6 in either of two ways. • Use SetUpEditor with no arguments. • Reset all memory (Chapter 18). Clearing All Elements from a List You can clear all elements from a list in any of five ways. • Use ClrList to clear specified lists. • In the stat list editor, press } to move the cursor onto a list name, and then press ‘ Í.
Editing a List Element To edit a list element, follow these steps. 1. Move the rectangular cursor onto the element you want to edit. 2. Press Í to move the cursor to the entry line. Note: If you want to replace the current value, you can enter a new value without first pressing Í. When you enter the first character, the current value is cleared automatically. 3. Edit the element in the entry line. • Press one or more keys to enter the new value.
Note: You can enter expressions and variables for elements. 4. Press Í, }, or † to update the list. If you entered an expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element. When you edit a list element in the stat list editor, the list is updated in memory immediately.
Attaching Formulas to List Names Attaching a Formula to a List Name in Stat List Editor You can attach a formula to a list name in the stat list editor, and then display and edit the calculated list elements. When executed, the attached formula must resolve to a list. Chapter 11 describes in detail the concept of attaching formulas to list names. To attach a formula to a list name that is stored in the stat list editor, follow these steps. 1. Press … Í to display the stat list editor. 2.
4. Press ƒ [ã], enter the formula, and press ƒ [ã]. Note: If you do not use quotation marks, the TI-83 Plus calculates and displays the same initial list of answers, but does not attach the formula for future calculations. Note: Any user-created list name referenced in a formula must be preceded by an Ù symbol (Chapter 11). 5. Press Í. The TI-83 Plus calculates each list element and stores it to the list name to which the formula is attached.
Using the Stat List Editor When Formula-Generated Lists Are Displayed When you edit an element of a list referenced in an attached formula, the TI-83 Plus updates the corresponding element in the list to which the formula is attached (Chapter 11). When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI-83 Plus takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view.
Handling Errors Resulting from Attached Formulas On the home screen, you can attach to a list a formula that references another list with dimension 0 (Chapter 11). However, you cannot display the formula-generated list in the stat list editor or on the home screen until you enter at least one element to the list that the formula references. All elements of a list referenced by an attached formula must be valid for the attached formula.
Detaching Formulas from List Names Detaching a Formula from a List Name You can detach (clear) a formula from a list name in several ways. For example: • In the stat list editor, move the cursor onto the name of the list to which a formula is attached. Press Í ‘ Í. All list elements remain, but the formula is detached and the lock symbol disappears. • In the stat list editor, move the cursor onto an element of the list to which a formula is attached. Press Í, edit the element, and then press Í.
Editing an Element of a Formula-Generated List As described above, one way to detach a formula from a list name is to edit an element of the list to which the formula is attached. The TI-83 Plus protects against inadvertently detaching the formula from the list name by editing an element of the formula-generated list. Because of the protection feature, you must press Í before you can edit an element of a formula-generated list.
Switching Stat List Editor Contexts Stat List Editor Contexts The stat list editor has four contexts. • View-elements context • Edit-elements context • View-names context • Enter-name context The stat list editor is first displayed in view-elements context. To switch through the four contexts, select 1:Edit from the STAT EDIT menu and follow these steps. 1. Press } to move the cursor onto a list name. You are now in view-names context.
3. Press Í again. You are now in view-elements context. Press ~, |, †, and } to view other list elements. The current element’s full value is displayed in the entry line. 4. Press Í again. You are now in edit-elements context. You may edit the current element in the entry line. 5. Press } until the cursor is on a list name, then press y 6. You are now in enter-name context. 6. Press ‘. You are now in view-names context. 7. Press †. You are now back in view-elements context.
Stat List Editor Contexts View-Elements Context In view-elements context, the entry line displays the list name, the current element’s place in that list, and the full value of the current element, up to 12 characters at a time. An ellipsis (...) indicates that the element continues beyond 12 characters. To page down the list six elements, press ƒ †. To page up six elements, press ƒ }. To delete a list element, press {. Remaining elements shift up one row. To insert a new element, press y 6.
• When you switch to edit-elements context from view-elements context, the full value of the current element is displayed. You can edit the value of this element, and then press † and } to edit other list elements. & • When you switch to edit-elements context from view-names context, the full values of all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press ~ and | to edit any element in the list.
View-Names Context In view-names context, the entry line displays the list name and the list elements. To remove a list from the stat list editor, press {. Remaining lists shift to the left one column. The list is not deleted from memory. To insert a name in the current column, press y 6. Remaining columns shift to the right one column. Enter-Name Context In enter-name context, the Name= prompt is displayed in the entry line, and alpha-lock is on.
To leave enter-name context without entering a list name, press ‘. The stat list editor switches to view-names context.
STAT EDIT Menu STAT EDIT Menu To display the STAT EDIT menu, press …. EDIT CALC TESTS 1:Edit... 2:SortA( 3:SortD( 4:ClrList 5:SetUpEditor Displays the stat list editor. Sorts a list in ascending order. Sorts a list in descending order. Deletes all elements of a list. Stores lists in the stat list editor. Note: Chapter 13: Inferential Statistics describes the STAT TESTS menu items. SortA(, SortD( SortA( (sort ascending) sorts list elements from low to high values.
• With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist by placing its elements in the same order as the corresponding elements in keylistname. This lets you sort two-variable data on X and keep the data pairs together. All lists must have the same dimension. The sorted lists are updated in memory. SortA(listname) SortD(listname) SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[,dependlist2,...
SetUpEditor With SetUpEditor you can set up the stat list editor to display one or more listnames in the order that you specify. You can specify zero to 20 listnames. Additionally, if you want to use listnames which happen to be archived, the SetUp Editor will automatically unarchive the listnames and place them in the stat list editor at the same time. SetUpEditor [listname1,listname2,...
Restoring L1 through L6 to the Stat List Editor SetUpEditor with no listnames removes all list names from the stat list editor and restores list names L1 through L6 in the stat list editor columns 1 through 6.
Regression Model Features Regression Model Features STAT CALC menu items 3 through C are regression models. The automatic residual list and automatic regression equation features apply to all regression models. Diagnostics display mode applies to some regression models. Automatic Residual List When you execute a regression model, the automatic residual list feature computes and stores the residuals to the list name RESID. RESID becomes an item on the LIST NAMES menu (Chapter 11).
Automatic Regression Equation Each regression model has an optional argument, regequ, for which you can specify a Y= variable such as Y1. Upon execution, the regression equation is stored automatically to the specified Y= variable and the Y= function is selected. Regardless of whether you specify a Y= variable for regequ, the regression equation always is stored to the TI-83 Plus variable RegEQ, which is item 1 on the VARS Statistics EQ secondary menu.
Diagnostics Display Mode When you execute some regression models, the TI-83 Plus computes and stores diagnostics values for r (correlation coefficient) and r2 (coefficient of determination) or for R2 (coefficient of determination). r and r2 are computed and stored for these regression models. LinReg(ax+b) LinReg(a+bx) LnReg ExpReg PwrReg R2 is computed and stored for these regression models.
Note: To set DiagnosticOn or DiagnosticOff from the home screen, press y N, and then select the instruction for the mode you want. The instruction is pasted to the home screen. Press Í to set the mode. When DiagnosticOn is set, diagnostics are displayed with the results when you execute a regression model. When DiagnosticOff is set, diagnostics are not displayed with the results when you execute a regression model.
STAT CALC Menu STAT CALC Menu To display the STAT CALC menu, press … ~. EDIT CALC TESTS 1:1-Var Stats 2:2-Var Stats 3:Med-Med 4:LinReg(ax+b) 5:QuadReg 6:CubicReg 7:QuartReg 8:LinReg(a+bx) 9:LnReg 0:ExpReg A:PwrReg B:Logistic C:SinReg Calculates 1-variable statistics. Calculates 2-variable statistics. Calculates a median-median line. Fits a linear model to data. Fits a quadratic model to data. Fits a cubic model to data. Fits a quartic model to data. Fits a linear model to data.
Frequency of Occurrence for Data Points For most STAT CALC menu items, you can specify a list of data occurrences, or frequencies (freqlist). Each element in freqlist indicates how many times the corresponding data point or data pair occurs in the data set you are analyzing. For example, if L1={15,12,9,14} and ÙFREQ={1,4,1,3}, then the TI-83 Plus interprets the instruction 1.Var Stats L1, ÙFREQ to mean that 15 occurs once, 12 occurs four times, 9 occurs once, and 14 occurs three times.
1.Var Stats [Xlistname,freqlist] 2.Var Stats 2.Var Stats (two-variable statistics) analyzes paired data. Xlistname is the independent variable. Ylistname is the dependent variable. Each element in freqlist is the frequency of occurrence for each data pair (Xlistname,Ylistname). 2.Var Stats [Xlistname,Ylistname,freqlist] Med.Med (ax+b) Med.
LinReg (ax+b) LinReg(ax+b) (linear regression) fits the model equation y=ax+b to the data using a least-squares fit. It displays values for a (slope) and b (y-intercept); when DiagnosticOn is set, it also displays values for r2 and r. LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ] QuadReg (ax2+bx+c) QuadReg (quadratic regression) fits the second-degree polynomial y=ax2+bx+c to the data. It displays values for a, b, and c; when DiagnosticOn is set, it also displays a value for R2.
CubicReg [Xlistname,Ylistname,freqlist,regequ] QuartReg—(ax 4+bx 3+cx 2+ dx+e) QuartReg (quartic regression) fits the fourth-degree polynomial y=ax 4+bx 3+cx 2+dx+e to the data. It displays values for a, b, c, d, and e; when DiagnosticOn is set, it also displays a value for R2. For five points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At least five points are required.
LnReg [Xlistname,Ylistname,freqlist,regequ] ExpReg—(ab x) ExpReg (exponential regression) fits the model equation y=abx to the data using a least-squares fit and transformed values x and ln(y). It displays values for a and b; when DiagnosticOn is set, it also displays values for r2 and r. ExpReg [Xlistname,Ylistname,freqlist,regequ] PwrReg—(axb) PwrReg (power regression) fits the model equation y=axb to the data using a least-squares fit and transformed values ln(x) and ln(y).
SinReg—a sin(bx+c)+d SinReg (sinusoidal regression) fits the model equation y=a sin(bx+c)+d to the data using an iterative least-squares fit. It displays values for a, b, c, and d. At least four data points are required. At least two data points per cycle are required in order to avoid aliased frequency estimates. SinReg [iterations,Xlistname,Ylistname,period,regequ] iterations is the maximum number of times the algorithm will iterate to find a solution.
SinReg Example: Daylight Hours in Alaska for One Year Compute the regression model for the number of hours of daylight in Alaska during one year. & & 1 period With noisy data, you will achieve better convergence results when you specify an accurate estimate for period. You can obtain a period guess in either of two ways. • Plot the data and trace to determine the x-distance between the beginning and end of one complete period, or cycle.
• Plot the data and trace to determine the x-distance between the beginning and end of N complete periods, or cycles. Then divide the total distance by N. After your first attempt to use SinReg and the default value for iterations to fit the data, you may find the fit to be approximately correct, but not optimal. For an optimal fit, execute SinReg 16,Xlistname,Ylistname,2p / b where b is the value obtained from the previous SinReg execution.
Statistical Variables The statistical variables are calculated and stored as indicated below. To access these variables for use in expressions, press , and select 5:Statistics. Then select the VARS menu shown in the column below under VARS menu. If you edit a list or change the type of analysis, all statistical variables are cleared. 1.Var Stats 2.
Variables 1.Var Stats 2.Var Stats maximum of x values maxX maxX XY minimum of y values minY XY maximum of y values maxY XY 1st quartile median 3rd quartile regression/fit coefficients polynomial, Logistic, and SinReg coefficients correlation coefficient coefficient of determination regression equation summary points (Med.
Statistical Analysis in a Program Entering Stat Data You can enter statistical data, calculate statistical results, and fit models to data from a program. You can enter statistical data into lists directly within the program (Chapter 11). Statistical Calculations To perform a statistical calculation from a program, follow these steps. 1. On a blank line in the program editor, select the type of calculation from the STAT CALC menu. 2. Enter the names of the lists to use in the calculation.
Statistical Plotting Steps for Plotting Statistical Data in Lists You can plot statistical data that is stored in lists. The six types of plots available are scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal probability plot. You can define up to three plots. To plot statistical data in lists, follow these steps. 1. Store the stat data in one or more lists. 2. Select or deselect Y= functions as appropriate. 3. Define the stat plot. 4. Turn on the plots you want to display. 5.
" (Scatter) Scatter plots plot the data points from Xlist and Ylist as coordinate pairs, showing each point as a box ( › ), cross ( + ), or dot ( ¦ ). Xlist and Ylist must be the same length. You can use the same list for Xlist and Ylist. Ó (xyLine) xyLine is a scatter plot in which the data points are plotted and connected in order of appearance in Xlist and Ylist. You may want to use SortA( or SortD( to sort the lists before you plot them.
Ò (Histogram) Histogram plots one-variable data. The Xscl window variable value determines the width of each bar, beginning at Xmin. ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to include all values, and also adjusts Xscl. The inequality (Xmax N Xmin) à Xscl 47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right. Õ (ModBoxplot) ModBoxplot (modified box plot) plots one-variable data, like the regular box plot, except points that are 1.
The prompt for outlier points is x=, except when the outlier is the maximum point (maxX) or the minimum point (minX). When outliers exist, the end of each whisker will display x=. When no outliers exist, minX and maxX are the prompts for the end of each whisker. Q1, Med (median), and Q3 define the box. Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle.
Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom. Ô (NormProbPlot) NormProbPlot (normal probability plot) plots each observation X in Data List versus the corresponding quantile z of the standard normal distribution.
Defining the Plots To define a plot, follow these steps. 1. Press y ,. The STAT PLOTS menu is displayed with the current plot definitions. 2. Select the plot you want to use. The stat plot editor is displayed for the plot you selected.
3. Press Í to select On if you want to plot the statistical data immediately. The definition is stored whether you select On or Off. 4. Select the type of plot. Each type prompts for the options checked in this table. Plot Type Data List Data Axis XList YList Mark Freq " Scatter œ œ œ Ó œ œ œ Ò œ œ œ œ Õ œ œ œ Ö œ œ œ œ Ô œ œ œ 5. Enter list names or select options for the plot type.
• Freq (frequency list for Xlist elements; default is 1) • Data List (list name for NormProbPlot) • Data Axis (axis on which to plot Data List) Displaying Other Stat Plot Editors Each stat plot has a unique stat plot editor. The name of the current stat plot (Plot1, Plot2, or Plot3) is highlighted in the top line of the stat plot editor. To display the stat plot editor for a different plot, press }, ~, and | to move the cursor onto the name in the top line, and then press Í.
PlotsOff [1,2,3] PlotsOn [1,2,3] Note: You also can turn on and turn off stat plots in the top line of the Y= editor (Chapter 3). Defining the Viewing Window Stat plots are displayed on the current graph. To define the viewing window, press p and enter values for the window variables. ZoomStat redefines the viewing window to display all statistical data points. Tracing a Stat Plot When you trace a scatter plot or xyLine, tracing begins at the first element in the lists.
When you trace a box plot, tracing begins at Med (the median). Press | to trace to Q1 and minX. Press ~ to trace to Q3 and maxX. When you press } or † to move to another plot or to another Y= function, tracing moves to the current or beginning point on that plot (not the nearest pixel). The ExprOn/ExprOff format setting applies to stat plots (Chapter 3). When ExprOn is selected, the plot number and plotted data lists are displayed in the top-left corner.
Statistical Plotting in a Program Defining a Stat Plot in a Program To display a stat plot from a program, define the plot, and then display the graph. To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps. 1. Press y , to display the STAT PLOTS menu. 2. Select the plot to define, which pastes Plot1(, Plot2(, or Plot3( to the cursor location.
3. Press y , ~ to display the STAT TYPE menu. 4. Select the type of plot, which pastes the name of the plot type to the cursor location. 5. Press ¢. Enter the list names, separated by commas. 6. Press ¢ y , | to display the STAT PLOT MARK menu. (This step is not necessary if you selected 3:Histogram or 5:Boxplot in step 4.) Select the type of mark (› or + or ¦) for each data point. The selected mark symbol is pasted to the cursor location.
7. Press ¤ Í to complete the command line. Displaying a Stat Plot from a Program To display a plot from a program, use the DispGraph instruction (Chapter 16) or any of the ZOOM instructions (Chapter 3).
Chapter 13: Inferential Statistics and Distributions Getting Started: Mean Height of a Population Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to estimate the mean height of a population of women given the random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean.
1. Press … Í to display the stat list editor. Press } to move the cursor onto L1, and then press y 6. The Name= prompt is displayed on the bottom line. The Ø cursor indicates that alpha-lock is on. The existing list name columns shift to the right. Note: Your stat editor may not look like the one pictured here, depending on the lists you have already stored. 2. Enter [H] [G] [H] [T] at the Name= prompt, and then press Í. The list to which you will store the women’s height data is created.
Enter the other nine height values the same way. 4. Press … | to display the STAT TESTS menu, and then press † until 8:TInterval is highlighted. 5. Press Í to select 8:TInterval. The inferential stat editor for TInterval is displayed. If Data is not selected for Inpt:, press | Í to select Data. Press † and [H] [G] [H] [T] at the List: prompt (alpha-lock is on). Press † † Ë 99 to enter a 99 percent confidence level at the C.Level: prompt. 6. Press † to move the cursor onto Calculate, and then press Í.
Interpret the results. The first line, (159.74,173.94), shows that the 99 percent confidence interval for the population mean is between about 159.74 centimeters and 173.94 centimeters. This is about a 14.2 centimeters spread. The .99 confidence level indicates that in a very large number of samples, we expect 99 percent of the intervals calculated to contain the population mean. The actual mean of the population sampled is 165.1 centimeters, which is in the calculated interval.
8. Press † 163 Ë 8 Í to store 163.8 to ü. Press 7 Ë 1 Í to store 7.1 to Sx. Press 90 Í to store 90 to n. 9. Press † to move the cursor onto Calculate, and then press Í to calculate the new 99 percent confidence interval. The results are displayed on the home screen. If the height distribution among a population of women is normally distributed with a mean m of 165.1 centimeters and a standard deviation σ of 6.35 centimeters, what height is exceeded by only 5 percent of the women (the 95th percentile)? 10.
11. Press 3 to paste invNorm( to the home screen. Press Ë 95 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤ Í. .95 is the area, 165.1 is µ, and 6.35 is σ. The result is displayed on the home screen; it shows that five percent of the women are taller than 175.5 centimeters. Now graph and shade the top 5 percent of the population. 12. Press p and set the window variables to these values. Xmin=145 Xmax=185 Xscl=5 Ymin=L.02 Ymax=.08 Yscl=0 Xres=1 13. Press y = ~ to display the DISTR DRAW menu.
14. Press Í to paste ShadeNorm( to the home screen. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. Ans (175.5448205 from step 11) is the lower bound. 1å99 is the upper bound. The normal curve is defined by a mean µ of 165.1 and a standard deviation σ of 6.35. 15. Press Í to plot and shade the normal curve. Area is the area above the 95th percentile. low is the lower bound. up is the upper bound.
Inferential Stat Editors Displaying the Inferential Stat Editors When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary according to each test or interval’s input requirements. Below is the inferential stat editor for T-Test. Note: When you select the ANOVA( instruction, it is pasted to the home screen. ANOVA( does not have an editor screen.
3. Enter real numbers, list names, or expressions for each argument in the editor. 4. Select the alternative hypothesis (ƒ, <, or >) against which to test, if the selection is available. 5. Select No or Yes for the Pooled option, if the selection is available. 6. Select Calculate or Draw (when Draw is available) to execute the instruction. • When you select Calculate, the results are displayed on the home screen. • When you select Draw, the results are displayed in a graph.
Selecting Data or Stats Most inferential stat editors prompt you to select one of two types of input. (1.PropZInt and 2.PropZTest, 1.PropZInt and 2.PropZInt, c2.Test, and LinRegTTest do not.) • Select Data to enter the data lists as input. • Select Stats to enter summary statistics, such as þ, Sx, and n, as input. To select Data or Stats, move the cursor to either Data or Stats, and then press Í. Entering the Values for Arguments Inferential stat editors require a value for every argument.
Selecting an Alternative Hypothesis (ƒ < >) Most of the inferential stat editors for the hypothesis tests prompt you to select one of three alternative hypotheses. • The first is a ƒ alternative hypothesis, such as mƒm0 for the Z.Test. • The second is a < alternative hypothesis, such as m1 alternative hypothesis, such as p1>p2 for the 2.PropZTest. To select an alternative hypothesis, move the cursor to the appropriate alternative, and then press Í.
Selecting Calculate or Draw for a Hypothesis Test After you have entered all arguments in an inferential stat editor for a hypothesis test, you must select whether you want to see the calculated results on the home screen (Calculate) or on the graph screen (Draw). • Calculate calculates the test results and displays the outputs on the home screen. • Draw draws a graph of the test results and displays the test statistic and p-value with the graph.
Bypassing the Inferential Stat Editors To paste a hypothesis test or confidence interval instruction to the home screen without displaying the corresponding inferential stat editor, select the instruction you want from the CATALOG menu. Appendix A describes the input syntax for each hypothesis test and confidence interval instruction. Note: You can paste a hypothesis test or confidence interval instruction to a command line in a program.
STAT TESTS Menu STAT TESTS Menu To display the STAT TESTS menu, press … |. When you select an inferential statistics instruction, the appropriate inferential stat editor is displayed. Most STAT TESTS instructions store some output variables to memory. For a list of these variables, see the Test and Interval Output Variables table. EDIT CALC TESTS 1: Z-Test... 2: T-Test... 3: 2-SampZTest... 4: 2-SampTTest... 5: 1-PropZTest... 6: 2-PropZTest... 7: ZInterval... 8: TInterval... 9: 2-SampZInt... 0: 2-SampTInt...
EDIT CALC TESTS E: LinRegTTest... F: ANOVA( t test for regression slope and r One-way analysis of variance Note: When a new test or interval is computed, all previous output variables are invalidated. Inferential Stat Editors for the STAT TESTS Instructions In this chapter, the description of each STAT TESTS instruction shows the unique inferential stat editor for that instruction with example arguments.
Z.Test Z.Test (one-sample z test; item 1) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is known. It tests the null hypothesis H0: m=m0 against one of the alternatives below. • Ha: mƒm0 (m:ƒm0) • Ha: mm0 (m:>m0) In the example: L1={299.4 297.7 301 298.9 300.
