TI-82 GRAPHING CALCULATOR GUIDEBOOK TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated. Macintosh is a registered trademark of Apple Computer, Inc. © 1993, 2000, 2001 Texas Instruments Incorporated. 8200$FNT.
Important Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an “as-is” basis.
Table of Contents This manual describes how to use the TI.82 Graphing Calculator. Getting Started gives a quick overview of its features. The first chapter gives general instructions on operating the TI.82. Other chapters describe its interactive features. The applications in Chapter 14 show how to use these features together. Using this Guidebook Effectively ................... Glossary ..................................... viii x Getting Started: Do This First! TI.82 Menus ............................
Chapter 2: Math, Angle, and Test Operations Getting Started: Lottery Chances ................... Keyboard Math Operations ....................... MATH MATH Operations ......................... MATH NUM (Number) Operations .................. MATH HYP (Hyperbolic) Operations ................. MATH PRB (Probability) Operations ................. ANGLE Operations ............................. TEST TEST (Relational) Operations ................. TEST LOGIC (Boolean) Operations .................
Chapter 6: Sequence Graphing Getting Started: Forest and Trees ................... Defining and Displaying a Sequence Graph ............ Exploring a Sequence Graph ...................... 6-2 6-3 6-6 Chapter 7: Tables Getting Started: Roots of a Function ................. Defining the Variables ........................... Defining the Dependent Variable ................... Displaying the Table ............................ 7-2 7-3 7-4 7-5 Chapter 8: DRAW Operations Getting Started: Shading a Graph ....
Chapter 10: Matrices Getting Started: Systems of Linear Equations .......... 10-2 Defining a Matrix .............................. 10-4 Viewing Matrix Elements ......................... 10-5 Editing Matrix Elements ......................... 10-6 About Matrices ................................ 10-8 Matrix Math Functions .......................... 10-10 MATRIX MATH Operations ........................ 10-12 Chapter 11: Lists Getting Started: Generating Sequences ............... About Lists ..................
Chapter 14: Applications Left-Brain, Right-Brain Test Results ................. Speeding Tickets ............................... Buying a Car, Now or Later? ...................... Graphing Inequalities ........................... Solving a System of Nonlinear Equations ............. Program: Sierpinski Triangle ...................... Cobweb Attractors ............................. Program: Guess the Coefficients ................... The Unit Circle and Trigonometric Curves ............
Using this Guidebook Effectively The structure of the TI.82 guidebook and the design of its pages can help you find the information you need quickly. Consistent presentation techniques are used throughout to make the guidebook easy to use. Structure of the Guidebook The guidebook contains sections that teach you how to use the calculator. ¦ Getting Started is a fast-paced keystroke-by-keystroke introduction.
Information-Mapping Conventions Several conventions are used to present information concisely and in an easily referenced format. ¦ Numbered procedures—A procedure is a sequence of steps that performs a task. In this guidebook, each step is numbered in the order in which it is performed. No other text in the guidebook is numbered; therefore, when you see numbered text, you know you must perform the steps sequentially.
Glossary This glossary provides definitions for important terms that are used throughout this guidebook. Expression An expression is a complete sequence of numbers, variables, functions, and their arguments that can be evaluated to a single answer. Function A function, which may have arguments, returns a value and can be used in an expression. A function is also the expression entered in the Y= editor used in graphing and TABLE.
Getting Started: Do This First! Getting Started contains two keystroke-by-keystroke examples, an interest rate problem and a volume problem, that introduce you to some principal operating and graphing features of the TI.82. You will learn to use the TI.82 much more quickly by completing both of these examples first. Contents TI.82 Menus ................................ First Steps ................................. Entering a Calculation: Compound Interest .......... Defining a Function: Box with Lid .....
TI-82 Menus To leave the keyboard uncluttered, the TI.82 uses full-screen menus to access many additional operations. The use of specific menus is described in the appropriate chapters. Displaying a Menu When you press a key that accesses a menu, such as , that menu screen temporarily replaces the screen where you are working. After you make a selection from a menu, you usually are returned to the screen where you were. Moving from One Menu to Another A menu key may access more than one menu.
First Steps Before beginning these sample problems, follow the steps on this page to reset the TI.82 to its factory settings. (Resetting the TI.82 erases all previously entered data.) This ensures that following the keystrokes in this section produces the illustrated actions. 1. Press É to turn the calculator on. 2. Press and release y and then press Ã. (Pressing y accesses the operation printed in blue to the left above the next key that you press. MEM is the 2nd operation of Ã.