Data Stats , , Calculated results: Drawn results: Note: All STAT TESTS examples assume a fixed-decimal mode setting of 4 (Chapter 1). If you set the decimal mode to Float or a different fixed-decimal setting, your output may differ from the output in the examples. T.Test T.Test (one-sample t test; item 2) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown. It tests the null hypothesis H0: m=m0 against one of the alternatives below.
In the example: TEST={91.9 97.8 111.4 122.3 105.
2.SampZTest 2.SampZTest (two-sample z test; item 3) tests the equality of the means of two populations (m1 and m2) based on independent samples when both population standard deviations (s1 and s2) are known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below.
Calculated results: , , Drawn results: 2.SampTTest 2.SampTTest (two-sample t test; item 4) tests the equality of the means of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below.
In the example: SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.
Drawn results: 1.PropZTest 1.PropZTest (one-proportion z test; item 5) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n. 1.PropZTest tests the null hypothesis H0: prop=p0 against one of the alternatives below.
Calculated results: , Drawn results: 2.PropZTest 2.PropZTest (two-proportion z test; item 6) computes a test to compare the proportion of successes (p1 and p2) from two populations. It takes as input the count of successes in each sample (x1 and x2) and the count of observations in each sample (n1 and n2). 2.PropZTest tests the null hypothesis H0: p1=p2 (using the pooled sample proportion Ç) against one of the alternatives below.
Input: , Calculated results: , Drawn results: TI-83 Plus Inferential Statistics and Distributions 404
ZInterval ZInterval (one-sample z confidence interval; item 7) computes a confidence interval for an unknown population mean m when the population standard deviation s is known. The computed confidence interval depends on the user-specified confidence level. In the example: L1={299.4 297.7 301 298.9 300.
TInterval TInterval (one-sample t confidence interval; item 8) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level. In the example: L6={1.6 1.7 1.8 1.
2.SampZInt 2.SampZInt (two-sample z confidence interval; item 9) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations ( s1 and s2) are known. The computed confidence interval depends on the user-specified confidence level.
Calculated results: 2.SampTInt 2.SampTInt (two-sample t confidence interval; item 0) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. The computed confidence interval depends on the userspecified confidence level. In the example: SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.
Data Stats , , Input: Calculated results: TI-83 Plus Inferential Statistics and Distributions 409
1.PropZInt 1.PropZInt (one-proportion z confidence interval; item A) computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample x and the count of observations in the sample n. The computed confidence interval depends on the user-specified confidence level.
2.PropZInt 2.PropZInt (two-proportion z confidence interval; item B) computes a confidence interval for the difference between the proportion of successes in two populations (p1Np2). It takes as input the count of successes in each sample (x1 and x2) and the count of observations in each sample (n1 and n2). The computed confidence interval depends on the user-specified confidence level.
c2.Test c2.Test (chi-square test; item C) computes a chi-square test for association on the two-way table of counts in the specified Observed matrix. The null hypothesis H 0 for a two-way table is: no association exists between row variables and column variables. The alternative hypothesis is: the variables are related. Before computing a c2.Test, enter the observed counts in a matrix. Enter that matrix variable name at the Observed: prompt in the c2.Test editor; default=[A].
, Note: Press y [B] Í to display matrix [B].
2.SampÜTest 2.SampÜTest (two-sample Û-test; item D) computes an Û-test to compare two normal population standard deviations (s1 and s2). The population means and standard deviations are all unknown. 2.SampÜTest, which uses the ratio of sample variances Sx12/Sx22, tests the null hypothesis H0: s1=s2 against one of the alternatives below.
Calculated results: , , Drawn results: LinRegTTest LinRegTTest (linear regression t test; item E) computes a linear regression on the given data and a t test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H0: b=0 (equivalently, r =0) against one of the alternatives below.
The regression equation is automatically stored to RegEQ (VARS Statistics EQ secondary menu). If you enter a Y= variable name at the RegEQ: prompt, the calculated regression equation is automatically stored to the specified Y= equation. In the example below, the regression equation is stored to Y1, which is then selected (turned on).
When LinRegTTest is executed, the list of residuals is created and stored to the list name RESID automatically. RESID is placed on the LIST NAMES menu. Note: For the regression equation, you can use the fix-decimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.
Input: , Calculated results: Note: SS is sum of squares and MS is mean square.
Inferential Statistics Input Descriptions The tables in this section describe the inferential statistics inputs discussed in this chapter. You enter values for these inputs in the inferential stat editors. The tables present the inputs in the same order that they appear in this chapter. Input Description m0 Hypothesized value of the population mean that you are testing. s The known population standard deviation; must be a real number > 0. List The name of the list containing the data you are testing.
Input Description s2 The known population standard deviation from the second population for the two-sample tests and intervals. Must be a real number > 0. List1, List2 The names of the lists containing the data you are testing for the two-sample tests and intervals. Defaults are L1 and L2, respectively. Freq1, Freq2 The names of the lists containing the frequencies for the data in List1 and List2 for the two-sample tests and intervals. Defaults=1. All elements must be integers | 0.
Input Description x2 The count of successes from sample two for the 2.PropZTest and 2.PropZInt. Must be an integer ‚ 0. n1 The count of observations in sample one for the 2.PropZTest and 2.PropZInt. Must be an integer > 0. n2 The count of observations in sample two for the 2.PropZTest and 2.PropZInt. Must be an integer > 0. C.Level The confidence level for the interval instructions. Must be ‚ 0 and <100. If it is ‚ 1, it is assumed to be given as a percent and is divided by 100. Default=0.95.
Test and Interval Output Variables The inferential statistics variables are calculated as indicated below. To access these variables for use in expressions, press , 5 (5:Statistics), and then select the VARS menu listed in the last column below.
Variables Tests confidence interval pair mean of x values sample standard deviation of x number of data points Intervals LinRegTTest ANOVA VARS Menu lower, upper TEST v v XY Sx Sx XY n n XY standard error about the line s TEST a, b EQ correlation coefficient r EQ coefficient of determination r2 EQ RegEQ EQ regression/fit coefficients regression equation Note: The variables listed above cannot be archived.
Distribution Functions DISTR menu To display the DISTR menu, press y =.
normalpdf( normalpdf( computes the probability density function (pdf) for the normal distribution at a specified x value. The defaults are mean m=0 and standard deviation s=1. To plot the normal distribution, paste normalpdf( to the Y= editor. The probability density function (pdf) is: − (x−µ) 1 e 2σ 2 ,σ > 0 2π σ 2 f ( x) = normalpdf(x[,m,s]) Note: For this example, Xmin = 28 Xmax = 42 Ymin = 0 Ymax = .
normalcdf( normalcdf( computes the normal distribution probability between lowerbound and upperbound for the specified mean m and standard deviation s. The defaults are m=0 and s=1. normalcdf(lowerbound,upperbound[,m,s]) invNorm( invNorm( computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean m and standard deviation s. It calculates the x value associated with an area to the left of the x value. 0 area 1 must be true.
tpdf( tpdf( computes the probability density function (pdf) for the Student-t distribution at a specified x value. df (degrees of freedom) must be >0. To plot the Student-t distribution, paste tpdf( to the Y= editor. The probability density function (pdf) is: f ( x) = Γ[( df + 1)/2] Γ( df /2) (1 + x 2/df ) − ( df πdf + 1)/2 tpdf(x,df) Note: For this example, Xmin = L4.5 Xmax = 4.5 Ymin = 0 Ymax = .
tcdf(lowerbound,upperbound,df) c2pdf( c2pdf( computes the probability density function (pdf) for the c2 (chi-square) distribution at a specified x value. df (degrees of freedom) must be an integer > 0. To plot the c2 distribution, paste c2pdf( to the Y= editor. The probability density function (pdf) is: f ( x) = 1 (1/2)df /2 xdf /2 − 1e − x /2, x ≥ 0 Γ(df /2) c2pdf(x,df) Note: For this example, Xmin = 0 Xmax = 30 Ymin = L.02 Ymax = .
c2cdf( c2cdf( computes the c2 (chi-square) distribution probability between lowerbound and upperbound for the specified df (degrees of freedom), which must be an integer > 0. c2cdf(lowerbound,upperbound,df) Üpdf( Üpdf( computes the probability density function (pdf) for the Û distribution at a specified x value. numerator df (degrees of freedom) and denominator df must be integers > 0. To plot the Û distribution, paste Üpdf( to the Y= editor.
Üpdf(x,numerator df,denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = 0 Ymax = 1 Ücdf( Ücdf( computes the Û distribution probability between lowerbound and upperbound for the specified numerator df (degrees of freedom) and denominator df. numerator df and denominator df must be integers >0.
probabilities from 0 to numtrials is returned. The probability density function (pdf) is: f ( x ) = n px (1 − p )n − x, x = 0,1,K,n x where n = numtrials binompdf(numtrials,p[,x]) binomcdf( binomcdf( computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be a real number or a list of real numbers. 0p1 must be true. numtrials must be an integer > 0.
poissonpdf( poissonpdf( computes a probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be an integer or a list of integers. The probability density function (pdf) is: f ( x ) = e − µ µx / x!, x = 0,1,2, poissonpdf(m,x) poissoncdf( poissoncdf( computes a cumulative probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be a real number or a list of real numbers.
geometpdf( geometpdf( computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. 0p1 must be true. x can be an integer or a list of integers.
Distribution Shading DISTR DRAW Menu To display the DISTR DRAW menu, press y = ~. DISTR DRAW instructions draw various types of density functions, shade the area specified by lowerbound and upperbound, and display the computed area value. To clear the drawings, select 1:ClrDraw from the DRAW menu (Chapter 8). Note: Before you execute a DISTR DRAW instruction, you must set the window variables so that the desired distribution fits the screen.
ShadeNorm( ShadeNorm( draws the normal density function specified by mean m and standard deviation s and shades the area between lowerbound and upperbound. The defaults are m=0 and s=1. ShadeNorm(lowerbound,upperbound[,m,s]) Note: For this example, Xmin = 55 Xmax = 72 Ymin = L.05 Ymax = .2 Shade_t( Shade_t( draws the density function for the Student-t distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound.
Shade_t(lowerbound,upperbound,df) Note: For this example, Xmin = L3 Xmax = 3 Ymin = L.15 Ymax = .5 Shadec2( Shadec2( draws the density function for the c2 (chi-square) distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. Shadec2(lowerbound,upperbound,df) Note: For this example, Xmin = 0 Xmax = 35 Ymin = L.025 Ymax = .
ShadeÜ( ShadeÜ( draws the density function for the Û distribution specified by numerator df (degrees of freedom) and denominator df and shades the area between lowerbound and upperbound. ShadeÜ(lowerbound,upperbound,numerator df,denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = L.25 Ymax = .
Chapter 14: Applications The Applications Menu The TI-83 Plus comes with Finance and CBLàCBR applications already listed on the APPLICATIONS menu. Except for the Finance application, you can add and remove applications as space permits. The Finance application is built into the TI-83 Plus code and cannot be deleted. You can buy additional TI-83 Plus software applications that allow you to customize further your calculator’s functionality. The calculator reserves 1.
Steps for Running the Finance Application Follow these basic steps when using the Finance application. Select the Finance application. Press 9 b. Select from list of functions.
Getting Started: Financing a Car Getting Started is a fast-paced introduction. Read the chapter for details. You have found a car you would like to buy. The car costs 9,000. You can afford payments of 250 per month for four years. What annual percentage rate (APR) will make it possible for you to afford the car? 1. Press z † ~ ~ ~ Í to set the fixeddecimal mode setting to 2. The TI-83 Plus will display all numbers with two decimal places). 2. Press Œ Í to select 1:Finance from the APPLICATIONS menu. 3.
Press 12 Í to store 12 payments per year to P/Y and 12 compounding periods per year to C/Y. Setting P/Y to 12 will compute an annual percentage rate (compounded monthly) for æ. Press † Í to select PMT:END, which indicates that payments are due at the end of each period. 4. Press } } } } } } to move the cursor to the æ prompt. Press ƒ \ to solve for æ.
Getting Started: Computing Compound Interest At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in 7 years? Note: Because there are no payments when you solve compound interest problems, PMT must be set to 0 and P/Y must be set to 1. 1. Press Œ Í to select 1:Finance from the APPLICATIONS menu. 2. Press Í to select 1:TVM Solver from the CALC VARS menu. The TVM Solver is displayed. Press 7 to enter the number of periods in years.
3. Press } } } } } to place the cursor on the æ prompt. 4. Press ƒ \ to solve for æ, the annual interest rate.
Using the TVM Solver Using the TVM Solver The TVM Solver displays the time-value-of-money (TVM) variables. Given four variable values, the TVM Solver solves for the fifth variable. The FINANCE VARS menu section describes the five TVM variables (Ú, æ, PV, PMT, and FV) and P/Y and C/Y. PMT: END BEGIN in the TVM Solver corresponds to the FINANCE CALC menu items Pmt_End (payment at the end of each period) and Pmt_Bgn (payment at the beginning of each period).
2. Enter the known values for four TVM variables. Note: Enter cash inflows as positive numbers and cash outflows as negative numbers. 3. Enter a value for P/Y, which automatically enters the same value for C/Y; if P/Y ƒ C/Y, enter a unique value for C/Y. 4. Select END or BEGIN to specify the payment method. 5. Place the cursor on the TVM variable for which you want to solve. 6. Press ƒ \. The answer is computed, displayed in the TVM Solver, and stored to the appropriate TVM variable.
Using the Financial Functions Entering Cash Inflows and Cash Outflows When using the TI-83 Plus financial functions, you must enter cash inflows (cash received) as positive numbers and cash outflows (cash paid) as negative numbers. The TI-83 Plus follows this convention when computing and displaying answers. FINANCE CALC Menu To display the FINANCE CALC menu, press Œ Í. CALC VARS 1: TVM Solver...
CALC VARS B: 4Nom( Computes the nominal interest rate. Computes the effective interest rate. Calculates the days between two dates. Selects ordinary annuity (end of period). Selects annuity due (beginning of period). C: 4Eff( D: dbd( E: Pmt_End F: Pmt_Bgn Use these functions to set up and perform financial calculations on the home screen. TVM Solver TVM Solver displays the TVM Solver.
Calculating Time Value of Money (TVM) Calculating Time Value of Money Use time-value-of-money (TVM) functions (menu items 2 through 6) to analyze financial instruments such as annuities, loans, mortgages, leases, and savings. Each TVM function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for these functions are not stored to the TVM variables.
tvm_Pmt tvm_Pmt computes the amount of each payment. tvm_Pmt[(Ú,æ,PV,FV,P/Y,C/Y)] Note: In the example above, the values are stored to the TVM variables in the TVM Solver. Then the payment (tvm_Pmt) is computed on the home screen using the values in the TVM Solver. Next, the interest rate is changed to 9.5 to illustrate the effect on the payment amount. tvm_æ tvm_æ computes the annual interest rate.
tvm_PV tvm_PV computes the present value. tvm_PV[(Ú,æ,PMT,FV,P/Y,C/Y)] tvm_Ú tvm_Ú computes the number of payment periods.
tvm_FV tvm_FV computes the future value.
Calculating Cash Flows Calculating a Cash Flow Use the cash flow functions (menu items 7 and 8) to analyze the value of money over equal time periods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntax descriptions for npv( and irr( use these arguments. • interest rate is the rate by which to discount the cash flows (the cost of money) over one period. • CF0 is the initial cash flow at time 0; it must be a real number.
CF0 = 2000 CFList = {2000,L3000,4000} CFFreq = {2,1,2} npv(, irr( npv( (net present value) is the sum of the present values for the cash inflows and outflows. A positive result for npv indicates a profitable investment. npv(interest rate,CF0,CFList[,CFFreq]) irr( (internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero.
Calculating Amortization Calculating an Amortization Schedule Use the amortization functions (menu items 9, 0, and A) to calculate balance, sum of principal, and sum of interest for an amortization schedule. bal( bal( computes the balance for an amortization schedule using stored values for æ, PV, and PMT. npmt is the number of the payment at which you want to calculate a balance. It must be a positive integer < 10,000.
GPrn(, GInt( GPrn( computes the sum of the principal during a specified period for an amortization schedule using stored values for æ, PV, and PMT. pmt1 is the starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the principal; if you do not specify roundvalue, the TI-83 Plus uses the current Float/Fix decimal-mode setting.
Amortization Example: Calculating an Outstanding Loan Balance You want to buy a home with a 30-year mortgage at 8 percent APR. Monthly payments are 800. Calculate the outstanding loan balance after each payment and display the results in a graph and in the table. 1. Press z. Press † ~ ~ ~ Í to set the fixed-decimal mode setting to 2. Press † † ~ Í to select Par graphing mode. 2. Press Œ Í Í to display the TVM Solver. 3. Press Í 360 to enter number of payments. Press † 8 to enter the interest rate.
4. Press } } } } } to place the cursor on the PV prompt. Press ƒ \ to solve for the present value. 5. Press o to display the parametric Y= editor. Turn off all stat plots. Press „ to define X1T as T. Press † Œ Í 9 „¤ to define Y1T as bal(T). 6. Press p to display the window variables. Enter the values below. Tmin=0 Tmax=360 Tstep=12 Xmin=0 Xmax=360 Xscl=50 Ymin=0 Ymax=125000 Yscl=10000 7. Press r to draw the graph and activate the trace cursor.
9. Press y 0 to display the table of outstanding balances (Y1T). 10. Press z † † † † † † † ~ ~ Í to select G.T split-screen mode, in which the graph and table are displayed simultaneously. Press r to display X1T (time) and Y1T (balance) in the table.
Calculating Interest Conversion Calculating an Interest Conversion Use the interest conversion functions (menu items B and C) to convert interest rates from an annual effective rate to a nominal rate (4Nom( ) or from a nominal rate to an annual effective rate (4Eff( ). 4Nom( 4Nom( computes the nominal interest rate. effective rate and compounding periods must be real numbers. compounding periods must be >0. 4Nom(effective rate,compounding periods) 4Eff( 4Eff( computes the effective interest rate.
Finding Days between Dates/Defining Payment Method dbd( Use the date function dbd( (menu item D) to calculate the number of days between two dates using the actual-day-count method. date1 and date2 can be numbers or lists of numbers within the range of the dates on the standard calendar. Note: Dates must be between the years 1950 through 2049. dbd(date1,date2) You can enter date1 and date2 in either of two formats. • MM.DDYY (United States) • DDMM.
Defining the Payment Method Pmt_End and Pmt_Bgn (menu items E and F) specify a transaction as an ordinary annuity or an annuity due. When you execute either command, the TVM Solver is updated. Pmt_End Pmt_End (payment end) specifies an ordinary annuity, where payments occur at the end of each payment period. Most loans are in this category. Pmt_End is the default. Pmt_End On the TVM Solver’s PMT:END BEGIN line, select END to set PMT to ordinary annuity.
Using the TVM Variables FINANCE VARS Menu To display the FINANCE VARS menu, press Œ Í ~. You can use TVM variables in TVM functions and store values to them on the home screen. CALC VARS 1:Ú 2:æ 3:PV 4:PMT 5:FV 6:P/Y 7:C/Y Total number of payment periods Annual interest rate Present value Payment amount Future value Number of payment periods per year Number of compounding periods/year Ú, æ, PV, PMT, FV Ú, æ, PV, PMT, and FV are the five TVM variables.
P/Y and C/Y P/Y is the number of payment periods per year in a financial transaction. C/Y is the number of compounding periods per year in the same transaction. When you store a value to P/Y, the value for C/Y automatically changes to the same value. To store a unique value to C/Y, you must store the value to C/Y after you have stored a value to P/Y.
The CBL/CBR Application The CBL/CBR application allows you to collect real world data. The TI-83 Plus comes with the CBLàCBR application already listed on the APPLICATIONS menu (9 2). Steps for Running the CBLàCBR Application Follow these basic steps when using the CBLàCBR application. You may not have to do all of them each time. Select the CBLàCBR application. Press 9 2. Press b. Specify the data collection method. TI-83 Plus Applications Press 1, 2, or 3.
Select options, if applicable. Collect the data. Follow directions, if applicable. Stop the data collection, if necessary. Repeat these steps or exit the APPLICATIONS menu. TI-83 Plus Applications Highlight options or enter value and press b. Select Go… or START NOW. Press ^ and ° or ±.
Selecting the CBL/CBR Application To use a CBL/CBR application, you need a CBL 2/CBL or CBR (as applicable), a TI-83 Plus, and a unit-to-unit link cable. 1. Press Œ. 2. Select 2:CBL/CBR to set up the TI-83 Plus to use either of the applications. An informational screen appears first. 3. Press any key to continue to the next menu.
Data Collection Methods and Options Specifying the Data Collection Method from the CBL/CBR APP Menu With a CBL 2/CBL or CBR, you can collect data in one of three ways: GAUGE (bar or meter), DATA LOGGER (a Temp-Time, Light-Time, Volt-Time, or Sonic-Time graph), or RANGER, which runs the RANGER program, the built-in CBR data collection program. The CBL/CBR APP menu contains the following data collection methods: CBL/CBR APP: 1: GAUGE Displays results as either a bar or meter.
Specifying Options for Each Data Collection Method After you select a data collection method from the CBL/CBR APP menu, a screen showing the options for that method is displayed. The method you choose, as well as the data collection options you choose for that method, determine whether you use the CBR or the CBL 2/CBL. Refer to the charts in the following sections to find the options for the application you are using.
When you select a probe option, all other options change accordingly. Use " and ! to move between the probe options. To select a probe, highlight the one you want with the cursor keys, and then press Í. GAUGE Options (Defaults) Probe: Temp Type: Min: Max: Units: Light Volt Sonic Bar or Meter 0 0 M10 0 100 1 10 6 ¡C or ¡F mWàcm2 Volt m or Ft Directions: On or Off TYPE The GAUGE data collection results are represented according to TYPE: Bar or Meter.
Bar Meter MIN and MAX and MAX refer to the minimum and maximum UNIT values for the specified probe. Defaults are listed in the Gauge Options table. See the CBL 2/CBL and CBR guidebook for specific MINàMAX ranges. Enter values using the number keys. MIN UNITS The results are displayed according to the UNITS specified. To specify a unit measurement (Temp or Sonic probes only), highlight the one you want using the cursor keys, enter a value using the number keys, and then press Í.
DIRECTNS (Directions) If DIRECTNS=On, the calculator displays step-by-step directions on the screen, which help you set up and run the data collection. To select On or Off, highlight the one you want with the cursor keys, and then press Í. With the Sonic data collection probe, if DIRECTNS=On, the calculator displays a menu screen before starting the application asking you to select 1:CBL or 2:CBR. This ensures that you get the appropriate directions. Press 1 to specify CBL 2/CBL or 2 to specify CBR.
To see all elements in one of these lists, you can insert these lists into the List editor just as you would any other list. Access list names from the - 9 NAMES menu. Note: These lists are only temporary placeholders for comment labels and data results for any particular probe. Therefore, every time you collect data and enter comments for one of the four probes, the two lists pertaining to that probe are overwritten with comment labels and data results from the most recently collected data..
DATA LOGGER 1. Press Œ 2 Í. 2. Select 2:DATA LOGGER. The DATA LOGGER data collection method lets you choose one of four different probes: Temp, Light, Volt, or Sonic. You can use the CBL 2/CBL with all probes; you can use the CBR only with the Sonic probe. When you select a probe option, all other options change accordingly. Use " and ! to move between the probe options. To select a probe, highlight the one you want with the cursor keys, and then press Í.
DATA LOGGER Options (Defaults) Temp #SAMPLES: INTRVL (SEC): UNITS: Light Volt Sonic 99 99 99 99 1 1 1 1 ¡C or ¡F PLOT: mW/cm2 Volt Cm or Ft RealTme or End DIRECTNS: On or Off Ymin ('): 0 0 M10 0 Ymax ('): 100 1 10 6 The DATA LOGGER data collection results are represented as a Temp-Time, Light-Time, Volt-Time, or Distance-Time graph. A Distance-Time graph in meters (Sonic probe).
#SAMPLES refers to how many data samples are collected and then graphed. For example, if #SAMPLES=99, data collection stops after the 99 th sample is collected. Enter values using the number keys. #SAMPLES INTRVL (SEC) specifies the interval in seconds between each data sample that is collected. For example, if you want to collect 99 samples and INTRVL=1, it takes 99 seconds to finish data collection. Enter values using the number keys.
PLOT You can specify whether you want the calculator to collect realtime (RealTme) samples, which means that the calculator graphs data points immediately as they are being collected, or you can wait and show the graph only after all data points have been collected (End). Highlight the option you want with the cursor keys, and then press Í. Ymin and Ymax To specify Ymin and Ymax values for the final graph, press p to view the PLOT WINDOW screen. Use $ and # to move between options.
Data Collection Results The calculator automatically converts all collected data points into list elements using the following list names (you cannot rename the lists): Probe Time Values (X) stored to: Data Results (Y) Stored to: Temp ¨TTEMP ¨TEMP Light ¨TLGHT ¨LIGHT Volt ¨TVOLT ¨VOLT Sonic ¨TDIST ¨DIST To see all elements in one of these lists, you can insert these lists into the List editor just as you would any other list. Access list names from the - 9 NAMES menu.
RANGER Selecting the RANGER data collection method runs the CBR RANGER program, a customized program especially for the TI-83 Plus that makes it compatible with the CBR. When the collection process is halted, the CBR RANGER is deleted from RAM. To run the CBR RANGER program again, press Πand select the CBL/CBR application. Note: The Ranger data collection method only uses the Sonic probe. 1. Press 9 2 b. 2. Select 3:RANGER. 3. Press b. 4. Select options.
Starting Data Collection Collecting the Data After you specify all of the options for your data collection method, select the Go option from the GAUGE or DATA LOGGER options screen. If you are using the RANGER data collection method, select 1:SETUPàSAMPLE from the MAIN menu, and then START NOW. • If DIRECTNS=Off, GAUGE and DATA LOGGER data collection begin immediately. • If DIRECTNS=On, the calculator displays step-by-step directions.
Stopping Data Collection To stop the GAUGE data collection method, press : on the TI-83 Plus. The DATA LOGGER and RANGER data collection methods stop after the specified number of samples have been collected. To stop them before this happens: 1. Press ^ on the TI-83 Plus. 2. Press ¤ on the CBR, T on the CBL 2, or P on the CBL. To exit from the GAUGE or DATA LOGGER option menus without beginning data collection, press - l.
Chapter 15: CATALOG, Strings, Hyperbolic Functions Browsing the TI-83 Plus CATALOG What Is the CATALOG? The CATALOG is an alphabetical list of all functions and instructions on the TI-83 Plus.
Selecting an Item from the CATALOG To select a CATALOG item, follow these steps. 1. Press y ãCATALOGä to display the CATALOG. The 4 in the first column is the selection cursor. 2. Press † or } to scroll the CATALOG until the selection cursor points to the item you want. • To jump to the first item beginning with a particular letter, press that letter; alpha-lock is on. • Items that begin with a number are in alphabetical order according to the first letter after the number. For example, 2.
3. Press Í to paste the item to the current screen. Tip: From the top of the CATALOG menu, press } to move to the bottom. From the bottom, press † to move to the top.
Entering and Using Strings What Is a String? A string is a sequence of characters that you enclose within quotation marks. On the TI-83 Plus, a string has two primary applications. • It defines text to be displayed in a program. • It accepts input from the keyboard in a program. Characters are the units that you combine to form a string. • Count each number, letter, and space as one character.
• Use any combination of numbers, letters, function names, or instruction names to create the string. • To enter a blank space, press ƒ [']. • To enter several alpha characters in a row, press y 7 to activate alpha-lock. 3. Press ƒ [ã] to indicate the end of the string. "string" 4. Press Í. On the home screen, the string is displayed on the next line without quotations. An ellipsis (...) indicates that the string continues beyond the screen. To scroll the entire string, press ~ and |.
Storing Strings to String Variables String Variables The TI-83 Plus has 10 variables to which you can store strings. You can use string variables with string functions and instructions. To display the VARS STRING menu, follow these steps. 1. Press to display the VARS menu. Move the cursor to 7:String. 2. Press Í to display the STRING secondary menu.
Storing a String to a String Variable To store a string to a string variable, follow these steps. 1. Press ƒ [ã], enter the string, and press ƒ [ã]. 2. Press ¿. 3. Press 7 to display the VARS STRING menu. 4. Select the string variable (from Str1 to Str9, or Str0) to which you want to store the string. The string variable is pasted to the current cursor location, next to the store symbol (!). 5. Press Í to store the string to the string variable.
Displaying the Contents of a String Variable To display the contents of a string variable on the home screen, select the string variable from the VARS STRING menu, and then press Í. The string is displayed.
String Functions and Instructions in the CATALOG Displaying String Functions and Instructions in the CATALOG String functions and instructions are available only from the CATALOG. The table below lists the string functions and instructions in the order in which they appear among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... Equ4String( expr( Converts an equation to a string. Converts a string to an expression. ...
+ (Concatenation) To concatenate two or more strings, follow these steps. 1. Enter string1, which can be a string or string name. 2. Press Ã. 3. Enter string2, which can be a string or string name. If necessary, press à and enter string3, and so on. string1+string2+string3. . . 4. Press Í to display the strings as a single string.
Equ4String( Equ4String( converts to a string an equation that is stored to any VARS variable. Yn contains the equation. Strn (from Str1 to Str9, or Str0) Y.VARS is the string variable to which you want the equation to be stored as a string. Equ4String(Yn,Strn) expr( expr( converts the character string contained in string to an expression and executes it. string can be a string or a string variable.
inString( inString( returns the character position in string of the first character of substring. string can be a string or a string variable. start is an optional character position at which to start the search; the default is 1. inString(string,substring[,start]) Note: If string does not contain substring, or start is greater than the length of string, inString( returns 0. length( length( returns the number of characters in string. string can be a string or string variable.
String4Equ( String4Equ( converts string into an equation and stores the equation to Yn. string can be a string or string variable. String4Equ( is the inverse of Equ4String(. String4Equ(string,Yn) sub( sub( returns a string that is a subset of an existing string. string can be a string or a string variable. begin is the position number of the first character of the subset. length is the number of characters in the subset.
Entering a Function to Graph during Program Execution In a program, you can enter a function to graph during program execution using these commands. Note: When you execute this program, enter a function to store to Y3 at the ENTRY= prompt.
Hyperbolic Functions in the CATALOG Hyperbolic Functions The hyperbolic functions are available only from the CATALOG. The table below lists the hyperbolic functions in the order in which they appear among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... cosh( cosh L1( Hyperbolic cosine Hyperbolic arccosine ... sinh( sinh L1( Hyperbolic sine Hyperbolic arcsine ... tanh( tanh L1( Hyperbolic tangent Hyperbolic arctangent ...
sinh(, cosh(, tanh( sinh(, cosh(, and tanh( are the hyperbolic functions. Each is valid for real numbers, expressions, and lists. sinh(value) cosh(value) tanh(value) sinhL1(, coshL1(, tanhL1( sinhL1( is the hyperbolic arcsine function. coshL1( is the hyperbolic arccosine function. tanhL1( is the hyperbolic arctangent function. Each is valid for real numbers, expressions, and lists.
Chapter 16: Programming Getting Started: Volume of a Cylinder Getting Started is a fast-paced introduction. Read the chapter for details. A program is a set of commands that the TI-83 Plus executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume. 1. Press ~ ~ to display the PRGM NEW menu. 2. Press Í to select 1:Create New. The Name= prompt is displayed, and alpha-lock is on.
3. Press ~ 2 to select 2:Prompt from the PRGM I/O menu. Prompt is copied to the command line. Press ƒ [R] ¢ ƒ [H] to enter the variable names for radius and height. Press Í. 4. Press y ãpä ƒ [R] ¡ ƒ [H] ¿ ƒ [V] Í to enter the expression pR 2H and store it to the variable V. 5. Press ~ 3 to select 3:Disp from the PRGM I/O menu. Disp is pasted to the command line.
8. Press Í to paste prgmCYLINDER to the current cursor location. (If CYLINDER is not item 1 on your PRGM EXEC menu, move the cursor to CYLINDER before you press Í.) 9. Press Í to execute the program. Enter 1.5 for the radius, and then press Í. Enter 3 for the height, and then press Í. The text VOLUME IS, the value of V, and Done are displayed. Repeat steps 7 through 9 and enter different values for R and H.
Creating and Deleting Programs What Is a Program? A program is a set of one or more command lines. Each line contains one or more instructions. When you execute a program, the TI-83 Plus performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI-83 Plus can store is limited only by available memory. Creating a New Program To create a new program, follow these steps. 1. Press | to display the PRGM NEW menu. 2.
4. Enter zero to seven letters, numbers, or q to complete the new program name. 5. Press Í. The program editor is displayed. 6. Enter one or more program commands. 7. Press y 5 to leave the program editor and return to the home screen. Managing Memory and Deleting a Program To check whether adequate memory is available for a program you want to enter: 1. Press y L to display the MEMORY menu. 2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu (Chapter 18). 3.
You can increase available memory in one of two ways. You can delete one or more programs or you can archive some programs. To increase available memory by deleting a specific program: 1. Press y L and then select 2:Mem Mgmt/Del from the MEMORY menu. 2. Select 7:Prgm to display the PRGM editor (Chapter 18). 3. Press } and † to move the selection cursor (4) next to the program you want to delete, and then press {. The program is deleted from memory.
To increase available memory by archiving a program: 1. Press y L and then select 2:Mem Mgmt/Del from the MEMORY menu. 2. Select 2:Mem Mgmt/Del to display the MEM MGMT/DEL menu. 3. Select 7:Prgm... to display the PRGM menu. 4. Press Í to archive the program. An asterisk will appear to the left of the program to indicate it is an archived program. To unarchive a program in this screen, put the cursor next to the archived program and press Í. The asterisk will disappear.
Entering Command Lines and Executing Programs Entering a Program Command Line You can enter on a command line any instruction or expression that you could execute from the home screen. In the program editor, each new command line begins with a colon. To enter more than one instruction or expression on a single command line, separate each with a colon. Note: A command line can be longer than the screen is wide; long command lines wrap to the next screen line.
Executing a Program To execute a program, begin on a blank line on the home screen and follow these steps. 1. Press to display the PRGM EXEC menu. 2. Select a program name from the PRGM EXEC menu. prgmname is pasted to the home screen (for example, prgmCYLINDER). 3. Press Í to execute the program. While the program is executing, the busy indicator is on. Last Answer (Ans) is updated during program execution. Last Entry is not updated as each command is executed (Chapter 1).
Breaking a Program To stop program execution, press É. The ERR:BREAK menu is displayed. • To return to the home screen, select 1:Quit. • To go where the interruption occurred, select 2:Goto.
Editing Programs Editing a Program To edit a stored program, follow these steps. 1. Press ~ to display the PRGM EDIT menu. 2. Select a program name from the PRGM EDIT menu. Up to the first seven lines of the program are displayed. Note: The program editor does not display a $ to indicate that a program continues beyond the screen. 3. Edit the program command lines. • Move the cursor to the appropriate location, and then delete, overwrite, or insert.
Inserting and Deleting Command Lines To insert a new command line anywhere in the program, place the cursor where you want the new line, press y 6, and then press Í. A colon indicates a new line. To delete a command line, place the cursor on the line, press ‘ to clear all instructions and expressions on the line, and then press { to delete the command line, including the colon.
Copying and Renaming Programs Copying and Renaming a Program To copy all command lines from one program into a new program, follow steps 1 through 5 for Creating a New Program, and then follow these steps. 1. Press y K. Rcl is displayed on the bottom line of the program editor in the new program (Chapter 1). 2. Press | to display the PRGM EXEC menu. 3. Select a name from the menu. prgmname is pasted to the bottom line of the program editor. 4. Press Í.
Note: You also can copy all the command lines from one existing program to another existing program using RCL. Scrolling the PRGM EXEC and PRGM EDIT Menus The TI-83 Plus sorts PRGM EXEC and PRGM EDIT menu items automatically into alphanumerical order. Each menu only labels the first 10 items using 1 through 9, then 0. To jump to the first program name that begins with a particular alpha character or q, press ƒ [letter from A to Z or q].
PRGM CTL (Control) Instructions PRGM CTL Menu To display the PRGM CTL (program control) menu, press from the program editor only. CTL I/O EXEC 1:If 2:Then 3:Else 4:For( 5:While 6:Repeat 7:End 8:Pause 9:Lbl 0:Goto A:IS>( B:DS<( C:Menu( D:prgm E:Return F:Stop G:DelVar H:GraphStyle( TI-83 Plus Programming Creates a conditional test. Executes commands when If is true. Executes commands when If is false. Creates an incrementing loop. Creates a conditional loop. Creates a conditional loop.
These menu items direct the flow of an executing program. They make it easy to repeat or skip a group of commands during program execution. When you select an item from the menu, the name is pasted to the cursor location on a command line in the program. To return to the program editor without selecting an item, press ‘. Controlling Program Flow Program control instructions tell the TI-83 Plus which command to execute next in a program.
:If condition :command (if true) :command Program Output If.Then Then following an If executes a group of commands if condition is true (nonzero). End identifies the end of the group of commands.
Program Output If.Then.Else Else following If.Then executes a group of commands if condition is false (zero). End identifies the end of the group of commands.
Program Output For( For( loops and increments. It increments variable from begin to end by increment. increment is optional (default is 1) and can be negative (end
Program Output While While performs a group of commands while condition is true. condition is frequently a relational test (Chapter 2). condition is tested when While is encountered. If condition is true (nonzero), the program executes a group of commands. End signifies the end of the group. When condition is false (zero), the program executes each command following End. While instructions can be nested.
Program Output Repeat Repeat repeats a group of commands until condition is true (nonzero). It is similar to While, but condition is tested when End is encountered; therefore, the group of commands is always executed at least once. Repeat instructions can be nested.
End End identifies the end of a group of commands. You must include an End instruction at the end of each For(, While, or Repeat loop. Also, you must paste an End instruction at the end of each If.Then group and each If.Then.Else group. Pause Pause suspends execution of the program so that you can see answers or graphs. During the pause, the pause indicator is on in the top-right corner. Press Í to resume execution. • Pause without a value temporarily pauses the program.
Program Output Lbl, Goto Lbl (label) and Goto (go to) are used together for branching. Lbl specifies the label for a command. label can be one or two characters (A through Z, 0 through 99, or q). Lbl label Goto causes the program to branch to label when Goto is encountered.
Program Output IS>( IS>( (increment and skip) adds 1 to variable. If the answer is > value (which can be an expression), the next command is skipped; if the answer is { value, the next command is executed. variable cannot be a system variable. :IS>(variable,value) :command (if answer value) :command (if answer > value) Program Output Note: IS>( is not a looping instruction.
DS<( DS<( (decrement and skip) subtracts 1 from variable. If the answer is < value (which can be an expression), the next command is skipped; if the answer is | value, the next command is executed. variable cannot be a system variable. :DS<(variable,value) :command (if answer ‚ value) :command (if answer < value) Program Output Note: DS<( is not a looping instruction. Menu( Menu( sets up branching within a program.
The menu title is enclosed in quotation marks ( " ). Up to seven pairs of menu items follow. Each pair comprises a text item (also enclosed in quotation marks) to be displayed as a menu selection, and a label item to which to branch if you select the corresponding menu selection. Menu("title","text1",label1,"text2",label2, . . .) Program Output The program above pauses until you select 1 or 2. If you select 2, for example, the menu disappears and the program continues execution at Lbl B.
Note: You cannot directly enter the subroutine name when using RCL. You must paste the name from the PRGM EXEC menu. Return Return quits the subroutine and returns execution to the calling program, even if encountered within nested loops. Any loops are ended. An implied Return exists at the end of any program that is called as a subroutine. Within the main program, Return stops execution and returns to the home screen. Stop Stop stops execution of a program and returns to the home screen.
GraphStyle( GraphStyle( designates the style of the graph to be drawn. function# is the number of the Y= function name in the current graphing mode. graphstyle is a number from 1 to 7 that corresponds to the graph style, as shown below. 1 2 3 4 = ç (line) = è (thick) = é (shade above) = ê (shade below) 5 = ë (path) 6 = ì (animate) 7 = í (dot) GraphStyle(function#,graphstyle) For example, GraphStyle(1,5) in Func mode sets the graph style for Y1 to ë (path; 5).
PRGM I/O (Input/Output) Instructions PRGM I/O Menu To display the PRGM I/O (program input/output) menu, press ~ from within the program editor only. CTL I/O EXEC 1:Input 2:Prompt 3:Disp 4:DispGraph 5:DispTable 6:Output( 7:getKey 8:ClrHome 9:ClrTable 0:GetCalc( A:Get( B:Send( Enters a value or uses the cursor. Prompts for entry of variable values. Displays text, value, or the home screen. Displays the current graph. Displays the current table. Displays text at a specified position.
Displaying a Graph with Input Input without a variable displays the current graph. You can move the free-moving cursor, which updates X and Y (and R and q for PolarGC format). The pause indicator is on. Press Í to resume program execution.
Storing a Variable Value with Input Input with variable displays a ? (question mark) prompt during execution. variable may be a real number, complex number, list, matrix, string, or Y= function. During program execution, enter a value, which can be an expression, and then press Í. The value is evaluated and stored to variable, and the program resumes execution. Input [variable] You can display text or the contents of Strn (a string variable) of up to 16 characters as a prompt.
Note: When a program prompts for input of lists and Yn functions during execution, you must include the braces ( { } ) around the list elements and quotation marks ( " ) around the expressions. Prompt During program execution, Prompt displays each variable, one at a time, followed by =?. At each prompt, enter a value or expression for each variable, and then press Í. The values are stored, and the program resumes execution. Prompt variableA[,variableB,...
Displaying Values and Messages Disp with one or more values displays the value of each. Disp [valueA,valueB,valueC,...,value n] • If value is a variable, the current value is displayed. • If value is an expression, it is evaluated and the result is displayed on the right side of the next line. • If value is text within quotation marks, it is displayed on the left side of the current display line. ! is not valid as text.
DispGraph DispGraph (display graph) displays the current graph. If Pause is encountered after DispGraph, the program halts temporarily so you can examine the screen. Press Í to resume execution. DispTable DispTable (display table) displays the current table. The program halts temporarily so you can examine the screen. Press Í to resume execution. Output( Output( displays text or value on the current home screen beginning at row (1 through 8) and column (1 through 16), overwriting any existing characters.
Program Output For Output( on a Horiz split screen, the maximum value for row is 4. getKey getKey returns a number corresponding to the last key pressed, according to the key code diagram below. If no key has been pressed, getKey returns 0. Use getKey inside loops to transfer control, for example, when creating video games. Program Output Note: , Œ, , and Í were pressed during program execution. Note: You can press É at any time during execution to break the program.
TI-83 Plus Key Code Diagram ClrHome, ClrTable ClrHome (clear home screen) clears the home screen during program execution. ClrTable (clear table) clears the values in the table during program execution.
GetCalc( GetCalc( gets the contents of variable on another TI-83 Plus and stores it to variable on the receiving TI-83 Plus. variable can be a real or complex number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture. GetCalc(variable) Note: GetCalc( does not work between TI.82 and TI-83 Plus calculators. Get(, Send( Get( gets data from the CBL 2/CBL or CBR and stores it to variable on the receiving TI-83 Plus.
Send(variable) Note: This program gets sound data and time in seconds from CBL 2/CBL. Note: You can access Get(, Send(, and GetCalc( from the CATALOG to execute them from the home screen (Chapter 15).
Calling Other Programs as Subroutines Calling a Program from Another Program On the TI-83 Plus, any stored program can be called from another program as a subroutine. Enter the name of the program to use as a subroutine on a line by itself. You can enter a program name on a command line in either of two ways. • Press | to display the PRGM EXEC menu and select the name of the program prgmname is pasted to the current cursor location on a command line.
Program Output & Subroutine ( ' Notes about Calling Programs Variables are global. label used with Goto and Lbl is local to the program where it is located. label in one program is not recognized by another program. You cannot use Goto to branch to a label in another program. Return exits a subroutine and returns to the calling program, even if it is encountered within nested loops.
Running an Assembly Language Program You can run programs written for the TI-83 Plus in assembly language. Typically, assembly language programs run much faster and provide greater control than than the keystroke programs that you write with the built-in program editor. Note: Because an assembly langauge program has greater control over the calculator, if your assembly language program has error(s), it may cause your calculator to reset and lose all data, programs, and applications stored in memory.