Entering a Calculation: Compound Interest Using trial and error, determine when an amount invested at 6% annual compounded interest will double in value. The TI.82 displays up to 8 lines of 16 characters so you see an expression and its solution at the same time. You also can store values to variables, enter multiple instructions on one line, and recall previous entries. 1. Press .06 ¿ ƒ Z (annual interest rate) to store the interest rate. 2. Press y ã:ä to enter more than one instruction on a line. 3.
7. The next guess should be greater than 10 years. Make the next guess 12 years. Press } to move the cursor over the 0, and then type 2 to change 10 to 12. Press Í to evaluate the expression. 8. To display answers in a format more appropriate for calculations involving money, press z to display the MODE screen. 9. Press † ~ ~ ~ to position the cursor over the 2 and then press Í. This changes the display format to two fixed decimal places. 10. Press y ãQUITä (above z) to return to the Home screen.
Defining a Function: Box with Lid Take a 200×250 mm. sheet of paper and cut X-by-X squares from two corners and X-by-125 mm. rectangles from the other two corners. Now fold the paper into a box with lid. What X would give the maximum volume V of a box made in this way? Use tables and graphs to determine the solution. Begin by defining a function that describes the volume of the box. From the diagram: 2X + A = W 2X + 2B = L V=ABX Substituting: V = (W – 2X) (L à 2 – X) X X W A X B X B L 1.
Defining a Table of Values The table feature of the TI.82 provides numeric information about a function. Use a table of values from the previously defined function to estimate an answer to the problem. 1. Press y ãTblSetä (above p) to display the TABLE SETUP menu. 2. Press Í to accept TblMin=0. 3. Press 10 Í to define the table increment @Tbl=10. Leave Indpnt: Auto and Depend: Auto so the table will be generated automatically. 4. Press y ãTABLEä (above s) to display the table.
Zooming In on the Table You can adjust the way a table is displayed to get more detailed information about any defined function. By varying the value of @Tbl, you can “zoom in” on the table. 1. Adjust the table setup to get a more accurate estimate of the maximum size of the cutout. Press 30 Í to set TblMin. Press 1 Í to set @Tbl. 2. Press y ãTABLEä. 3. Use † and } to scroll the table. Note that the maximum value displayed is 410256, which occurs at X=37. The maximum occurs between 36 and 38.
4. Press y ãTblSetä. Press 36 Í to set TblMin. Press .1 Í to set @Tbl. 5. Press y ãTABLEä and use † and } to scroll the table. 6. Press † and } to move the cursor. The maximum value of Y1 at 36.8 is 410264. 7. Press ~ to display the value of Y1 at 36.8 in full precision, 410264.064. This would be the maximum volume of the box if you could cut your piece of paper at 1 mm. increments. Getting Started 9 8200GETS.
Changing the Viewing WINDOW The viewing WINDOW defines the portion of the coordinate plane that appears in the display. The values of the WINDOW variables determine the size of the viewing WINDOW. You can view and change these values. 1. Press p to display the WINDOW variables edit screen. You can view and edit the values of the WINDOW variables here. The standard WINDOW variables define the viewing WINDOW as shown. Xmin, Xmax, Ymin, and Ymax define the boundaries of the display.
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 with TRACE. 1. Press s to graph the selected function in the viewing WINDOW. The graph of Y1=(W–2X)(Là2–X)X is shown in the display. 2. Press ~ once to display the free-moving graph cursor just to the right of the center of the screen.
Zooming on the Graph You can magnify the viewing WINDOW around a specific location using the ZOOM instructions to help identify maximums, minimums, roots, and intersections of functions. 1. Press q to display the ZOOM menu. This menu is typical of TI.82 menus. To select an item, you may either press the number to the left of the item, or you may press † until the item number is highlighted and then press Í. 2. To zoom in, press 2. The graph is displayed again.
Finding the Calculated Maximum You can use a CALC operation to calculate a local maximum of a function. 1. Press y ãCALCä to display the CALCULATE menu. Press 4 to select maximum. The graph is displayed again, with a prompt for Lower Bound? 2. Use | to trace along the curve to a point to the left of the maximum and then press Í. A triangle at the top of the screen indicates the selected bound. A new prompt is displayed for Upper Bound? 3.