Instructions Comments AsmComp(prgmASM1, prgmASM2) Compiles an assembly language program written in ASCII and stores the hex version AsmPrgm Identifies an assembly language program; must be entered as the first line of an assembly language program To compile an assembly program that you have written: 1. Follow the steps for writing a program (16-4) but be sure to include AsmPrgm as the first line of your program. 2. From the home screen, press y N and then select AsmComp( to paste it to the screen 3.
7. Press ¤ to complete the sequence. The sequence of the arguments should be as follows: AsmComp(prgmASM1, prgmASM2) 8. Press Í to compile your program and generate the output program.
Chapter 17: Activities The Quadratic Formula Entering a Calculation Use the quadratic formula to solve the quadratic equations 3X2 + 5X + 2 = 0 and 2X2 N X + 3 = 0. Begin with the equation 3X2 + 5X + 2 = 0. 1. Press 3 ¿ ƒ [A] (above ) to store the coefficient of the X2 term. 2. Press ƒ [ : ] (above Ë). The colon allows you to enter more than one instruction on a line. 3. Press 5 ¿ ƒ [B] (above Œ) to store the coefficient of the X term. Press ƒ [ : ] to enter a new instruction on the same line.
4. Press Í to store the values to the variables A, B, and C. The last value you stored is shown on the right side of the display. The cursor moves to the next line, ready for your next entry. 5. Press £ Ì ƒ [B] Ã y C ƒ [B] ¡ ¹ 4 ƒ [A] ƒ [C] ¤ ¤ ¥ £ 2 ƒ [A] ¤ to enter the expression for one of the solutions for the quadratic formula, − b± b2−4ac 2a 6. Press Í to find one solution for the equation 3X2 + 5X + 2 = 0. The answer is shown on the right side of the display.
The Quadratic Formula Converting to a Fraction You can show the solution as a fraction. 1. Press to display the MATH menu. 2. Press 1 to select 1:4Frac from the MATH menu. When you press 1, Ans4Frac is displayed on the home screen. Ans is a variable that contains the last calculated answer. 3. Press Í to convert the result to a fraction.
To save keystrokes, you can recall the last expression you entered, and then edit it for a new calculation. 4. Press y [ (above Í) to recall the fraction conversion entry, and then press y [ again to recall the quadratic-formula expression, − b+ b2−4ac 2a 5. Press } to move the cursor onto the + sign in the formula. Press ¹ to edit the quadraticformula expression to become: − b− b2−4ac 2a 6. Press Í to find the other solution for the quadratic equation 3X2 + 5X + 2 = 0.
The Quadratic Formula Displaying Complex Results Now solve the equation 2X2 N X + 3 = 0. When you set a+bi complex number mode, the TI-83 Plus displays complex results. 1. Press z † † † † † † (6 times), and then press ~ to position the cursor over a+bi. Press Í to select a+bi complex-number mode. 2. Press y 5 (above z) to return to the home screen, and then press ‘ to clear it. 3. Press 2 ¿ ƒ [A] ƒ [ : ] Ì 1 ¿ ƒ [B] ƒ [ : ] 3 ¿ ƒ [C] Í.
4. Press y [ to recall the store instruction, and then press y [ again to recall the quadratic-formula expression, − b− b2−4ac 2a 5. Press Í to find one solution for the equation 2X2 N X + 3 = 0. 6. Press y [ repeatedly until this quadraticformula expression is displayed: − b+ b2−4ac 2a 7. Press Í to find the other solution for the quadratic equation: 2X2 N X + 3 = 0. Note: An alternative for solving equations for real numbers is to use the built-in Equation Solver (Chapter 2).
Box with Lid Defining a Function Take a 20 cm × 25 cm. sheet of paper and cut X × X squares from two corners. Cut X × 12.5 cm rectangles from the other two corners as shown in the diagram below. Fold the paper into a box with a lid. What value of X would give your box the maximum volume V? Use the table and graphs to determine the solution. Begin by defining a function that describes the volume of the box.
2. Press £ 20 ¹ 2 „ ¤ £ 25 ¥ 2 ¹ „ ¤ „ Í to define the volume function as Y1 in terms of X. „ lets you enter X quickly, without having to press ƒ. The highlighted = sign indicates that Y1 is selected. Box with Lid Defining a Table of Values The table feature of the TI-83 Plus displays numeric information about a function. You can use a table of values from the function you just defined to estimate an answer to the problem. 1. Press y - (above p) to display the TABLE SETUP menu. 2.
4. Press y 0 (above s) to display the table. Notice that the maximum value for Y1 (box’s volume) occurs when X is about 4, between 3 and 5. 5. Press and hold † to scroll the table until a negative result for Y1 is displayed. Notice that the maximum length of X for this problem occurs where the sign of Y1 (box’s volume) changes from positive to negative, between 10 and 11. 6. Press y -. Notice that TblStart has changed to 6 to reflect the first line of the table as it was last displayed.
Box with Lid Zooming In on the Table You can adjust the way a table is displayed to get more information about a defined function. With smaller values for @Tbl, you can zoom in on the table. 1. Press 3 Í to set TblStart. Press Ë 1 Í to set @Tbl. This adjusts the table setup to get a more accurate estimate of X for maximum volume Y1. 2. Press y 0. 3. Press † and } to scroll the table. Notice that the maximum value for Y1 is 410.26, which occurs at X=3.7. Therefore, the maximum occurs where 3.6
4. Press y -. Press 3 Ë 6 Í to set TblStart. Press Ë 01 Í to set @Tbl. 5. Press y 0, and then press † and } to scroll the table. Four equivalent maximum values are shown, 410.26 at X=3.67, 3.68, 3.69, and 3.70. 6. Press † or } to move the cursor to 3.67. Press ~ to move the cursor into the Y1 column. The value of Y1 at X=3.67 is displayed on the bottom line in full precision as 410.261226.
7. Press † to display the other maximum. The value of Y1 at X=3.68 in full precision is 410.264064, at X=3.69 is 410.262318 and at X=3.7 is 410.256. The maximum volume of the box would occur at 3.68 if you could measure and cut the paper at .01-centimeter increments. Box with Lid Setting the Viewing Window You also can use the graphing features of the TI-83 Plus to find the maximum value of a previously defined function.
The standard window variables define the viewing window as shown. Xmin, Xmax, Ymin, and Ymax define the boundaries of the display. Xscl and Yscl define the distance between tick marks on the X and Y axes. Xres controls resolution. Ymax Xscl Xmin Xmax Yscl Ymin 2. Press 0 Í to define Xmin. 3. Press 20 ¥ 2 to define Xmax using an expression. 4. Press Í. The expression is evaluated, and 10 is stored in Xmax. Press Í to accept Xscl as 1. 5. Press 0 Í 500 Í 100 Í 1 Í to define the remaining window variables.
Box with Lid Displaying and Tracing the Graph Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function using the TRACE feature. 1. Press s to graph the selected function in the viewing window. The graph of Y1=(20N2X)(25à2NX)X is displayed. 2. Press ~ to activate the free-moving graph cursor. The X and Y coordinate values for the position of the graph cursor are displayed on the bottom line.
3. Press |, ~, }, and † to move the freemoving cursor to the apparent maximum of the function. As you move the cursor, the X and Y coordinate values are updated continually. 4. Press r. The trace cursor is displayed on the Y1 function. The function that you are tracing is displayed in the top-left corner. 5. Press | and ~ to trace along Y1, one X dot at a time, evaluating Y1 at each X. You also can enter your estimate for the maximum value of X. 6. Press 3 Ë 8.
7. Press Í. The trace cursor jumps to the point on the Y1 function evaluated at X=3.8. 8. Press | and ~ until you are on the maximum Y value. This is the maximum of Y1(X) for the X pixel values. The actual, precise maximum may lie between pixel values. Box with Lid Zooming In on the Graph To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the ZOOM instructions.
1. Press q to display the ZOOM menu. This menu is a typical TI-83 Plus menu. To select an item, you can either press the number or letter next to the item, or you can press † until the item number or letter is highlighted, and then press Í. 2. Press 2 to select 2:Zoom In. The graph is displayed again. The cursor has changed to indicate that you are using a ZOOM instruction. 3. With the cursor near the maximum value of the function, press Í. The new viewing window is displayed.
4. Press p to display the new window settings. Box with Lid Finding the Calculated Maximum You can use a CALCULATE menu operation to calculate a local maximum of a function. 1. Press y / (above r) to display the CALCULATE menu. Press 4 to select 4:maximum. The graph is displayed again with a Left Bound? prompt.
2. Press | to trace along the curve to a point to the left of the maximum, and then press Í. A 4 at the top of the screen indicates the selected bound. A Right Bound? prompt is displayed. 3. Press ~ to trace along the curve to a point to the right of the maximum, and then press Í. A 3 at the top of the screen indicates the selected bound. A Guess? prompt is displayed. 4. Press | to trace to a point near the maximum, and then press Í.
Or, press 3 Ë 8, and then press Í to enter a guess for the maximum. When you press a number key in TRACE, the X= prompt is displayed in the bottom-left corner. Notice how the values for the calculated maximum compare with the maximums found with the free-moving cursor, the trace cursor, and the table. Note: In steps 2 and 3 above, you can enter values directly for Left Bound and Right Bound, in the same way as described in step 4.
Comparing Test Results Using Box Plots Problem An experiment found a significant difference between boys and girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains. The TI Graphics team conducted a similar test for adult men and women. The test involved 30 small objects, which participants were not allowed to see.
Women Left 12 7 9 11 Women Right 13 12 11 12 Men Left Men Right 11 4 10 14 13 5 12 8 12 11 9 9 Procedure 1. Press … 5 to select 5:SetUpEditor. Enter list names WLEFT, WRGHT, MLEFT, and MRGHT, separated by commas. Press Í. The stat list editor now contains only these four lists. 2. Press … 1 to select 1:Edit. 3. Enter into WLEFT the number of correct guesses each woman made using her left hand (Women Left).
5. Press y ,. Select 1:Plot1. Turn on plot 1; define it as a modified box plot Õ that uses WLEFT. Move the cursor to the top line and select Plot2. Turn on plot 2; define it as a modified box plot that uses WRGHT. 6. Press o. Turn off all functions. 7. Press p. Set Xscl=1 and Yscl=0. Press q 9 to select 9:ZoomStat. This adjusts the viewing window and displays the box plots for the women’s results. 8. Press r.
% Men’s left-hand data % Men’s right-hand data Press | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. What difference do you see between the plots? 10. Compare the left-hand results. Redefine plot 1 to use WLEFT, redefine plot 2 to use MLEFT, and then press r to examine minX, Q1, Med, Q3, and maxX for each plot. Who were the better left-hand guessers, men or women? 11. Compare the right-hand results.
Graphing Piecewise Functions Problem The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the cost of the ticket.
3. Press p and set Xmin=L2, Xscl=10, Ymin=L5, and Yscl=10. Ignore Xmax and Ymax; they are set by @X and @Y in step 4. 4. Press y 5 to return to the home screen. Store 1 to @X, and then store 5 to @Y. @X and @Y are on the VARS Window X/Y secondary menu. @X and @Y specify the horizontal and vertical distance between the centers of adjacent pixels. Integer values for @X and @Y produce nice values for tracing. 5. Press r to plot the function.
Graphing Inequalities Problem Graph the inequality 0.4X3 N 3X + 5 < 0.2X + 4. Use the TEST menu operations to explore the values of X where the inequality is true and where it is false. Procedure 1. Press z. Select Dot, Simul, and the default settings. Setting Dot mode changes all graph style icons to í (dot) in the Y= editor. 2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as Y4 and the right side as Y5. 3. Enter the statement of the inequality as Y6.
4. Press q 6 to graph the inequality in the standard window. 5. Press r † † to move to Y6. Then press | and ~ to trace the inequality, observing the value of Y. 6. Press o. Turn off Y4, Y5, and Y6. Enter equations to graph only the inequality. 7. Press r. Notice that the values of Y7 and Y8 are zero where the inequality is false.
Solving a System of Nonlinear Equations Problem Using a graph, solve the equation X3 N 2X = 2cos(X). Stated another way, solve the system of two equations and two unknowns: Y = X 3N2X and Y = 2cos(X). Use ZOOM factors to control the decimal places displayed on the graph. Procedure 1. Press z. Select the default mode settings. Press o. Turn off all functions and stat plots. Enter the functions. 2. Press q 4 to select 4:ZDecimal.
3. Press q ~ 4 to select 4:SetFactors from the ZOOM MEMORY menu. Set XFact=10 and YFact=10. 4. Press q 2 to select 2:Zoom In. Use |, ~, }, and † to move the free-moving cursor onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the X and Y values have one decimal place. 5. Press Í to zoom in. Move the cursor over the intersection. As you move the cursor, notice that now the X and Y values have two decimal places. 6. Press Í to zoom in again.
Using a Program to Create the Sierpinski Triangle Setting up the Program This program creates a drawing of a famous fractal, the Sierpinski Triangle, and stores the drawing to a picture. To begin, press ~ ~ 1. Name the program SIERPINS, and then press Í. The program editor is displayed. Program PROGRAM:SIERPINS :FnOff :ClrDraw :PlotsOff :AxesOff :0!Xmin:1!Xmax :0!Ymin:1!Ymax :rand!X:rand!Y :For(K,1,3000) :rand!N :If N1 à 3 :Then :.5X!X :.5Y!Y :End TI-83 Plus Activities Set viewing window.
:If 1 à 3
Graphing Cobweb Attractors Problem Using Web format, you can identify points with attracting and repelling behavior in sequence graphing. Procedure 1. Press z. Select Seq and the default mode settings. Press y .. Select Web format and the default format settings. 2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K X(1NX). u(n)=Ku(nN1)(1Nu(nN1)) u(nMin)=.01 3. Press y 5 to return to the home screen, and then store 2.9 to K. 4. Press p.
5. Press r to display the graph, and then press ~ to trace the cobweb. This is a cobweb with one attractor. 6. Change K to 3.44 and trace the graph to show a cobweb with two attractors. 7. Change K to 3.54 and trace the graph to show a cobweb with four attractors.
Using a Program to Guess the Coefficients Setting Up the Program This program graphs the function A sin(BX) with random integer coefficients between 1 and 10. Try to guess the coefficients and graph your guess as C sin(DX). The program continues until your guess is correct.
:1!Yscl :DispGraph :Pause :FnOn 2 :Lbl Z :Prompt C,D Display graph. Prompt for guess. :DispGraph :Pause :If C=A :Text(1,1,"C IS OK") :If CƒA :Text(1,1,"C IS WRONG") :If D=B :Text(1,50,"D IS OK") :If DƒB :Text(1,50,"D IS WRONG") :DispGraph :Pause :If C=A and D=B :Stop :Goto Z TI-83 Plus Activities Display graph. Display results. Display graph. Quit if guesses are correct.
Graphing the Unit Circle and Trigonometric Curves Problem Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them. Any function that can be plotted in Func mode can be plotted in Par mode by defining the X component as T and the Y component as F(T). Procedure 1. Press z. Select Par, Simul, and the default settings. 2. Press p. Set the viewing window. Tmin=0 Tmax=2p Tstep=.1 Xmin=L2 Xmax=7.4 Xscl=pà2 Ymin=L3 Ymax=3 Yscl=1 3. Press o.
4. Enter the expressions to define the sine curve. 5. Press r. As the graph is plotting, you may press Í to pause and Í again to resume graphing as you watch the sine function “unwrap” from the unit circle. Note: You can generalize the unwrapping. Replace sin(T) in Y2T with any other trig function to unwrap that function.
Finding the Area between Curves Problem Find the area of the region bounded by f(x) = 300x / (x2 + 625) g(x) = 3cos(.1x) x = 75 Procedure 1. Press z. Select the default mode settings. 2. Press p. Set the viewing window. Xmin=0 Xmax=100 Xscl=10 Ymin=L5 Ymax=10 Yscl=1 Xres=1 3. Press o. Turn off all functions and stat plots. Enter the upper and lower functions. Y1=300Xà(X2+625) Y2=3cos(.
4. Press y / 5 to select 5:Intersect. The graph is displayed. Select a first curve, second curve, and guess for the intersection toward the left side of the display. The solution is displayed, and the value of X at the intersection, which is the lower limit of the integral, is stored in Ans and X. 5. Press y 5 to go to the home screen. Press y < 7 and use Shade( to see the area graphically. Shade(Y2,Y1,Ans,75) 6. Press y 5 to return to the home screen.
Using Parametric Equations: Ferris Wheel Problem Problem Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane. A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds.
Procedure 1. Press z. Select Par, Simul, and the default settings. Simul (simultaneous) mode simulates the two objects in motion over time. 2. Press p. Set the viewing window. Tmin=0 Tmax=12 Tstep=.1 Xmin=L13 Xmax=34 Xscl=10 Ymin=0 Ymax=31 Yscl=10 3. Press o. Turn off all functions and stat plots. Enter the expressions to define the path of the ferris wheel and the path of the ball. Set the graph style for X2T to ë (path).
4. Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross in the top-right quadrant of the ferris wheel. 5. Press p. Change the viewing window to concentrate on this portion of the graph. Tmin=1 Tmax=3 Tstep=.03 Xmin=0 Xmax=23.5 Xscl=10 Ymin=10 Ymax=25.5 Yscl=10 6. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross.
7. Press † to move to the path of the ball. Notice the values of X and Y (T is unchanged). Notice where the cursor is located. This is the position of the ball when the ferris wheel passenger passes the intersection. Did the ball or the passenger reach the intersection first? You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion.
Demonstrating the Fundamental Theorem of Calculus Problem 1 Using the functions fnInt( and nDeriv( from the MATH menu to graph functions defined by integrals and derivatives demonstrates graphically that: x F ( x ) = ∫ dt = ln ( x ), x > 0 and that 1 x1 1 Dx ∫ dt = 1 t x Procedure 1 1. Press z. Select the default settings. 2. Press p. Set the viewing window. Xmin=.01 Xmax=10 Xscl=1 TI-83 Plus Activities Ymin=M1.5 Ymax=2.
3. Press o. Turn off all functions and stat plots. Enter the numerical integral of 1àT from 1 to X and the function ln(X). Set the graph style for Y1 to ç (line) and Y2 to ë (path). 4. Press r. Press |, }, ~, and † to compare the values of Y1 and Y2. 5. Press o. Turn off Y1 and Y2, and then enter the numerical derivative of the integral of 1àX and the function 1àX. Set the graph style for Y3 to ç (line) and Y4 to è (thick). 6. Press r.
Problem 2 Explore the functions defined by x y = ∫ t 2dt , 2 x ∫0 t 2dt , and x ∫2 t 2dt, Procedure 2 1. Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously. Store the function in Y5. 2. Press q 6 to select 6:ZStandard. 3. Press r. Notice that the functions appear identical, only shifted vertically by a constant.
4. Press o. Enter the numerical derivative of Y5 in Y6. 5. Press r. Notice that although the three graphs defined by Y5 are different, they share the same derivative.
Computing Areas of Regular N-Sided Polygons Problem Use the equation solver to store a formula for the area of a regular N-sided polygon, and then solve for each variable, given the other variables. Explore the fact that the limiting case is the area of a circle, pr2. Consider the formula A = NB 2 sin(pàN) cos(pàN) for the area of a regular polygon with N sides of equal length and B distance from the center to a vertex. N = 4 sides N = 8 sides N = 12 sides Procedure 1.
interactive solver editor is displayed, press } to display the equation editor. 2. Enter the formula as 0=ANNB2sin(p / N)cos(p / N), and then press Í. The interactive solver editor is displayed. 3. Enter N=4 and B=6 to find the area (A) of a square with a distance (B) from center to vertex of 6 centimeters. 4. Press } } to move the cursor onto A, and then press ƒ \. The solution for A is displayed on the interactive solver editor. 5. Now solve for B for a given area with various number of sides.
6. Enter N=8. To find the distance B, move the cursor onto B, and then press ƒ \. Find B for N=9, and then for N=10. Find the area given B=6, and N=10, 100, 150, 1000, and 10000. Compare your results with p62 (the area of a circle with radius 6), which is approximately 113.097. 7. Enter B=6. To find the area A, move the cursor onto A, and then press ƒ \. Find A for N=10, then N=100, then N=150, then N=1000, and finally N=10000. Notice that as N gets large, the area A approaches pB2.
11. Press r. After the graph is plotted, press 100 Í to trace to X=100. Press 150 Í. Press 188 Í. Notice that as X increases, the value of Y converges to p62, which is approximately 113.097. Y2=pB2 (the area of the circle) is a horizontal asymptote to Y1. The area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr 2) as N gets large.
Computing and Graphing Mortgage Payments Problem You are a loan officer at a mortgage company, and you recently closed on a 30-year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now. Procedure 1. Press z and set the fixed-decimal mode to 2 decimal places. Set the other mode settings to the defaults. 2.
since the future value of a loan is 0 once it is paid in full. Enter PMT: END, since payment is due at the end of a period. 3. Move the cursor onto the PV= prompt, and then press ƒ \. The present value, or mortgage amount, of the house is displayed at the PV= prompt. Now compare the graph of the amount of interest with the graph of the amount of principal for each payment. 4. Press z. Set Par and Simul. 5. Press o. Turn off all functions and stat plots.
6. Press p. Set these window variables. Tmin=1 Tmax=360 Tstep=12 Xmin=0 Xmax=360 Xscl=10 Ymin=0 Ymax=1000 Yscl=100 Tip: To increase the graph speed, change Tstep to 24. 7. Press r. After the graph is drawn, press 240 Í to move the trace cursor to T=240, which is equivalent to 20 years of payments. The graph shows that for the 240th payment (X=240), 358.03 of the 800 payment is applied to principal (Y=358.03). Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800. 8.
The graph shows that for the 240th payment (X=240), 441.97 of the 800 payment is interest (Y=441.97). 9. Press y 5 Œ Í 9 to paste 9:bal( to the home screen. Check the figures from the graph.
Chapter 18: Memory and Variable Management Checking Available Memory MEMORY Menu At any time you can check available memory or manage existing memory by selecting items from the MEMORY menu. To access this menu, press y L. MEMORY 1:About... 2:Mem Mgmt/Del... 3:Clear Entries 4:ClrAllLists 5:Archive... 6:UnArchive... 7:Reset... 8:Group... Displays information about the calculator. Reports memory availability and variable usage. Clears ENTRY (last-entry storage). Clears all lists in memory.
Displaying the MEMORY MANAGEMENT/DELETE Menu Mem Mgmt/Del displays the MEMORY MANAGEMENT/DELETE menu. The two lines at the top report the total amount of available RAM and ARCHIVE memory. By selecting menu items on this screen, you can see the amount of memory each variable type is using. This information can help you determine if some variables need to be deleted from memory to make room for new data, such as programs or applications. To check memory usage, follow these steps. 1.
3. Select variable types from the list to display memory usage. Note: Real, List, Y.Vars, and Prgm variable types never reset to zero, even after memory is cleared. Apps are independent applications which are stored in Flash ROM. AppVars is a variable holder used to store variables created by independent applications. You cannot edit or change variables in AppVars unless you do so through the application which created them. To leave the MEMORY MANAGEMENT/DELETE menu, press either y 5 or ‘.
Deleting Items from Memory Deleting an Item To increase available memory by deleting the contents of any variable (real or complex number, list, matrix, Y= variable, program, Apps, AppVars, picture, graph database, or string), follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu. 3. Select the type of data you want to delete, or select 1:All for a list of all variables of all types.
4. Press } and † to move the selection cursor (4) next to the item you want to delete, and then press {. The variable is deleted from memory. You can delete individual variables one by one from this screen. Note: If you are deleting programs or Apps, you will receive a message asking you to confirm this delete action. Select 2:Yes to continue. To leave any variable screen without deleting anything, press y 5, which displays the home screen.
Clearing Entries and List Elements Clear Entries Clear Entries clears the contents of the ENTRY (last entry) storage area (Chapter 1). To clear the ENTRY storage area, follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 3:Clear Entries to paste the instruction to the home screen. 3. Press Í to clear the ENTRY storage area. To cancel Clear Entries, press ‘.
ClrAllLists ClrAllLists sets the dimension of each list in RAM only to 0. To clear all elements from all lists, follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 4:ClrAllLists to paste the instruction to the home screen. 3. Press Í to set to 0 the dimension of each list in memory. To cancel ClrAllLists, press ‘. ClrAllLists does not delete list names from memory, from the LIST NAMES menu, or from the stat list editor.
Resetting the TI-83 Plus RAM ARCHIVE ALL Menu The RAM ARCHIVE ALL menu gives you the option of resetting all memory (including default settings) or resetting selected portions of memory while preserving other data stored in memory, such as programs and Y= functions. For instance, you can choose to reset all of RAM or just restore the default settings. Be aware that if you choose to reset RAM, all data and programs in RAM will be erased.
• Window variable values such as Xmin=L10; Xmax=10; Xscl=1; Yscl=1; and Xres=1 • Stat plots off • Format settings such as CoordOn (graphing coordinates on); AxesOn; and ExprOn (expression on) • rand seed value to 0 Displaying the RAM ARCHIVE ALL Menu To display the RAM ARCHIVE ALL menu on the TI-83 Plus, follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 7:Reset to display the RAM ARCHIVE ALL menu.
and programs in RAM. Resetting RAM or resetting defaults does not affect variables and applications in user data archive. Tip: Before you reset all RAM memory, consider restoring sufficient available memory by deleting only selected data. To reset all RAM memory or RAM defaults on the TI-83 Plus, follow these steps. 1. From the RAM ARCHIVE ALL menu, select 1:ALL RAM to display the RESET RAM menu or 2:Defaults to display the RESET DEFAULTS menu. 2.
Resetting Archive Memory When resetting archive memory on the TI-83 Plus, you can choose to delete from user data archive all variables, all applications, or both variables and applications. To reset all or part of user data archive memory, follow these steps. 1. From the RAM ARCHIVE ALL menu, press ~ to display the ARCHIVE menu. 2.
2:Apps to display the RESET ARC APPS menu. 3:Both to display the RESET ARC BOTH menu. 3. Read the message below the menu. • To cancel the reset and return to the home screen, press Í. • To continue with the reset, select 2:Reset. A message indicating the type of archive memory cleared will be displayed on the home screen.
Resetting All Memory When resetting all memory on the TI-83 Plus, RAM and user data archive memory is restored to factory settings. All nonsystem variables, applications, and programs are deleted. All system variables are reset to default settings. Tip: Before you reset all memory, consider restoring sufficient available memory by deleting only selected data. To reset all memory on the TI-83 Plus, follow these steps. 1. From the RAM ARCHIVE ALL menu, press ~ ~ to display the ALL menu. 2.
3. Read the message below the RESET MEMORY menu. • To cancel the reset and return to the home screen, press Í. • To continue with the reset, select 2:Reset. The message MEM cleared is displayed on the home screen. Note: When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast by pressing y } or †.
Archiving and UnArchiving Variables Archiving and UnArchiving Variables Archiving allows you to store data, programs, or other variables to the user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory. Archived variables cannot be edited or executed. They can only be seen and unarchived.
A, B, ... , Z Archive? (yes/no) yes UnArchive? (yes/no) yes Complex numbers A, B, ... , Z yes yes Matrices ãAä, ãBä, ãCä, ... , ãJä yes yes Lists L1, L2, L3, L4, L5, L6, and user-defined names yes yes yes yes not applicable not applicable Variable Type Real numbers Names Programs Functions Y1, Y2, . . . , Y9, Y0 no Parametric equations X1T and Y1T, ...
Variable Type Tables Names Apps Applications AppVars Application variables TblStart, Tb1, TblInput Groups Variables with reserved names minX, maxX, RegEQ, and others System variables Xmin, Xmax, and others Archive? (yes/no) no UnArchive? (yes/no) not applicable see Note above yes no see Note above no no no yes not applicable not applicable Archiving and unarchiving can be done in two ways: • Use the 5:Archive or 6:UnArchive commands from the MEMORY menu or CATALOG.
For: Sizes must be such that: Archive Archive free size > variable size UnArchive RAM free size > variable size Note: If there is not enough space, unarchive or delete variables as necessary. Be aware that when you unarchive a variable, not all the memory associated with that variable in user data archive will be released since the system keeps track of where the variable has been and where it is now in RAM.
3. Press y d to place the L1 variable in the edit screen. 4. Press Í to complete the archive process. Note: An asterisk will be displayed to the left of the Archived variable name to indicate it is archived. To archive or unarchive a list variable (L1) using a Memory Management editor: 1. Press y L to display the MEMORY menu. 2. Select 2:Mem Mgmt/Del... to display the MEMORY MANAGEMENT/DELETE menu.
3. Select 4:List... to display the LIST menu. 4. Press Í to archive L1. An asterisk will appear to the left of L1 to indicate it is an archived variable. To unarchive a variable in this screen, put the cursor next to the archived variable and press Í. The asterisk will disappear. 5. Press y 5 to leave the LIST menu. Note: You can access an archived variable for the purpose of linking, deleting, or unarchiving it, but you cannot edit it.
Grouping and Ungrouping Variables Grouping Variables Grouping allows you to make a copy of two or more variables residing in RAM and then store them as a group in user data archive. The variables in RAM are not erased. The variables must exist in RAM before they can be grouped. In other words, archived data cannot be included in a group. To create a group of variables: 1. Press y L to display the MEMORY menu. 2. Select 8:Group... to display GROUP UNGROUP menu.
3. Press Í to display the GROUP menu. 4. Enter a name for the new group and press Í. Note: A group name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q. 5. Select the type of data you want to group. You can select 1:All+ which shows all variables of all types available and selected. You can also select 1:All- which shows all variables of all types available but not selected.
6. Press } and † to move the selection cursor (4) next to the first item you want to copy into a group, and then press Í. A small square will remain to the left of all variables selected for grouping. Repeat the selection process until all variables for the new group are selected and then press ~ to display the DONE menu. 7. Press Í to complete the grouping process.
Note: You can only group variables in RAM. You cannot group some system variables, such as the last-answer variable Ans and the statistical variable RegEQ. Ungrouping Variables Ungrouping allows you to make a copy of variables in a group stored in user data archive and place them ungrouped in RAM. DuplicateName Menu During the ungrouping action, if a duplicate variable name is detected in RAM, the DUPLICATE NAME menu is displayed. DuplicateName 1:Rename Prompts to rename receiving variable.
• When you select 2:Overwrite, the unit overwrites the data of the duplicate variable name found in RAM. Ungrouping resumes. • When you select 3: Overwrite All, the unit overwrites the data of all duplicate variable names found in RAM. Ungrouping resumes. • When you select 4:Omit, the unit does not ungroup the variable in conflict with the duplicated variable name found in RAM. Ungrouping resumes with the next item. • When you select 5:Quit, ungrouping stops, and no further changes are made.
4. Press } and † to move the selection cursor (4) next to the group variable you want to ungroup, and then press Í. The ungroup action is completed. Note: Ungrouping does not remove the group from user data archive. You must delete the group in user data archive to remove it.
Garbage Collection Garbage Collection Message If you use the user data archive extensively, you may see a Garbage Collect? message. This occurs if you try to archive a variable when there is not enough free contiguous archive memory. The TI-83 Plus will attempt to rearrange the archived variables to make additional room. Responding to the Garbage Collection Message • To cancel, select 1:No. • If you choose 1:No, the message ERR:ARCHIVE FULL will be displayed. • To continue archiving, select 2:Yes.
After garbage collection, depending on how much additional space is freed, the variable may or may not be archived. If not, you can unarchive some variables and try again. Why Not Perform Garbage Collection Automatically Without a Message? The message: • Lets you know an archive will take longer than usual. It also alerts you that the archive will fail if there is not enough memory. • Can alert you when a program is caught in a loop that repetitively fills the user data archive.
Each variable that you archive is stored in the first empty block large enough to hold it. variable A variable B variable D Depending on its size, variable D is stored in one of these locations. Sector 1 Empty block Sector 2 variable C Sector 3 This process continues to the end of the last sector. Depending on the size of individual variables, the empty blocks may account for a significant amount of space. Garbage collection occurs when the variable you are archiving is larger than any empty block.
How Unarchiving a Variable Affects the Process When you unarchive a variable, it is copied to RAM but it is not actually deleted from user data archive memory. variable A After you unarchive variables B and C, they continue to take up space. Sector 1 Sector 2 variable D Sector 3 Unarchived variables are “marked for deletion,” meaning they will be deleted during the next garbage collection.
If the MEMORY Screen Shows Enough Free Space Even if the MEMORY screen shows enough free space to archive a variable or store an application, you may still get a Garbage Collect? message or an ERR: ARCHIVE FULL message. When you unarchive a variable, the Archive free amount increases immediately, but the space is not actually available until after the next garbage collection.
Using the GarbageCollect Command You can reduce the number of automatic garbage collections by periodically optimizing memory. This is done by using the GarbageCollect command. To use the GarbageCollect command, follow these steps. 1. Press y ãCATALOGä to display the CATALOG. 2. Press † or } to scroll the CATALOG until the selection cursor points to the GarbageCollect command. 3. Press Í to paste the command to the current screen. 4. Press Í to display the Garbage Collect? message. 5.
ERR:ARCHIVE FULL Message Even if the MEMORY screen shows enough free space to archive a variable or store an application, you may still get an ERR: ARCHIVE FULL message. An ERR:ARCHIVE FULL message may be displayed: • When there is insufficient space to archive a variable within a continuous block and within a single sector. • When there is insufficient space to store an application within a continuous block of memory.
Chapter 19: Communication Link Getting Started: Sending Variables Getting Started is a fast-paced introduction. Read the chapter for details. Create and store a variable and a matrix, and then transfer them to another TI-83 Plus. 1. On the home screen of the sending unit, press 5 Ë 5 ¿ ƒ Q. Press Í to store 5.5 to Q. 2. Press y H y H 1 ¢ 2 y I y H 3 ¢ 4 y I y I ¿ y > 1. Press Í to store the matrix to [A]. 3. On the sending unit, press y L to display the MEMORY menu.
4. On the sending unit, press 2 to select 2:Mem Mgmt/Del. The MEMORY MANAGEMENT menu is displayed. 5. On the sending unit, press 5 to select 5:Matrix. The MATRIX editor screen is displayed. 6. On the sending unit, press Í to archive [A]. An asterisk ( ) will appear, signifying that [A] is now archived. * 7. Connect the calculators with the link cable. Push both ends in firmly. 8. On the receiving unit, press y 8 ~ to display the RECEIVE menu. Press 1 to select 1:Receive. The message Waiting...
11. Press † until the selection cursor ( 4 ) is next to [A] MATRX. Press Í. 12. Press † until the selection cursor is next to Q REAL. Press Í. A square dot next to [A] and Q indicates that each is selected to send. 13. On the sending unit, press ~ to display the TRANSMIT menu. 14. On the sending unit, press 1 to select 1:Transmit and begin transmission. The receiving unit displays the message Receiving....When the items are transmitted, both units display the name and type of each transmitted variable.
TI-83 Plus Silver Edition LINK This chapter describes how to communicate with compatible TI units. A unit-to-unit link cable is included with the TI-83 Plus Silver Edition for this purpose.
Connecting Two Calculators with a Unit-to-Unit Cable The TI-83 Plus link port is located at the center of the bottom edge of the calculator. 1. Firmly insert either end of the unit-to-unit cable into the port. 2. Insert the other end of the cable into the other calculator’s port. Linking to the CBL/CBR System The CBL 2/CBL and the CBR are optional accessories that also connect to a TI-83 Plus with the unit-to-unit link cable.
Selecting Items to Send LINK SEND Menu To display the LINK SEND menu, press y 8. SEND RECEIVE 1:All+... 2:AllN... 3:Prgm... 4:List... 5:Lists to TI82... 6:GDB... 7:Pic... 8:Matrix... 9:Real... 0:Complex... A:Y-Vars... B:String... C:Apps... D:AppVars... E:Group... F:SendId TI-83 Plus Displays all items as selected, including RAM and Flash applications. Displays all items as deselected. Displays all program names. Displays all list names. Displays list names L1 through L6. Displays all graph databases.
SEND RECEIVE G:SendOS H:Back Up... Sends operating system updates to another TI-83 Plus Silver Edition or TI-83 Plus. Selects all RAM and mode settings (no Flash applications or archived items) for backup to another TI-83 Plus Silver Edition or to a TI-83 Plus. When you select an item on the LINK SEND menu, the corresponding SELECT screen is displayed. Note: Each SELECT screen, except All+…, is initially displayed with nothing preselected. All+… is displayed with everything pre-selected.
4. Press Í to select or deselect the item. Selected names are marked with a 0. Note: An asterisk (*) to the left of an item indicates the item is archived (Chapter 18). 5. Repeat steps 3 and 4 to select or deselect additional items. Sending the Selected Items After you have selected items to send on the sending unit and set the receiving unit to receive, follow these steps to transmit the items. To set the receiving unit, see Receiving Items. 1. Press ~ on the sending unit to display the TRANSMIT menu.
3. Press Í to select 1:Transmit. The name and type of each item are displayed line-by-line on the sending unit as the item is queued for transmission, and then on the receiving unit as each item is accepted. Note: Items sent from the RAM of the sending unit are transmitted to the RAM of the receiving unit. Items sent from user data archive of the sending unit are transmitted to user data archive of the receiving unit.
Sending to a TI-83 Plus Silver Edition or TI-83 Plus You can transfer variables (all types), programs, and Flash applications to another TI-83 Plus Silver Edition or TI-83 Plus. You can also backup the RAM memory of one unit to another. Note: Keep in mind that the TI.83 Plus has less Flash memory than the TI-83 Plus Silver Edition. • Variables stored in RAM on the sending TI-83 Plus Silver Edition will be sent to the RAM of the receiving TI-83 Plus Silver Edition or TI-83 Plus.
To send data to an additional TI-83 Plus Silver Edition or a TI-83 Plus: 1. Use a unit-to-unit cable to link two units together. 2. On the sending unit press y 8 and select a data type and items to SEND. 3. Press ~ on the sending unit to display the TRANSMIT menu. 4. On the other unit, press y 8 ~ to display the RECEIVE menu. 5. Press Í on the receiving unit. 6. Press Í on the sending unit. A copy of the selected item(s) is sent to the receiving unit. 7.
an item, all selections or deselections from the last transmission are cleared. 10. Press ~ on the sending unit to display the TRANSMIT menu. 11. On the new receiving unit, press y 8 ~ to display the RECEIVE menu. 12. Press Í on the receiving unit. 13. Press Í on the sending unit. A copy of the selected item(s) is sent to the receiving unit. 14. Repeat steps 7 through 13 until the items are sent to all additional units.
Note: You cannot perform a RAM memory backup from a TI-83 Plus to a TI-83 or from a TI-83 to a TI-83 Plus. To send data to a TI-83: 1. Use a unit-to-unit cable to link the two units together. 2. Set the TI-83 to receive. 3. Press y 8 on the sending TI-83 Plus to display the LINK SEND menu. 4. Select the menu of the items you want to transmit. 5. Press ~ on the sending TI-83 Plus to display the LINK TRANSMIT menu. 6. Confirm that the receiving unit is set to receive. 7.
Note: You cannot perform a memory backup from a TI-83 Plus to a TI-82 or from a TI-82 to a TI-83 Plus. To send lists to a TI-82: 1. Use a unit-to-unit cable to link the two units together. 2. Set the TI-82 to receive. 3. Press y 8 5 on the sending TI-83 Plus to select 5:Lists to TI82. The SELECT screen is displayed. 4. Select each list to transmit. 5. Press ~ to display the LINK TRANSMIT menu. 6. Confirm that the receiving unit is set to receive. 7. Press Í to select 1:Transmit and begin transmitting.
Note: You cannot perform a RAM memory backup from a TI-83 Plus to a TI-73 or from a to a TI-73 to a TI-83 Plus. To transmit data to a TI-73: 1. Use a unit-to-unit cable to link two units together. 2. Set the TI-73 to receive. 3. Press y 8 2 on the sending TI-83 Plus to select 2:All-.... The SELECT screen is displayed. 4. Select items you want to send. 5. Press ~ on the sending TI-83 Plus to display the LINK TRANSMIT menu. 6. Confirm that the receiving unit is set to receive. 7.
Receiving Items LINK RECEIVE Menu To display the LINK RECEIVE menu, press y 8 ~. SEND RECEIVE 1:Receive Sets unit to receive data transmission. Receiving Unit When you select 1:Receive from the LINK RECEIVE menu on the receiving unit, the message Waiting... and the busy indicator are displayed. The receiving unit is ready to receive transmitted items. To exit the receive mode without receiving items, press É, and then select 1:Quit from the Error in Xmit menu.
DuplicateName 1:Rename 2:Overwrite 3:Omit 4:Quit Prompts to rename receiving variable. Overwrites data in receiving variable. Skips transmission of sending variable. Stops transmission at duplicate variable. When you select 1:Rename, the Name= prompt is displayed, and alphalock is on. Enter a new variable name, and then press Í. Transmission resumes. When you select 2:Overwrite, the sending unit’s data overwrites the existing data stored on the receiving unit. Transmission resumes.
Receiving from a TI-83 You can transfer all variables and programs from a TI-83 to a TI-83 Plus if they fit in the RAM of the TI-83 Plus. The RAM of the TI-83 Plus is slightly less than the RAM of the TI-83. Receiving from a TI-82 — Resolved Differences Generally, you can transmit items to a TI-83 Plus from a TI-82, but differences between the two products may affect some transmitted data.
Note: You can transfer all real variables, pics, and programs from a TI-82 to a TI-83 Plus if they fit in the RAM of the TI-83 Plus. The RAM of the TI-83 Plus is slightly less than the RAM of the TI-82. Receiving from a TI-82 — Unresolved Differences The software built into the TI-83 Plus cannot resolve some differences between the TI-82 and TI-83 Plus. These differences are described below. You must edit the transmitted data on the receiving TI-83 Plus to account for these differences.
For example, on the TI-82, the character group Un-1 is pasted to the cursor location when you press y [UnN1]. The TI-83 Plus cannot directly translate Un-1 to the TI-83 Plus syntax u(nN1), so the ERR:INVALID menu is displayed. Note: TI-83 Plus implied multiplication rules differ from those of the TI-82. For example, the TI-83 Plus evaluates 1à2X as (1à2)äX, while the TI-82 evaluates 1à2X as 1à(2äX) (Chapter 2).
5. Press ~ on the sending TI-73 to display the LINK TRANSMIT menu. 6. Confirm that the receiving unit is set to receive. 7. Press Í on the sending TI-73 to select 1:Transmit and begin transmitting.
Backing Up RAM Memory Warning: H:Back Up overwrites the RAM memory and mode settings in the receiving unit. All information in the RAM memory of the receiving unit is lost. Note: Archived items on the receiving unit are not overwritten. You can backup the contents of RAM memory and mode settings (no Flash applications or archived items) to another TI-83 Plus Silver Edition. You can also backup RAM memory and mode settings to a TI-83 Plus. To perform a RAM memory backup: 1.
5. Press Í on the sending unit. A WARNING — Backup message displays on the receiving unit. 6. Press Í on the receiving unit to continue the backup. — or — Press 2:Quit on the receiving unit to cancel the backup and return to the LINK SEND menu Note: If a transmission error is returned during a backup, the receiving unit is reset. Memory Backup Complete When the backup is complete, both the sending calculator and receiving calculator display a confirmation screen.
Error Conditions A transmission error occurs after one or two seconds if: • A cable is not attached to the sending unit. • A cable is not attached to the receiving unit. Note: If the cable is attached, push it in firmly and try again. • The receiving unit is not set to receive transmission. • You attempt a backup between a TI-73, a TI-82, or a TI-83 and a TI-83 Plus.
• You attempt a data transfer from a TI-83 Plus to a TI-73 with data other than real numbers, pics, real lists L1 through L6 or named lists with q as part of the name. Although a transmission error does not occur, these two conditions may prevent successful transmission. • You try to use Get( with a calculator instead of a CBL 2/CBL or CBR. • You try to use GetCalc( with a TI-83 instead of a TI-83 Plus Silver Edition or TI-83 Plus.
Appendix A: Tables and Reference Information Table of Functions and Instructions Functions return a value, list, or matrix. You can use functions in an expression. Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table.
Function or Instruction/ Arguments abs(value) abs(complex value) valueA and valueB angle(value) ANOVA(list1,list2 [,list3,...,list20]) Ans Archive Asm(assemblyprgmname) AsmComp(prgmASM1, prgmASM2) AsmPrgm TI-83 Plus Result Key or Keys/ Menu or Screen/Item Returns the absolute value of a real number, expression, list, or matrix. NUM Returns the magnitude of a complex number or list. Returns 1 if both valueA and valueB are ƒ 0. valueA and valueB can be real numbers, expressions, or lists.