Other Features Getting Started introduced you to basic calculator operation and the table and function graphing features of the TI.82. The remainder of this guidebook describes these features in more detail and also covers other capabilities of the TI.82. Graphing You can store, graph, and analyze up to ten functions (Chapter 3), up to six parametric functions (Chapter 4), and up to six polar functions (Chapter 5). You can use DRAW operations to annotate graphs (Chapter 8).
Chapter 1: Operating the TI-82 This chapter describes the TI.82 and provides general information about its operation. Chapter Contents Turning the TI.82 On and Off ...................... 1-2 Setting the Display Contrast ..................... The Display ................................ Entering Expressions and Instructions ............. TI.82 Edit Keys .............................. Setting Modes ............................... TI.82 Modes ................................ Variable Names ................
Turning the TI-82 On and Off To turn the TI.82 on, press the É key. To turn it off, press and release y and then press M. After about five minutes without any activity, APDé (Automatic Power Down™) turns the TI.82 off automatically. Turning the Calculator On Press É to turn the TI.82 on. ¦ If you pressed y ãOFFä to turn the calculator off, the display shows the Home screen as it was when you last used it, and errors are cleared. ¦ If APD turned the calculator off, the TI.
Setting the Display Contrast The brightness and contrast of the display depends on room lighting, battery freshness, viewing angle, and adjustment of the display contrast. The contrast setting is retained in memory when the TI.82 is turned off. Adjusting the Display Contrast You can adjust the display contrast to suit your viewing angle and lighting conditions at any time.
The Display The TI.82 displays both text and graphics. Graphics are described in Chapter 3. The TI.82 also can display a split screen, showing graphics and text simultaneously (Chapter 9). Home Screen The Home screen is the primary screen of the TI.82, where you enter instructions to be executed and expressions to be evaluated and see the answers. Displaying Entries and Answers When text is displayed, the TI.82 screen can have up to eight lines of up to 16 characters per line.
Display Cursors In most cases, the appearance of the cursor indicates what will happen when you press the next key. Cursor Appearance Meaning Entry Solid blinking rectangle The next keystroke is entered at the cursor; it types over any character. INS (insert) Blinking underline The next keystroke is inserted in front of the cursor location. 2nd Blinking # (arrow) The next keystroke is a 2nd operation. ALPHA Blinking A The next keystroke is an alphabetic character.
Entering Expressions and Instructions On the TI.82, you can enter expressions, which return a value, in most places where a value is required. You enter instructions, which initiate an action, on the Home screen or in the program editor (Chapter 13). Expressions An expression is a complete sequence of numbers, variables, functions, and their arguments that evaluate to a single answer. On the TI.82, you enter an expression in the same order that it normally is written. For example, pR2 is an expression.
Entering a Number in Scientific Notation 1. Type the part of the number that precedes the exponent. This value can be an expression. 2. Press y ãEEä. E appears in the display. 3. If the exponent is negative, press Ì and then type the exponent, which can be one or two digits. Entering a number in scientific notation does not cause the answers to be displayed in scientific or engineering notation. The display format is determined by the MODE settings (page 1.10) and the size of the number.
TI-82 Edit Keys ~ or | Moves the cursor within an expression. These keys repeat. } or † Moves the cursor between lines. These keys repeat. ¦ ¦ On top line of an expression on the Home screen, } moves the cursor to beginning of expression. On bottom line of an expression on the Home screen, † moves the cursor to end of expression. y| Moves the cursor to beginning of expression. y~ Moves the cursor to end of expression. Í Evaluates an expression or executes an instruction.
Setting Modes Modes control how numbers and graphs are displayed and interpreted. MODE settings are retained by Constant Memoryé when the TI.82 is turned off. All numbers, including elements of matrices and lists, are displayed according to the current MODE settings. Checking MODE Settings Press z to display the MODE settings. The current settings are highlighted. The specific MODE settings are described on the following pages.
TI-82 Modes The TI.82 has seven MODE settings. Three are related to how numeric entries are interpreted or displayed and four are related to how graphs appear in the display. Modes are set on the MODE screen (page 1.9). Normal, Sci, Eng Notation formats affect only how an answer is displayed on the Home screen. Numeric answers can display with up to 10 digits and a two-digit exponent. You can enter a number in any format.
Radian, Degree Angle settings control how the TI.82 interprets angle values in trig functions and polar/rectangular conversions. Radian interprets the values as radians. Answers display in radians. Degree interprets the values as degrees. Answers display in degrees. Func, Par, Pol, Seq Func (function) graphing plots functions where Y is a function of X (Chapter 3). Par (parametric) graphing plots relations where X and Y are functions of T (Chapter 4).