Function or Instruction/ Arguments augment(matrixA, matrixB) augment(listA,listB) Result Returns a matrix, which is matrixB appended to matrixA as new columns. Returns a list, which is listB concatenated to the end of listA. AxesOff Turns off the graph axes. AxesOn Turns on the graph axes. a+bi Sets the mode to rectangular complex number mode (a+bi).
Function or Instruction/ Arguments c2cdf(lowerbound, upperbound,df) c2pdf(x,df) c2.Test(observedmatrix, expectedmatrix [,drawflag]) Circle(X,Y,radius) Clear Entries ClrAllLists ClrDraw ClrHome Result Computes the c2 distribution probability between lowerbound and upperbound for the specified degrees of freedom df. Computes the probability density function (pdf) for the c2 distribution at a specified x value for the specified degrees of freedom df. Performs a chi-square test.
Function or Instruction/ Arguments ClrList listname1 [,listname2, ..., listname n] ClrTable Result Sets to 0 the dimension of one or more listnames. Clears all values from the table. Key or Keys/ Menu or Screen/Item … EDIT 4:ClrList † I/O conj(value) Connected CoordOff CoordOn cos(value) cosL1(value) cosh(value) coshL1(value) CubicReg [Xlistname, Ylistname,freqlist, regequ] TI-83 Plus Returns the complex conjugate of a complex number or list of complex numbers.
Function or Instruction/ Arguments cumSum(list) cumSum(matrix) dbd(date1,date2) value4Dec Degree DelVar variable DependAsk DependAuto det(matrix) Result Returns a list of the cumulative sums of the elements in list, starting with the first element. Returns a matrix of the cumulative sums of matrix elements. Each element in the returned matrix is a cumulative sum of a matrix column from top to bottom. Calculates the number of days between date1 and date2 using the actual-day-count method.
Function or Instruction/ Arguments DiagnosticOff DiagnosticOn dim(listname) Result Sets diagnostics-off mode; r, r2, and R2 are not displayed as regression model results. Sets diagnostics-on mode; r, r2, and R2 are displayed as regression model results. Returns the dimension of listname. Key or Keys/ Menu or Screen/Item yN DiagnosticOff yN DiagnosticOn y9 OPS dim(matrixname) length!dim(listname) Returns the dimension of matrixname as a list.
Function or Instruction/ Arguments DispTable Result Displays the table. Key or Keys/ Menu or Screen/Item † Displays value in DMS format. 5:DispTable y; I/O value4DMS ANGLE Dot DrawF expression DrawInv expression :DS<(variable,value) :commandA :commands e^(power) e^(list) Exponent: valueEexponent Exponent: listEexponent Exponent: matrixEexponent TI-83 Plus Sets dot plotting mode; resets all Y= editor graph-style settings to í . Draws expression (in terms of X) on the graph.
Function or Instruction/ Arguments 4Eff(nominal rate, Result Computes the effective interest rate. compounding periods) Key or Keys/ Menu or Screen/Item Π1:Finance CALC C:4Eff( Else See If:Then:Else Identifies end of For(, If-Then-Else, Repeat, or While loop. End Eng Sets engineering display mode. Equ4String(Y= var,Strn) Converts the contents of a Y= var to a string and stores it in Strn. Converts string to an expression and executes it.
Function or Instruction/ Arguments Fill(value,matrixname) Fill(value,listname) Result Stores value to each element in matrixname. Stores value to each element in listname. Fix # Sets fixed-decimal mode for # of decimal places. Float Sets floating decimal mode. fMax(expression,variable, lower,upper[,tolerance]) Returns the value of variable where the local maximum of expression occurs, between lower and upper, with specified tolerance.
Function or Instruction/ Arguments FnOn [function#, function#,...,function n] :For(variable,begin,end [,increment]) :commands :End :commands fPart(value) Result Selects all Y= functions or specified Y= functions. Executes commands through End, incrementing variable from begin by increment until variable>end. Full Returns the fractional part or parts of a real or complex number, expression, list, or matrix.
Function or Instruction/ Arguments gcd(valueA,valueB) geometcdf(p,x) geometpdf(p,x) Get(variable) GetCalc(variable) getKey Goto label Result Returns the greatest common divisor of valueA and valueB, which can be real numbers or lists. Computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p.
Function or Instruction/ Arguments GridOff Result Turns off grid format. GridOn Turns on grid format. G-T Horiz Sets graph-table vertical split-screen mode. Sets horizontal split-screen mode. Horizontal y Draws a horizontal line at y. Key or Keys/ Menu or Screen/Item †y. GridOff †y. GridOn †z G-T †z Horiz y< DRAW identity(dimension) :If condition :commandA :commands :If condition :Then :commands :End :commands TI-83 Plus Returns the identity matrix of dimension rows × dimension columns.
Function or Instruction/ Arguments :If condition :Then :commands :Else :commands :End :commands imag(value) IndpntAsk IndpntAuto Input Result Executes commands from Then to Else if condition = 1 (true); from Else to End if condition = 0 (false). Returns the imaginary (nonreal) part of a complex number or list of complex numbers. Sets table to ask for independentvariable values. Sets table to generate independentvariable values automatically. Displays graph.
Function or Instruction/ Arguments int(value) GInt(pmt1,pmt2 [,roundvalue]) invNorm(area[,m,s]) iPart(value) irr(CF0,CFList[,CFFreq]) :IS>(variable,value) :commandA :commands Ùlistname Result Returns the largest integer a real or complex number, expression, list, or matrix. Computes the sum, rounded to roundvalue, of the interest amount between pmt1 and pmt2 for an amortization schedule.
Function or Instruction/ Arguments Lbl label lcm(valueA,valueB) length(string) Line(X1,Y1,X2,Y2) Result Creates a label of one or two characters. Returns the least common multiple of valueA and valueB, which can be real numbers or lists. Returns the number of characters in string. Draws a line from (X1,Y1) to (X2,Y2).
Function or Instruction/ Arguments List 4 matr(listname1,..., listname n,matrixname) ln(value) LnReg [Xlistname, Ylistname,freqlist, regequ] log(value) Logistic [Xlistname, Ylistname,freqlist, regequ] Matr 4 list(matrix, listnameA,...,listname n) Matr 4 list(matrix, column#,listname) max(valueA,valueB) max(list) Result Fills matrixname column by column with the elements from each specified listname. Returns the natural logarithm of a real or complex number, expression, or list.
Function or Instruction/ Arguments max(listA,listB) max(value,list) mean(list[,freqlist]) median(list[,freqlist]) Result Returns a real or complex list of the larger of each pair of elements in listA and listB. Returns a real or complex list of the larger of value or each list element. Returns the mean of list with frequency freqlist. Returns the median of list with frequency freqlist.
Function or Instruction/ Arguments min(value,list) valueA nCr valueB Result Returns a real or complex list of the smaller of value or each list element. Returns the number of combinations of valueA taken valueB at a time. value nCr list Returns a list of the combinations of value taken each element in list at a time. Returns a list of the combinations of list nCr value each element in list taken value at a time.
Function or Instruction/ Arguments normalpdf(x[,m,s]) not(value) valueA nPr valueB value nPr list list nPr value listA nPr listB npv(interest rate,CF0, CFList[,CFFreq]) valueA or valueB Output(row,column, "text") Result Computes the probability density function for the normal distribution at a specified x value for the specified m and s. Returns 0 if value is ƒ 0. value can be a real number, expression, or list. Returns the number of permutations of valueA taken valueB at a time.
Function or Instruction/ Arguments Output(row,column, value) Result Displays value beginning at specified row and column. Param Sets parametric graphing mode. Pause Suspends program execution until you press Í. Pause [value] Displays value; suspends program execution until you press Í. Plot#(type,Xlistname, Ylistname,mark) Plot#(type,Xlistname, freqlist) Plot#(type,Xlistname, freqlist,mark) TI-83 Plus Defines Plot# (1, 2, or 3) of type Scatter or xyLine for Xlistname and Ylistname using mark.
Function or Instruction/ Arguments Plot#(type,datalistname, data axis,mark) PlotsOff [1,2,3] PlotsOn [1,2,3] Pmt_Bgn Pmt_End poissoncdf(m,x) poissonpdf(m,x) Polar complex value 4Polar Result Defines Plot# (1, 2, or 3) of type NormProbPlot for datalistname on data axis using mark. data axis can be X or Y. Deselects all stat plots or one or more specified stat plots (1, 2, or 3). Selects all stat plots or one or more specified stat plots (1, 2, or 3).
Function or Instruction/ Arguments PolarGC prgmname Result Sets polar graphing coordinates format. Executes the program name. Key or Keys/ Menu or Screen/Item †y. PolarGC † CTRL GPrn(pmt1,pmt2 [,roundvalue]) prod(list[,start,end]) Prompt variableA [,variableB,...,variable n] 1.PropZInt(x,n [,confidence level]) 2.PropZInt(x1,n1,x2,n2 [,confidence level]) 1.
Function or Instruction/ Arguments 2.PropZTest(x1,n1,x2,n2 [,alternative,drawflag]) Pt.Change(x,y) Result Computes a two-proportion z test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Reverses a point at (x,y). Key or Keys/ Menu or Screen/Item †… TESTS 6:2-PropZTest( y< POINTS Pt.Off(x,y[,mark]) Erases a point at (x,y) using mark. 3:Pt.Change( y< POINTS Pt.On(x,y[,mark]) Draws a point at (x,y) using mark. 2:Pt.
Function or Instruction/ Arguments pxl.Test(row,column) P4Rx(r,q) P4Ry(r,q) Returns Y, given polar coordinates r and q or a list of polar coordinates. QuadReg [Xlistname, Ylistname,freqlist, regequ] QuartReg [Xlistname, Ylistname,freqlist, regequ] Radian rand[(numtrials)] randBin(numtrials,prob [,numsimulations]) TI-83 Plus Result Returns 1 if pixel (row, column) is on, 0 if it is off; 0 row 62 and 0 column 94. Returns X, given polar coordinates r and q or a list of polar coordinates.
Function or Instruction/ Arguments randInt( lower,upper [,numtrials]) randM(rows,columns) randNorm(m,s[,numtrials]) re^qi Real real(value) RecallGDB n Result Generates and displays a random integer within a range specified by lower and upper integer bounds for a specified number of trials numtrials. Returns a random matrix of rows (1– 99) × columns (1–99). Generates and displays a random real number from a specified Normal distribution specified by m and s for a specified number of trials numtrials.
Function or Instruction/ Arguments RectGC ref(matrix) :Repeat condition :commands :End :commands Return Result Sets rectangular graphing coordinates format. Returns the row-echelon form of a matrix. Executes commands until condition is true. Key or Keys/ Menu or Screen/Item †y. RectGC y> MATH A:ref( † CTL 6:Repeat Returns to the calling program.
Function or Instruction/ Arguments rref(matrix) R4Pr(x,y) R4Pq(x,y) 2.SampÜTest [listname1, listname2,freqlist1, freqlist2,alternative, drawflag] (Data list input) 2.SampÜTest Sx1,n1, Sx2,n2[,alternative, drawflag] (Summary stats input) Result Returns the reduced row-echelon form of a matrix. Returns R, given rectangular coordinates x and y or a list of rectangular coordinates. Returns q, given rectangular coordinates x and y or a list of rectangular coordinates. Performs a two-sample Û test.
Function or Instruction/ Arguments 2.SampTTest [listname1, listname2,freqlist1, freqlist2,alternative, pooled,drawflag] (Data list input) 2.SampTTest v1,Sx1,n1, v2,Sx2,n2[,alternative, pooled,drawflag] (Summary stats input) 2.SampZInt(s1,s2 [,listname1,listname2, freqlist1,freqlist2, confidence level]) (Data list input) 2.SampZInt(s1,s2, v1,n1,v2,n2 [,confidence level]) (Summary stats input) 2.
Function or Instruction/ Arguments 2.SampZTest(s1,s2, v1,n1,v2,n2 [,alternative,drawflag]) (Summary stats input) Sci Select(Xlistname, Ylistname) Send(variable) seq(expression,variable, begin,end[,increment]) Seq Sequential SetUpEditor TI-83 Plus Result Computes a two-sample z test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Sets scientific notation display mode.
Function or Instruction/ Arguments SetUpEditor listname1 [,listname2,..., listname20] Shade(lowerfunc, upperfunc[,Xleft,Xright, pattern,patres]) Shadec2(lowerbound, upperbound,df) ShadeÜ(lowerbound, upperbound, numerator df, denominator df) ShadeNorm(lowerbound, upperbound[,m,s]) Shade_t(lowerbound, upperbound,df) TI-83 Plus Result Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting with column 1.
Function or Instruction/ Arguments Simul sin(value) sinL1(value) sinh(value) sinhL1(value) SinReg [iterations, Xlistname,Ylistname, period,regequ] solve(expression,variable, guess,{lower,upper}) SortA(listname) SortA(keylistname, dependlist1[,dependlist2, ...,dependlist n]) SortD(listname) TI-83 Plus Result Sets mode to graph functions simultaneously. Returns the sine of a real number, expression, or list. Returns the arcsine of a real number, expression, or list.
Function or Instruction/ Arguments SortD(keylistname, dependlist1[,dependlist2, ..., dependlist n]) stdDev(list[,freqlist]) Stop Store: value!variable StoreGDB n StorePic n Result Sorts elements of keylistname in descending order, then sorts each dependlist as a dependent list. Returns the standard deviation of the elements in list with frequency freqlist. Ends program execution; returns to home screen. Stores value in variable. Stores current graph in database GDBn.
Function or Instruction/ Arguments Tangent(expression,value) tanh(value) tanhL1(value) tcdf(lowerbound, upperbound,df) Text(row,column,text1, text2,...,text n) Result Draws a line tangent to expression at X=value. Returns hyperbolic tangent of a real number, expression, or list. Returns the hyperbolic arctangent of a real number, expression, or list. Computes the Student-t distribution probability between lowerbound and upperbound for the specified degrees of freedom df.
Function or Instruction/ Arguments Trace T-Test m0[,listname, freqlist,alternative, drawflag] (Data list input) T-Test m0, v,Sx,n [,alternative,drawflag] (Summary stats input) tvm_FV[(Ú,æ,PV,PMT, P/Y,C/Y)] tvm_æ[(Ú,PV,PMT,FV, P/Y,C/Y)] tvm_Ú[(æ,PV,PMT,FV, P/Y,C/Y)] tvm_Pmt[(Ú,æ,PV,FV, P/Y,C/Y)] tvm_PV[(Ú,æ,PMT,FV, P/Y,C/Y)] Result Displays the graph and enters TRACE mode. Performs a t test with frequency freqlist. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >.
Function or Instruction/ Arguments UnArchive uvAxes uwAxes 1-Var Stats [Xlistname, freqlist] 2-Var Stats [Xlistname, Ylistname,freqlist] variance(list[,freqlist]) Vertical x Result Moves the specified variables from the user data archive memory to RAM. To archive variables, use Archive. Sets sequence graphs to plot u(n) on the x-axis and v(n) on the y-axis. Sets sequence graphs to plot u(n) on the x-axis and w(n) on the y-axis.
Function or Instruction/ Arguments valueA xor valueB ZBox ZDecimal ZInteger ZInterval s[,listname, freqlist,confidence level] (Data list input) ZInterval s,v,n [,confidence level] (Summary stats input) Zoom In Zoom Out TI-83 Plus Result Returns 1 if only valueA or valueB = 0. valueA and valueB can be real numbers, expressions, or lists. Displays a graph, lets you draw a box that defines a new viewing window, and updates the window. Adjusts the viewing window so that @X=0.1 and @Y=0.
Function or Instruction/ Arguments ZoomFit ZoomRcl ZoomStat ZoomSto ZPrevious ZSquare ZStandard TI-83 Plus Result Recalculates Ymin and Ymax to include the minimum and maximum Y values, between Xmin and Xmax, of the selected functions and replots the functions. Graphs the selected functions in a user-defined viewing window. Redefines the viewing window so that all statistical data points are displayed. Immediately stores the current viewing window.
Function or Instruction/ Arguments ZNTest(m0,s[,listname, freqlist,alternative, drawflag]) (Data list input) ZNTest(m0,s,v,n [,alternative,drawflag]) (Summary stats input) ZTrig Factorial: value! Result Performs a z test with frequency freqlist. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Performs a z test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
Function or Instruction/ Arguments Transpose: matrixT x throotx‡value Result Returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of matrix. Returns x throot of value. Key or Keys/ Menu or Screen/Item y> MATH 2:T MATH x throotx‡list Returns x throot of list elements. 5:x( MATH listx‡value Returns list roots of value. 5:x( MATH listAx‡listB Returns listA roots of listB.
Function or Instruction/ Arguments Not equal: valueAƒvalueB Less than: valueAvalueB Less than or equal: valueAvalueB Greater than or equal: valueA‚valueB Inverse: valueL1 Inverse: listL1 Inverse: matrixL1 Square: value2 TI-83 Plus Result Returns 1 if valueA ƒ valueB. Returns 0 if valueA = valueB. valueA and valueB can be real or complex numbers, expressions, lists, or matrices. Returns 1 if valueA < valueB. Returns 0 if valueA ‚ valueB.
Function or Instruction/ Arguments Square: list2 Square: matrix2 Powers: value^power Powers: list^power Powers: value^list Powers: matrix^power Negation: Lvalue Power of ten: 10^(value) Power of ten: 10^(list) Square root: ‡(value) Multiplication: valueAävalueB Multiplication: valueälist Multiplication: listävalue TI-83 Plus Result Returns list elements squared. Returns matrix multiplied by itself. Returns value raised to power. value can be a real or complex number or expression.
Function or Instruction/ Arguments Multiplication: listAälistB Multiplication: valueämatrix Multiplication: matrixAämatrixB Division: valueAàvalueB Division: listàvalue Division: valueàlist Division: listAàlistB Addition: valueA+valueB Addition: list+value Addition: listA+listB Addition: matrixA+matrixB Concatenation: string1+string2 Subtraction: valueANvalueB Subtraction: valueNlist TI-83 Plus Result Returns listA elements times listB elements. Returns value times matrix elements.
Function or Instruction/ Arguments Subtraction: listNvalue Subtraction: listANlistB Subtraction: matrixANmatrixB Minutes notation: degrees¡minutes'seconds" Seconds notation: degrees¡minutes'seconds" TI-83 Plus Result Subtracts value from list elements. Subtracts listB elements from listA elements. Subtracts matrixB elements from matrixA elements. Interprets minutes angle measurement as minutes. Interprets seconds angle measurement as seconds.
TI-83 Plus Menu Map The TI-83 Plus Menu Map begins at the top-left corner of the keyboard and follows the keyboard layout from left to right. Default values and settings are shown. o ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ (Par mode) Plot1 Plot2 Plot3 çX1T= Y1T= çX2T= Y2T= ... çX6T= Y6T= (Func mode) Plot1 Plot2 Plot3 çY1= çY2= çY3= çY4= ...
p ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ (Func mode) WINDOW Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 Xres=1 (Par mode) WINDOW Tmin=0 Tmax=pä2 Tstep=pà24 Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 (Pol mode) WINDOW qmin=0 qmax=pä2 qstep=pà24 Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1 y- y- ÚÄÄÄÙ ÚÄÄÄÄÙ TABLE SETUP TblStart=0 @Tbl=1 Indpnt:Auto Ask Depend:Auto Ask TI-83 Plus (Seq mode) WINDOW nMin=1 nMax=10 PlotStart=1 PlotStep=1 Xmin=-10 Xmax=10 Xscl=1 Ymin=-10 Ymax=10 Yscl=1
q ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ZOOM 1:ZBox 2:Zoom In 3:Zoom Out 4:ZDecimal 5:ZSquare 6:ZStandard 7:ZTrig 8:ZInteger 9:ZoomStat 0:ZoomFit MEMORY 1:ZPrevious 2:ZoomSto 3:ZoomRcl 4:SetFactors… MEMORY (Set Factors...) ZOOM FACTORS XFact=4 YFact=4 y .
y/ ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ (Func mode) CALCULATE 1:value 2:zero 3:minimum 4:maximum 5:intersect 6:dy/dx 7:‰f(x)dx (Par mode) CALCULATE 1:value 2:dy/dx 3:dy/dt 4:dx/dt (Pol mode) CALCULATE 1:value 2:dy/dx 3:dr/dq (Seq mode) CALCULATE 1:value z ÚÙ Normal Sci Eng Float 0123456789 Radian Degree Func Par Pol Seq Connected Dot Sequential Simul Real a+b× re^q× Full Horiz G-T TI-83 Plus Tables and Reference Information 701
y8 ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ SEND 1:All+… 2:AllN… 3:Prgm… 4:List… 5:Lists to TI82… 6:GDB… 7:Pic… 8:Matrix… 9:Real… 0:Complex… A:Y-Vars… B:String… C:Apps… D:AppVars… E:Group… F:SendId G:SendOS H:Back Up… TI-83 Plus RECEIVE 1:Receive Tables and Reference Information 702
… ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ EDIT 1:Edit… 2:SortA( 3:SortD( 4:ClrList 5:SetUpEditor TI-83 Plus CALC 1:1-Var Stats 2:2-Var Stats 3:Med-Med 4:LinReg(ax+b) 5:QuadReg 6:CubicReg 7:QuartReg 8:LinReg(a+bx) 9:LnReg 0:ExpReg A:PwrReg B:Logistic C:SinReg TESTS 1:Z-Test… 2:T-Test… 3:2-SampZTest… 4:2-SampTTest… 5:1-PropZTest… 6:2-PropZTest… 7:ZInterval… 8:TInterval… 9:2-SampZInt… 0:2-SampTInt… A:1-PropZInt… B:2-PropZInt… C:c 2-Test… D:2-SampÛTest… E:LinRegTTest… F:ANOVA( Tables and Reference Informatio
y9 ÚÄÄÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ NAMES 1:listname 2:listname 3:listname ...
y: ÚÄÄÁÄÄÄÄÄÄÄÄÄ¿ TEST 1:= 2:ƒ 3:> 4:‚ 5:< 6: LOGIC 1:and 2:or 3:xor 4:not( y> y; ÚÁÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ NAMES 1:[A] 2:[B] 3:[C] 4:[D] 5:[E] 6:[F] 7:[G] 8:[H] 9:[I] 0:[J] TI-83 Plus MATH 1:det( 2: T 3:dim( 4:Fill( 5:identity( 6:randM( 7:augment( 8:Matr4list( 9:List4matr( 0:cumSum( A:ref( B:rref( C:rowSwap( D:row+( E:…row( F:…row+( EDIT 1:[A] 2:[B] 3:[C] 4:[D] 5:[E] 6:[F] 7:[G] 8:[H] 9:[I] 0:[J] Tables and Reference Information ÚÄÄÄÙ ANGLE 1:¡ 2:' 3: r 4:4DMS 5:R4Pr( 6:R4Pq( 7:P4Rx( 8:P4Ry(
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ EXEC 1:name 2:name ... EDIT 1:name 2:name ... NEW 1:Create New ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ (PRGM editor) CTL 1:If 2:Then 3:Else 4:For( 5:While 6:Repeat 7:End 8:Pause 9:Lbl 0:Goto A:IS>( B:DS<( C:Menu( D:prgm E:Return F:Stop G:DelVar H:GraphStyle( TI-83 Plus (PRGM editor) I/O 1:Input 2:Prompt 3:Disp 4:DispGraph 5:DispTable 6:Output( 7:getKey 8:ClrHome 9:ClrTable 0:GetCalc( A:Get( B:Send( (PRGM editor) EXEC 1:name 2:name ...
y< ÚÄÄÄÄÁÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ DRAW 1:ClrDraw 2:Line( 3:Horizontal 4:Vertical 5:Tangent( 6:DrawF 7:Shade( 8:DrawInv 9:Circle( 0:Text( A:Pen POINTS 1:Pt-On( 2:Pt-Off( 3:Pt-Change( 4:Pxl-On( 5:Pxl-Off( 6:Pxl-Change( 7:pxl-Test( STO 1:StorePic 2:RecallPic 3:StoreGDB 4:RecallGDB ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ VARS 1:Window… 2:Zoom… 3:GDB… 4:Picture… 5:Statistics… 6:Table… 7:String… TI-83 Plus Y-VARS 1:Function… 2:Parametric… 3:Polar… 4:On/Off… Tables and Reference Information 707
VARS ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂ (Window…) X/Y 1:Xmin 2:Xmax 3:Xscl 4:Ymin 5:Ymax 6:Yscl 7:Xres 8:@X 9:@Y 0:XFact A:YFact (Window…) T/q 1:Tmin 2:Tmax 3:Tstep 4:qmin 5:qmax 6:qstep (Window…) U/V/W 1:u(nMin) 2:v(nMin) 3:w(nMin) 4:nMin 5:nMax 6:PlotStart 7:PlotStep VARS ÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄ (Zoom…) ZX/ZY 1:ZXmin 2:ZXmax 3:ZXscl 4:ZYmin 5:ZYmax 6:ZYscl 7:ZXres TI-83 Plus (Zoom…) ZT/Zq 1:ZTmin 2:ZTmax 3:ZTstep 4:Zqmin 5:Zqmax 6:Zqstep (Zoom…) ZU 1:Zu(nMin) 2:Zv(nMin) 3:Zw(nMin) 4:ZnMin 5:Z
VARS ÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄ (GDB…) GRAPH DATABASE 1:GDB1 2:GDB2 ... 9:GDB9 0:GDB0 TI-83 Plus (Picture… ) PICTURE 1:Pic1 2:Pic2 ...
VARS ÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄ (Statistics…) XY 1:n 2:v 3:Sx 4:sx 5:w 6:Sy 7:sy 8:minX 9:maxX 0:minY A:maxY TI-83 Plus (Statistics…) G 1:Gx 2:Gx 2 3:Gy 4:Gy2 5:Gxy (Statistics…) EQ 1:RegEQ 2:a 3:b 4:c 5:d 6:e 7:r 8:r 2 9:R 2 Tables and Reference Information (Statistics…) TEST 1:p 2:z 3:t 4:c 2 5:Û 6:df 7:Ç 8:Ç1 9:Ç2 0:s A:ü1 B:ü2 C:Sx1 D:Sx2 E:Sxp F:n1 G:n2 H:lower I:upper (Statistics…) PTS 1:x1 2:y1 3:x2 4:y2 5:x3 6:y3 7:Q1 8:Med 9:Q 3 710
VARS ÄÂÄÄÄÄÄÄÄÄÄÄÄ¿ (Table…) TABLE 1:TblStart 2:@Tbl 3:TblInput (String…) STRING 1:Str1 2:Str2 3:Str3 4:Str4 ... 9:Str9 0:Str0 Y-VARS ÚÄÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄ¿ (Function…) FUNCTION 1:Y1 2:Y2 3:Y3 4:Y4 ... 9:Y9 0:Y0 (Parametric…) (Polar…) PARAMETRIC POLAR 1:X1T 1:r1 2:Y1T 2:r2 3:X2T 3:r3 4:Y2T 4:r4 ...
y= ÚÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ DISTR 1:normalpdf( 2:normalcdf( 3:invNorm( 4:tpdf( 5:tcdf( 6:c 2 pdf( 7:c 2 cdf( 8:Ûpdf( 9:Ûcdf( 0:binompdf( A:binomcdf( B:poissonpdf( C:poissoncdf( D:geometpdf( E:geometcdf( TI-83 Plus DRAW 1:ShadeNorm( 2:Shade_t( 3:Shadec 2 ( 4:ShadeÛ( Tables and Reference Information 712
Œ ÚÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄ¿ 1:Finance 2:CBL/CBR CBL/CBR Finance ÚÄÄÄÄÄÁÄÄÄÄÄ¿ ÚÄÄÄÙ CALC 1:TVM Solver… 2:tvm_Pmt 3:tvm_æ 4:tvm_PV 5:tvm_Ú 6:tvm_FV 7:npv( 8:irr( 9:bal( 0:GPrn( A:GInt( B:4Nom( C:4Eff( D:dbd( E:Pmt_End F:Pmt_Bgn VARS 1:Ú 2:æ 3:PV 4:PMT 5:FV 6:P/Y 7:C/Y TI-83 Plus Tables and Reference Information 1:GAUGE 2:DATA LOGGER 3:CBR 4:QUIT 713
yL MEMORY ÚÄÄÙ ÚÄÄÙ MEMORY 1:About 2:Mem Mgmt/Del… 3:Clear Entries 4:ClrAllLists 5:Archive 6:UnArchive 7:Reset… 8:Group TI-83 Plus (Mem Mgmt/Del…) RAM FREE 25631 ARC FREE 131069 1:All… 2:Real… 3:Complex… 4:List… 5:Matrix… 6:Y-Vars… 7:Prgm… 8:Pic… 9:GDB… 0:String… A:Apps… B:AppVars… C:Group… Tables and Reference Information 714
MEMORY (Reset…) ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ RAM 1:All RAM… 2:Defaults… Resetting RAM erases all data and programs from RAM. ARCHIVE 1:Vars… 2:Apps… B:Both… Resetting Both erases all data, programs and Apps from Archive. ALL 1:All Memory… Resetting ALL erases all data, programs and Apps from RAM and Archive. RAM ÚÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄ¿ RESET RAM 1:No 2:Reset Resetting RAM erases all data and programs from RAM.
ARCHIVE ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ RESET ARC VARS 1:No 2:Reset Resetting Vars erases all data and programs from Archive. RESET ARC APPS 1:No 2:Reset Resetting Apps erases all Apps from Archive. RESET ARC BOTH 1:No 2:Reset Resetting Both erases all data, programs and Apps from Archive. ALL ÚÄÄÙ RESET MEMORY 1:No 2:Reset Resetting ALL will delete all data, programs & Apps from RAM & Archive. MEMORY (GROUP...
MEMORY (UNGROUP...) ÚÄÄÙ 1:name 2:name ... yN ÚÄÄÙ CATALOG cosh( cosh L1( ... Equ4String( expr( ... inString( ... length( ... sinh( sinh L1( ... String4Equ( sub( ...
Variables User Variables The TI-83 Plus uses the variables listed below in various ways. Some variables are restricted to specific data types. The variables A through Z and q are defined as real or complex numbers. You may store to them. The TI-83 Plus can update X, Y, R, q, and T during graphing, so you may want to avoid using these variables to store nongraphing data. The variables (list names) L1 through L6 are restricted to lists; you cannot store another type of data to them.
Except for system variables, you can store any string of characters, functions, instructions, or variables to the functions Yn, (1 through 9, and 0), XnT/YnT (1 through 6), rn (1 through 6), u(n), v(n), and w(n) directly or through the Y= editor. The validity of the string is determined when the function is evaluated. Archive Variables You can store data, programs or any variable from RAM to user data archive memory where they cannot be edited or deleted inadvertantly.
The variables below are reserved for use by the TI-83 Plus. You cannot store to them. n, v, Sx, sx, minX, maxX, Gy, Gy2, Gxy, a, b, c, RegEQ, x1, x2, y1, z, t, F, c2, Ç, v1, Sx1, n1, lower, upper, r2, R2 and other statistical variables.
Statistics Formulas This section contains statistics formulas for the Logistic and SinReg regressions, ANOVA, 2.SampÜTest, and 2.SampTTest.
SinReg The sine regression algorithm applies nonlinear recursive least-squares techniques to optimize the following cost function: N J = ∑ [a sin(bxi + c ) + d − yi ] 2 i =1 which is the sum of the squares of the residual errors, where: x = the independent variable list y = the dependent variable list N = the dimension of the lists This technique attempts to recursively estimate the constants a, b, c, and d to make J as small as possible.
The mean squares (MS) that make up Û are: Factor MS = Error MS = Factor SS Factor df Error SS Errordf The sum of squares (SS) that make up the mean squares are: I Factor SS = ∑ ni ( x i − x )2 i =1 I Error SS = ∑ ( ni − 1) Sxi 2 i =1 The degrees of freedom df that make up the mean squares are: Factordf = I − 1 = numeratordf for Û I Error df = ∑ ( ni − 1) = denominator df for Û i =1 TI-83 Plus Tables and Reference Information 723
where: I = = Sxi = ni = x = xi number of populations the mean of each list the standard deviation of each list the length of each list the mean of all lists 2.SampÜTest Below is the definition for the 2.SampÜTest. Sx1, Sx2 = Sample standard deviations having n1-1 and n2-1 degrees of freedom df, respectively.
2.SampÜTest for the alternative hypothesis s 1 > s 2. p= ∞ ∫F f ( x, n1 − 1, n2 − 1)dx 2.SampÜTest for the alternative hypothesis s 1 < s 2. F p= ∫0 f ( x, n1 − 1, n2 − 1)dx 2.SampÜTest for the alternative hypothesis s 1 ƒ s 2. Limits must satisfy the following: p = 2 Lbnd ∫0 f ( x, n1 − 1, n 2 − 1)dx = ∞ ∫ f ( x, n1 − 1, n2 − 1)dx Ubnd where: [Lbnd,Ubnd] = lower and upper limits The Û-statistic is used as the bound producing the smallest integral.
2.SampTTest The following is the definition for the 2.SampTTest. The two-sample t statistic with degrees of freedom df is: t= x1 − x 2 S where the computation of S and df are dependent on whether the variances are pooled.
otherwise: Sxp = ( n1 − 1) Sx12 + ( n 2 − 1) Sx 22 df S= 1 1 + Sxp n1 n 2 df = n1 + n 2 − 2 and Sxp is the pooled variance.
Financial Formulas This section contains financial formulas for computing time value of money, amortization, cash flow, interest-rate conversions, and days between dates. Time Value of Money i = [e( y × ln ( x + 1))] − 1 where: PMT y x C/Y P/Y I% ƒ = = = = = 0 C/Y ÷ P/Y (.
I % = 100 × C/Y × [e( y × ln( x + 1)) − 1] where: x = i y = P/Y ÷ C/Y Gi = 1 + i × k where: k = 0 for end-of-period payments k = 1 for beginning-of-period payments PMT × Gi − FV × i ln PMT × Gi + PV × i N= ln(1 + i ) where: i ƒ 0 N = −( PV + FV ) ÷ PMT where: PMT = TI-83 Plus i = 0 PV + FV × PV + (1 + i ) N − 1 Gi −i Tables and Reference Information 729
where: i ƒ 0 PMT = −( PV + FV ) ÷ N where: i = 0 1 PMT × Gi PMT × Gi − FV × − PV = i i (1 + i ) N where: i ƒ 0 PV = −( FV + PMT × N ) where: FV = where: i = 0 PMT × Gi PMT × Gi − (1 + i ) N × PV + i i i ƒ 0 FV = −( PV + PMT × N ) where: i = 0 TI-83 Plus Tables and Reference Information 730
Amortization If computing bal(), pmt2 = npmt Let bal(0) = RND(PV) Iterate from m = 1 to pmt2 Im = RND[ RND12( −i × bal ( m − 1))] bal ( m) = bal ( m − 1) − Im + RND( PMT ) then: bal () = bal ( pmt 2) Σ Pr n () Σ Int () TI-83 Plus = bal ( pmt 2) − bal ( pmt1) = ( pmt 2 − pmt1 + 1) × RND( PMT ) − Σ Pr n () Tables and Reference Information 731
where: RND = round the display to the number of decimal places selected RND12 = round to 12 decimal places Balance, principal, and interest are dependent on the values of PMT, PV, æ, and pmt1 and pmt2. Cash Flow N npv () = CF0 + ∑ CFj(1 + i ) − Sj − 1 j =1 where: j n Sj = ∑ i i =1 0 (1 − (1 + i ) − nj ) i j ≥1 j=0 Net present value is dependent on the values of the initial cash flow (CF0), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i).
Internal rate of return is dependent on the values of the initial cash flow (CF0) and subsequent cash flows (CFj). i = I% ÷ 100 Interest Rate Conversions 4Eff = 100 × ( eCP × ln ( x + 1) − 1) x = .01 × Nom ÷ CP where: 4Nom = 100 × CP × [e1 ÷ CP × ln ( x + 1) − 1] where: x Eff CP Nom = = = = .01 × Eff effective rate compounding periods nominal rate Days between Dates With the dbd( function, you can enter or compute a date within the range Jan. 1, 1950, through Dec. 31, 2049.
Actual/actual day-count method (assumes actual number of days per month and actual number of days per year): dbd( (days between dates) = Number of Days II - Number of Days I Number of Days I = (Y1-YB) × 365 + (number of days MB to M1) + DT1 (Y 1 − YB ) + 4 Number of Days II = (Y2-YB) × 365 + (number of days MB to M2) + DT2 (Y 2 − YB ) + 4 where: TI-83 Plus M1 DT1 Y1 M2 DT2 Y2 MB DB YB = = = = = = = = = month of first date day of first date year of first date month of second date day of second date y
Appendix B: General Information Battery Information When to Replace the Batteries The TI-83 Plus uses five batteries: four AAA alkaline batteries and one lithium battery. The lithium battery provides auxiliary power to retain memory while you replace the AAA batteries. When the battery voltage level drops below a usable level, the TI-83 Plus: Displays this message when you turn on the unit. Displays this message when you attempt to download an application.
After Message A is first displayed, you can expect the batteries to function for about one or two weeks, depending on usage. (This oneweek to two-week period is based on tests with alkaline batteries; the performance of other kinds of batteries may vary.) The low-battery message continues to be displayed each time you turn on the unit until you replace the batteries.
Battery Precautions Take these precautions when replacing batteries. • Do not leave batteries within reach of children • Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. • Do not mix rechargeable and nonrechargeable batteries. • Install batteries according to polarity (+ and N) diagrams. • Do not place nonrechargeable batteries in a battery recharger. • Properly dispose of used batteries immediately. Do not leave them within the reach of children.
Note: To avoid loss of information stored in memory, you must turn off the calculator. Do not remove the AAA batteries and the lithium battery simultaneously. 3. Replace all four AAA alkaline batteries simultaneously. Or, replace the lithium battery. • To replace the AAA alkaline batteries, remove all four discharged AAA batteries and install new ones according to the polarity (+ and N) diagram in the battery compartment.
In Case of Difficulty Handling a Difficulty To handle a difficulty, follow these steps. 1. If you cannot see anything on the screen, the contrast may need to be adjusted. To darken the screen, press and release y, and then press and hold } until the display is sufficiently dark. To lighten the screen, press and release y, and then press and hold † until the display is sufficiently light. 2. If an error menu is displayed, follow the steps in Chapter 1.
• Press y L 2 to display the MEMORY MANAGEMENT DELETE menu. • Select the type of data you want to delete, or select 1:All for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using. • Press } and † to move the selection cursor (4) next to the item you want to delete, and then press {. (Chapter 18). 5.
• II. If the above solution does not work, reset all memory as follows: a. Remove one battery from the calculator and then press and hold down the ‘ key while re-installing the battery. While continuing to hold down the ‘ key, press and hold down the É key. When the home screen is displayed, release the keys. b. Press y L to display the MEMORY menu. c. Select 7:Reset to display the RAM ARCHIVE ALL menu. d. Press ~ ~ to display the ALL menu. e. Select 1:All Memory to display the RESET MEMORY menu. f.
Error Conditions When the TI-83 Plus detects an error, it displays ERR:message and an error menu. Chapter 1 describes the general steps for correcting errors. This table contains each error type, possible causes, and suggestions for correction. Error Type Possible Causes and Suggested Remedies ARCHIVED You have attempted to use, edit, or delete an archived variable. For example, dim(L1) is an error if L1 is archived.
Error Type Possible Causes and Suggested Remedies BAD GUESS • In a CALC operation, you specified a Guess that is not between Left Bound and Right Bound. • For the solve( function or the equation solver, you specified a guess that is not between lower and upper. • Your guess and several points around it are undefined. Examine a graph of the function. If the equation has a solution, change the bounds and/or the initial guess.
Error Type Possible Causes and Suggested Remedies DATA TYPE You entered a value or variable that is the wrong data type. • For a function (including implied multiplication) or an instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is required. See Appendix A and the appropriate chapter. • In an editor, you entered a type that is not allowed, such as a matrix entered as an element in the stat list editor. See the appropriate chapter.
Error Type Possible Causes and Suggested Remedies • You specified an argument to a function or instruction outside the valid range. This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph. See Appendix A and the appropriate chapter. DOMAIN • You attempted a logarithmic or power regression with a LX or an exponential or power regression with a LY. • You attempted to compute GPrn( or GInt( with pmt2 < pmt1. • You attempted to create a duplicate group name.
Error Type Possible Causes and Suggested Remedies • The TI-83 Plus was unable to transmit an item. Check to see that the cable is firmly connected to both units and that the receiving unit is in receive mode. Error in Xmit • You pressed É to break during transmission. • You attempted to perform a backup from a TI.82 to a TI-83 Plus. • You attempted to transfer data (other than L1 through L6) from a TI-83 Plus to a TI.82. • You attempted to transfer L1 through L6 from a TI-83 Plus to a TI.
Error Type INVALID Possible Causes and Suggested Remedies • You attempted to reference a variable or use a function where it is not valid. For example, Yn cannot reference Y, Xmin, @X, or TblStart. • You attempted to reference a variable or function that was transferred from the TI.82 and is not valid for the TI-83 Plus. For example, you may have transferred UnN1 to the TI-83 Plus from the TI.82 and then tried to reference it.
Error Type Possible Causes and Suggested Remedies INVALID DIM • You specified dimensions for an argument that are not appropriate for the operation. • You specified a list dimension as something other than an integer between 1 and 999. • You specified a matrix dimension as something other than an integer between 1 and 99. • You attempted to invert a matrix that is not square. ITERATIONS • The solve( function or the equation solver has exceeded the maximum number of permitted iterations.
Error Type MEMORY Possible Causes and Suggested Remedies Memory is insufficient to perform the instruction or function. You must delete items from memory (Chapter 18) before executing the instruction or function. Recursive problems return this error; for example, graphing the equation Y1=Y1. Branching out of an If/Then, For(, While, or Repeat loop with a Goto also can return this error because the End statement that terminates the loop is never reached.
Error Type Possible Causes and Suggested Remedies NO SIGN CHNG • The solve( function or the equation solver did not detect a sign change. • You attempted to compute æ when FV, (ÚäPMT), and PV are all ‚ 0, or when FV, (ÚäPMT), and PV are all 0. • You attempted to compute irr( when neither CFList nor CFO is > 0, or when neither CFList nor CFO is < 0. NONREAL ANS In Real mode, the result of a calculation yielded a complex result. This error is not returned during graphing.
Error Type SINGULARITY STAT Possible Causes and Suggested Remedies expression in the solve( function or the equation solver contains a singularity (a point at which the function is not defined). Examine a graph of the function. If the equation has a solution, change the bounds or the initial guess or both. You attempted a stat calculation with lists that are not appropriate. • Statistical analyses must have at least two data points. • Med.Med must have at least three points in each partition.
Error Type UNDEFINED VALIDATION VARIABLE Possible Causes and Suggested Remedies You referenced a variable that is not currently defined. For example, you referenced a stat variable when there is no current calculation because a list has been edited, or you referenced a variable when the variable is not valid for the current calculation, such as a after Med.Med. Electrical interference caused a link to fail or this calculator is not authorized to run the application.
Error Type Possible Causes and Suggested Remedies WINDOW RANGE A problem exists with the window variables. • You defined Xmax Xmin or Ymax Ymin. • You defined qmax qmin and qstep > 0 (or vice versa). • You attempted to define Tstep=0. • You defined Tmax Tmin and Tstep > 0 (or vice versa). • Window variables are too small or too large to graph correctly. You may have attempted to zoom in or zoom out to a point that exceeds the TI-83 Plus’s numerical range.
Accuracy Information Computational Accuracy To maximize accuracy, the TI-83 Plus carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a twodigit exponent. • You can store a value in the window variables using up to 10 digits (12 for Xscl, Yscl, Tstep, and qstep). • Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a two-digit exponent. • RegEQ displays up to 14 digits in Float mode.
Ymin is the center of the next-to-the-bottom pixel; Ymax is the center of the top pixel. @Y is the distance between the centers of two adjacent pixels. • In Full screen mode, @Y is calculated as (Ymax N Ymin) à 62. In Horiz split-screen mode, @Y is calculated as (Ymax N Ymin) à 30. In G.T split-screen mode, @Y is calculated as (Ymax N Ymin) à 50. • If you enter a value for @Y from the home screen or a program in Full screen mode, Ymax is calculated as Ymin + @Y … 62.
Function Limits Function Range of Input Values sin x, cos x, tan x 0 |x| < 10 12 (radian or degree) sinL1 x, cosL1 x L1 x 1 ln x, log x 10 L100 < x < 10 100 ex L10 100 < x 230.25850929940 10x L10 100 < x < 100 sinh x, cosh x |x| 230.25850929940 tanh x |x| < 10 100 sinhL1 x |x| < 5 × 10 99 coshL1 x 1 x < 5 × 10 99 tanhL1 x L1 < x < 1 ‡x (real mode) 0 x < 10 100 ‡x (complex mode) |x| < 10 100 x! L.5 x 69, where x is a multiple of .
Function Results Function Range of Result sinL1 x, tanL1 x L90¡ to 90¡ or Lpà2 to pà2 (radians) cosL1 x 0¡ to 180¡ or 0 to p (radians) TI-83 Plus General Information 757
Support and Service Information Product Support Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands For general questions, contact Texas Instruments Customer Support: phone: e-mail: 1.800.TI.CARES (1.800.842.2737) ti-cares@ti.com For technical questions, call the Programming Assistance Group of Customer Support: phone: 1.972.917.8324 Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands Contact TI by e-mail or visit the TI calculator home page on the World Wide Web.
Product Service Customers in the U.S. and Canada Only Always contact Texas Instruments Customer Support before returning a product for service. Customers outside the U.S. and Canada Refer to the leaflet enclosed with this product or contact your local Texas Instruments retailer/distributor. Other TI Products and Services Visit the TI calculator home page on the World Wide Web. Internet: education.ti.
Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for 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. This TI electronic product is warranted against defective materials and construction.
Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from state to state or province to province. Warranty Performance. During the above one (1) year warranty period, your defective product will be either repaired or replaced with a reconditioned model of an equivalent quality (at TI’s option) when the product is returned, postage prepaid, to Texas Instruments Service Facility.
Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction. This warranty is void if the product has been damaged by accident or unreasonable use, neglect, improper service, or other causes not arising out of defects in materials or construction. Warranty Disclaimers.
Software: Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided “AS IS.” Copyright: The software and any documentation supplied with this product are protected by copyright. All Customers Outside the U.S.
Index ! (factorial), 94, 692 " " (string indicator), 484 " (seconds notation), 97, 697 æ (annual interest rate variable), ‡( 444, 462 ¡ (degrees notation), à (division), 63, 696 å 692 (exponent), 14, 20, 661 ì (graph style, animate), 117 í (graph style, dot), 117 ç (graph style, line), 117 ‚ (greater than or equal to), 101, 694 (less than or equal to), 101, 694 ä (multiplication), 63, 695 M (negation), 49, 66, 695 ƒ (not equal to), 101, 694 Ú (number of payment periods variable), 444, 462 p (pi),
4Rect (to rectangular), 91, 679 …row(, 282, 680 …row+(, 282, 680 @Tbl (table step variable), 205 ¨TEMP, 471 ¨TREF, 471 ¨VOLT, 471 ¨VREF, 471 @X window variable, 124 @Y window variable, 124 ' (minutes notation), 97, 697 ( ) (parentheses), 48 + (addition), 63, 696 + (concatenation), 490, 696 + (pixel mark), 235, 373 : (colon), 504 < (less than), 101, 694 = (equal-to relational test), 101, 693 > (greater than), 101, 694 [ ] (matrix indicator), 265 ^ (power), 64, 695 { } (list indicator), 288 1.
addition (+), 63, 696 alpha cursor, 12 alpha-lock, 18 alternative hypothesis, 391 amortization GInt( (sum of interest), 455, 668 GPrn( (sum of principal), 455, 676 bal( (amortization balance), 454, 656 calculating schedules, 454 formula, 731 and (Boolean operator), 103, 655 ANGLE menu, 97 angle modes, 22 angle(, 90, 655 animate graph style (ì), 117 ANOVA( (one-way variance analysis), 417, 655 formula, 722 Ans (last answer), 36, 599, 655 APD (Automatic Power Down), 6 applications.
Boxplot plot type ( Ö), 371 busy indicator, 11 —C— (compounding-periods-per-year variable), 444, 463 CALCULATE menu, 147 Calculate output option, 388, 392 cash flow calculating, 452 formula, 732 irr( (internal rate of return), 453, 668 npv( (net present value), 453, 673 CATALOG, 481 CBL 2/CBL, 464 CBL/CBR Quitting, 480 Running, 464 Selecting, 464 CBL/CBR APP menu, 467 CBR, 464, 533, 633, 665 check memory, 596 chi-square cdf (c2cdf(), 429, 657 chi-square pdf (c2pdf(), 428, 657 chi-square test (c2.
4Dec (to decimal), 67, 659 4DMS (to degrees/minutes/ seconds), 99, 661 4Eff (to effective interest rate), 459 4Frac (to fraction conversion), 67, 664 4Nom (to nominal interest rate conversion), 459, 672 4Polar (to polar conversion), 91, 675 4Rect (to rectangular conversion), 91, 679 Equ4String( (equation-to-string conversion), 491, 662 List4matr( (list-to-matrix conversion), 279, 308, 670 Matr4list( (matrix-to-list conversion), 278, 308, 670 P4Rx(, P4Ry( (polar-to-rectangular conversion), 100, 678 R4Pr(,
defragmenting, 622 Degree angle mode, 22, 97, 659 degrees notation (¡), 98, 692 delete variable contents (DelVar), 523, 659 deleting items from memory, 599 DelVar (delete variable contents), 659 DependAsk, 206, 209, 659 DependAuto, 206, 209, 659 derivative.
DRAW STO (draw store menu), 239 DrawF (draw a function), 224, 661 drawing on a graph circles (Circle(), 228 line segments (Line(), 218 lines (Horizontal, Line(, Vertical), 221 pixels (Pxl.Change, Pxl.Off, Pxl.On, pxl.Test), 237 points (Pt.Change, Pt.Off, Pt.
inequalities, 566 mortgage payments, 592 parametric equations, ferris wheel problem, 580 piecewise functions, 564 quadratic formula converting to a fraction, 542 displaying complex results, 544 entering a calculation, 540 Sierpinski triangle, 570 solving a system of nonlinear equations, 568 unit circle and trig curves, 576 examples—Getting Started coin flip, 61 compound interest, 442 drawing a tangent line, 212 financing a car, 440 forest and trees, 176 generating a sequence, 283 graphing a circle, 105 mean
cash flows, 452 days between dates, 460 interest rate conversions, 459 payment method, 461 time value of money (TVM), 448 Fix (fixed-decimal mode), 21, 663 fixed-decimal mode (Fix), 21, 663 Float (floating-decimal mode), 21, 663 floating-decimal mode (Float), 21, 663 fMax( (function maximum), 69, 663 fMin( (function minimum), 69, 663 fnInt( (function integral), 71, 663 FnOff (function off), 115, 663 FnOn (function on), 115, 664 For(, 515, 664 format settings, 125, 187 formulas amortization, 731 ANOVA, 722 c
Smart Graph, 129 tracing, 134 viewing window, 121 window variables, 121, 122, 123 Y= editor, 111 ZOOM MEMORY menu, 144 ZOOM menu, 138 function integral (fnInt(), 71, 663 function, definition of, 15 functions and instructions table, 654 future value, 444, 451 FV (future-value variable), 444, 462 —G— (graph-table split-screen mode), 25, 252, 666 garbage collecting, 622 GarbageCollect, 626, 664 Gauge, 468 gcd( (greatest common divisor), 82, 665 GDB (graph database), 242 geometcdf(, 433, 665 geometpdf(, 433, 6
identity(, 277, 666 If instructions If, 512, 666 If-Then, 513, 666 If-Then-Else, 514, 667 imag( (imaginary part), 89, imaginary part (imag(), 89, 667 667 implied multiplication, 48 increment and skip (IS>(), 520, 668 independent variable, 206, 209, 667 IndpntAsk, 206, 209, 667 IndpntAuto, 206, 209, 667 inferential stat editors, 388 inferential statistics.
key-code diagram, 532 LinReg(a+bx) (linear regression), 360, 669 —L— LabelOff, 127, 668 LabelOn, 127, 668 labels graph, 127, 668 program, 519, 669 Last Entry, 33 Lbl (label), 519, 669 lcm( (least common multiple), 82, 669 least common multiple (lcm(), 82, 669 length( of string, 492, 669 less than (<), 101, 694 less than or equal to (), 101, 694 Light-Time, 468 line graph style (ç), 117 line segments, drawing, 218 Line( (draw line), 220, 669 lines, drawing, 220, 221 LINK RECEIVE menu, 644 LINK SEND men
using to select data points from a plot, 305 using with math operations, 63, 298 ln(, 65, 670 LnReg (logarithmic regression), 360, 670 log(, 65, 670 logic (Boolean) operators, 103 Logistic (regression), 361, 670 logistic regression formula, 721 —M— marked for deletion, 623 MATH CPX (complex menu), 88 MATH menu, 67 MATH NUM (number menu), 79 math operations, 63 MATH PRB (probability menu), 92 Matr4list( (matrix-to-list conversion), 278, 308, 670 matrices accessing elements, 268 copying, 267 defined, 258 del
error, 626 insufficient during transmission, 653 resetting defaults, 604 resetting memory, 604 MEMORY menu, 596 Menu( (define menu), 521, 671 menus, 39, 40 defining (Menu(), 521, 671 map, 698 scrolling, 41 meter, 468 min, 470 min( (minimum), 81, 311, 671 minimum of a function (fMin(), 69, 663 minimum operation on a graph, 150 minutes notation ('), 97, 697 ModBoxplot plot type (Õ), 370 mode settings, 19 a+bi (complex rectangular), 24, 84, 656 Connected (plotting), 23, 658 Degree (angle), 22, 99, 659 Dot (plo
not equal to (ƒ), 101, 694 not( (Boolean operator), 104, 673 nPr (permutations), 93, 673 npv( (net present value), 453, 673 numerical derivative, 70, 152, 165, 175 numerical integral, 70, 153 —O— Omit, 619, 645 ON/HALT, 480 one-proportion z confidence interval (1.PropZInt), 410, 676 one-proportion z test (1.PropZTest), 402, 676 one-sample t confidence interval (TInterval), 406, 687 one-variable statistics (1.
PLOT, 476 Plot1(, 373, 674 Plot2(, 373, 674 Plot3(, 373, 674 PlotsOff, 375, 675 PlotsOn, 375, 675 plotting modes, 23 plotting stat data, 368 PMT (payment amount variable), 444, 462 Pmt_Bgn (payment beginning variable), 461, 675 Pmt_End (payment end variable), 461, 675 poissoncdf(, 432, 675 poissonpdf(, 432, 675 Pol/Polar (polar graphing mode), 23, 168, 675 polar equations, 169 polar form, complex numbers, 87 polar graphing CALC (calculate operations on a graph), 175 defining and displaying, 168 equations,
editing, 507 entering command lines, 504 executing, 505 inserting command lines, 508 instructions, 511 name (prgm), 522, 676 renaming, 509 running assembly language program, 537 stopping, 506 subroutines, 535 Prompt, 528, 676 Pt.Change(, 235, 677 Pt.Off(, 234, 677 Pt.On(, 233, 677 PV (present value variable), 444, 462 p-value, 422 PwrReg (power regression), 361, 677 Pxl.Change(, 237, 677 Pxl.Off(, 237, 677 Pxl.On(, 237, 677 pxl.
(rectangular graphing coordinates), 126, 680 recursive sequences, 183 ref( (row-echelon form), 280, 680 reference#, 471 RegEQ (regression equation variable), 353, 599 regression model automatic regression equation, 353 automatic residual list feature, 352 diagnostics display mode, 354 models, 357 relational operations, 101, 272 Repeat, 517, 680 RESET MEMORY menu, 608 resetting all memory, 608 archive memory, 606 defaults, 604 memory, 604 RAM memory, 604 residual list (RESID), 352 Return, 523, 680 root (x‡),
free-moving cursor, 189 graph format, 188 graph styles, 181 moving the cursor to a value, 190 nonrecursive sequences, 182 phase plots, 197 recursive sequences, 183 selecting and deselecting, 181 setting sequence mode, 179 TI.83 Plus versus TI.
setting, 248, 255 split-screen values, 231, 238, 254 square (2), 64, 694 square root (‡(), 64, 695 STAT CALC menu, 356 STAT EDIT menu, 348 stat list editor attaching formulas to list names, 336 clearing elements from lists, 333 creating list names, 332 detaching formulas from list names, 340 displaying, 329 edit-elements context, 344 editing elements of formulagenerated lists, 341 editing list elements, 334 entering list names, 330 enter-names context, 346 formula-generated list names, 338 removing lists, 3
statistical distribution functions.
tangent lines, drawing, 222 Tangent( (draw line), 222, 687 tanhM1( (hyperbolic arctangent), 496, 687 tanh( (hyperbolic tangent), 496, 687 TblStart (table start variable), 205 tcdf( (student-t distribution probability), 427, 687 technical support, 758 Temperature, 468 Temp-Time, 468 TEST (relational menu), 101 TEST LOGIC (Boolean menu), 103 Text( instruction, 230, 254, 687 placing on a graph, 230, 254 Then, 513, 666 thick (è) graph style, 117 TI.82 link differences, 646 transmitting to/from, 644 TI.83 Link.
entering numbers during, 135, 164, 173, 189 expression display, 128, 135 Trace instruction in a program, 137, 688 transmitting error conditions, 652 from a TI.73 to a TI.83 Plus, 648 from a TI.82 to a TI.83 Plus, 646 lists to a TI.73, 642 lists to a TI.82, 641 lists to a TI.83 Plus, 648 stopping, 637 to an additional TI.
equation solver, 75 graph databases, 26 graph pictures, 26 independent/dependent, 209 list, 26, 286 matrix, 26, 258 real, 26 recalling values, 31 solver editor, 74 statistical, 365 string, 486, 487 test and interval output, 422 types, 26 user and system, 27, 718 VARS and Y.
editor function graphing, 111 parametric graphing, 158 polar graphing, 168 sequence graphing, 180 YFact zoom factor, 145 Y= —Z— Z.
Quick-Find Locator Chapter 1: Operating the TI-83 Plus Silver Edition........................ 1 Documentation Conventions.....................................................................1 TI-83 Plus Keyboard .................................................................................2 Keyboard Zones..................................................................................2 Using the Color.Coded Keyboard .......................................................4 Using the y and ƒ Keys ........
Entering a Number in Scientific Notation ..........................................14 Functions ..........................................................................................15 Instructions........................................................................................16 Interrupting a Calculation ..................................................................16 TI-83 Plus Edit Keys ...............................................................................17 Setting Modes .......
Accessing a Previous Entry ..............................................................34 Reexecuting the Previous Entry........................................................34 Multiple Entry Values on a Line ........................................................35 Clearing ENTRY ...............................................................................36 Using Ans in an Expression ..............................................................36 Continuing an Expression ..........................
Calculator-Based Laboratory™ (CBL 2™, CBL™) and Calculator-Based Ranger™ (CBR™)..........................................52 Other TI-83 Plus Features ......................................................................53 Graphing ...........................................................................................53 Sequences ........................................................................................53 Tables ..............................................................................
log(, 10^(, ln( .....................................................................................65 e^( (Exponential) .................................................................................65 e (Constant) ......................................................................................65 L (Negation).......................................................................................66 p (Pi) ...............................................................................................
int( ....................................................................................................81 min(, max( .........................................................................................81 lcm(, gcd( ..........................................................................................82 Entering and Using Complex Numbers...................................................84 Complex-Number Modes ..................................................................
ANGLE Menu....................................................................................97 Entry Notation ...................................................................................97 ¡ (Degree) .........................................................................................98 r (Radians) ........................................................................................99 8DMS................................................................................................
Displaying Functions in the Y= Editor .............................................111 Defining or Editing a Function.........................................................111 Defining a Function from the Home Screen or a Program..............112 Evaluating Y= Functions in Expressions.........................................113 Selecting and Deselecting Functions....................................................114 Selecting and Deselecting a Function.............................................
LabelOff, LabelOn...........................................................................127 ExprOn, ExprOff..............................................................................128 Displaying Graphs ................................................................................129 Displaying a New Graph .................................................................129 Pausing or Stopping a Graph..........................................................129 Smart Graph ........................
ZTrig................................................................................................142 ZInteger...........................................................................................143 ZoomStat ........................................................................................143 ZoomFit...........................................................................................143 Using ZOOM MEMORY........................................................................
Displaying the Parametric Y= Editor ...............................................158 Selecting a Graph Style ..................................................................159 Defining and Editing Parametric Equations ....................................159 Selecting and Deselecting Parametric Equations ...........................160 Setting Window Variables ...............................................................160 Setting the Graph Format ......................................................
Exploring Polar Graphs.........................................................................173 Free-Moving Cursor ........................................................................173 TRACE............................................................................................173 Moving the Trace Cursor to Any Valid q Value ...............................174 ZOOM .............................................................................................174 CALC ..............................
ZOOM .............................................................................................191 CALC ..............................................................................................191 Evaluating u, v, and w.....................................................................192 Graphing Web Plots..............................................................................193 Graphing a Web Plot.......................................................................
Displaying the Table .............................................................................209 The Table........................................................................................209 Independent and Dependent Variables ..........................................209 Clearing the Table from the Home Screen or a Program ...............210 Scrolling Independent-Variable Values...........................................210 Displaying Other Dependent Variables...................................
Shading Areas on a Graph ...................................................................226 Shading a Graph.............................................................................226 Drawing Circles.....................................................................................228 Drawing a Circle Directly on a Graph..............................................228 Drawing a Circle from the Home Screen or a Program ..................229 Placing Text on a Graph .................................
Storing Graph Databases (GDB) ..........................................................242 What Is a Graph Database? ...........................................................242 Storing a Graph Database ..............................................................242 Recalling Graph Databases (GDB).......................................................244 Recalling a Graph Database...........................................................244 Deleting a Graph Database ...................................
Chapter 10: Matrices .................................................................... 256 Getting Started: Systems of Linear Equations ......................................256 Defining a Matrix ...................................................................................258 What Is a Matrix? ............................................................................258 Selecting a Matrix ...........................................................................
Powers ............................................................................................272 Relational Operations .....................................................................272 iPart(, fPart(, int(..............................................................................273 Using the MATRX MATH Operations ...................................................274 MATRX MATH Menu ......................................................................274 det(...............................
Creating a List Name on the Home Screen ....................................286 Storing and Displaying Lists..................................................................288 Storing Elements to a List ...............................................................288 Displaying a List on the Home Screen............................................288 Copying One List to Another...........................................................289 Accessing a List Element..........................................
@List( ...............................................................................................303 Select(.............................................................................................304 Before Using Select( .......................................................................304 Using Select( to Select Data Points from a Plot..............................305 augment(.........................................................................................307 List4matr(..............
Attaching Formulas to List Names ........................................................336 Attaching a Formula to a List Name in Stat List Editor ...................336 Using the Stat List Editor When Formula-Generated Lists Are Displayed ..................................................................................338 Handling Errors Resulting from Attached Formulas........................339 Detaching Formulas from List Names ..................................................
Frequency of Occurrence for Data Points.......................................357 1.Var Stats......................................................................................357 2.Var Stats......................................................................................358 Med.Med (ax+b) .............................................................................358 LinReg (ax+b) .................................................................................359 QuadReg (ax2+bx+c)...............
Defining the Plots............................................................................373 Displaying Other Stat Plot Editors...................................................375 Turning On and Turning Off Stat Plots............................................375 Defining the Viewing Window .........................................................376 Tracing a Stat Plot ..........................................................................376 Statistical Plotting in a Program ...................
2.SampTTest ..................................................................................400 1.PropZTest....................................................................................402 2.PropZTest....................................................................................403 ZInterval ..........................................................................................405 TInterval ..........................................................................................406 2.
poissonpdf( .....................................................................................432 poissoncdf(......................................................................................432 geometpdf(......................................................................................433 geometcdf( ......................................................................................433 Distribution Shading..............................................................................
tvm_FV............................................................................................451 Calculating Cash Flows ........................................................................452 Calculating a Cash Flow .................................................................452 npv(, irr(...........................................................................................453 Calculating Amortization .......................................................................
Specifying the Data Collection Method from the CBL/CBR APP Menu .................................................................................467 Specifying Options for Each Data Collection Method .....................468 GAUGE ...........................................................................................468 TYPE...............................................................................................469 MIN and MAX........................................................................
Entering a String .............................................................................484 Storing Strings to String Variables ........................................................486 String Variables...............................................................................486 Storing a String to a String Variable................................................487 Displaying the Contents of a String Variable ..................................
Entering a Program Command Line ...............................................504 Executing a Program ......................................................................505 Breaking a Program ........................................................................506 Editing Programs ..................................................................................507 Editing a Program ...........................................................................507 Inserting and Deleting Command Lines....
GraphStyle(.....................................................................................524 PRGM I/O (Input/Output) Instructions...................................................525 PRGM I/O Menu .............................................................................525 Displaying a Graph with Input .........................................................526 Storing a Variable Value with Input.................................................527 Prompt ........................................
Defining a Table of Values..............................................................547 Zooming In on the Table .................................................................549 Setting the Viewing Window ...........................................................551 Displaying and Tracing the Graph ..................................................553 Zooming In on the Graph ................................................................555 Finding the Calculated Maximum............................
Problem...........................................................................................576 Procedure .......................................................................................576 Finding the Area between Curves ........................................................578 Problem...........................................................................................578 Procedure .......................................................................................
ClrAllLists ........................................................................................602 Resetting the TI-83 Plus .......................................................................603 RAM ARCHIVE ALL Menu..............................................................603 Displaying the RAM ARCHIVE ALL Menu ......................................604 Resetting RAM Memory..................................................................604 Resetting Archive Memory..............................
Chapter 19: Communication Link ................................................ 629 Getting Started: Sending Variables.......................................................629 TI-83 Plus Silver Edition LINK...............................................................632 Connecting Two Calculators with a Unit-to-Unit Cable ...................633 Linking to the CBL/CBR System .....................................................633 Linking to a Computer......................................................
Appendix A: Tables and Reference Information........................ 654 Table of Functions and Instructions ......................................................654 TI-83 Plus Menu Map ...........................................................................698 Variables ...............................................................................................718 User Variables ................................................................................718 Archive Variables ....................
In Case of Difficulty ...............................................................................739 Handling a Difficulty ........................................................................739 Error Conditions ....................................................................................742 Accuracy Information ............................................................................754 Computational Accuracy .................................................................