Variable Names On the TI.82 you can enter and use several types of data, including real numbers, matrices, lists, functions, stat plots, graph databases, and graph pictures. Variables and Defined Items The TI.82 uses preassigned names for variables and other items saved in memory. Variable type Names Real numbers A, B, . . . , Z, q Matrices ãAä, ãBä, ãCä, ãDä, ãEä Lists L1, L2, L3, L4, L5, L6 Functions Y1, Y2, . . . , Y9, Y0 Parametric equations X1T/Y1T, . . .
Storing and Recalling Variable Values 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. Storing Values in a Variable You can store a value to a variable from the Home screen or a program using the ¿ key. Begin on a blank line. 1. Enter the value that you want to store (which can be an expression). 2. Press ¿. The symbol ! is copied to the cursor location. 3.
Last Entry When you press Í on the Home screen to evaluate an expression or execute an instruction, the expression or instruction is stored in a storage area called Last Entry, which you can recall. When you turn the TI.82 off, Last Entry is retained in memory. Using Last Entry You can recall Last Entry and edit it from the Home screen or any editor. Press y ãENTRYä. On the Home screen or a numeric editor, the current line is cleared and the Last Entry is copied to the line.
Reexecuting the Previous Entry To execute Last Entry press Í on a blank line on the Home screen; the entry does not display again. 0¿ƒN Í ƒNÃ1¿ƒN y ã:ä ƒ N ¡ Í Í Í Accessing a Previous Entry The TI.82 retains as many of the previous entries as is possible (up to a total of 128 bytes) in the Last Entry storage area. You can access those entries by continuing to press y ãENTRYä.
Last Answer When an expression is evaluated successfully from the Home screen or from a program, the TI.82 stores the answer to a variable, Ans (Last Answer). Ans may be a real number, a list, or a matrix. When you turn the TI.82 off, the value in Ans is retained in memory. Using Ans in an Expression You can use the variable Ans to represent the last answer in most places. Press y ãANSä and the variable name Ans is copied to the cursor location. When the expression is evaluated, the TI.
TI-82 Menus To leave the keyboard uncluttered, the TI.82 uses full-screen menus to access many operations. The use of specific menus is described in the appropriate chapters. Moving from One Menu to Another A menu key may access more than one menu. The names of the menus appear on the top line. The current menu is highlighted and the items in that menu are displayed. Use ~ or | to move the cursor to a different menu. Selecting an Item from a Menu The number of the current item is highlighted.
Calculate 6 3‡27. 1. Press 6. Press to display the MATH menu. 2. To select 3‡, you may either press 4 or press † † † Í. 3. Press 27 and then press Í to evaluate the expression. 1-18 Operating the TI.82 8201OPER.
VARS and Y-VARS Menus Occasionally you may want to access the names of functions and system variables to use in an expression or to store to them directly. Use the VARS or Y.VARS menus to access the names of variables such as Xmin and functions such Y1.
EOS™ (Equation Operating System) The Equation Operating System (EOSé) defines the order in which functions in expressions are entered and evaluated on the TI.82. EOS lets you enter numbers and functions in a simple, straightforward sequence. Order of Evaluation A function returns a value. EOS evaluates the functions in an expression in the following order: 1 Functions that are entered after the argument, such as 2, -1, !, ¡, r, T, and conversions. 2 Powers and roots, such as 2^5 or 5x‡32.
Implied Multiplication The TI.82 recognizes implied multiplication. For example, it understands 2p, 4 sin 46, 5(1+2), and (2…5)7 as implied multiplication. Parentheses All calculations inside a pair of parentheses are completed first. For example, in the expression 4(1+2), EOS first evaluates the portion inside the parentheses, 1+2, and then multiplies the answer, 3, by 4. You can omit any right (close) parenthesis at the end of an expression.
Error Conditions The TI.82 detects any errors at the time it evaluates an expression, executes an instruction, plots a graph, or stores a value. Calculations stop and an error message with a menu displays immediately. Error codes and conditions are described in detail in Appendix B. Diagnosing an Error If the TI.82 detects an error, it displays the error screen. The top line indicates the general type of error, such as SYNTAX or DOMAIN. Additional information about each error message is in Appendix B.
Chapter 2: Math, Angle, and Test Operations This chapter describes math, angle, and relational operations that are available on the TI.82. The most commonly used functions are accessed from the keyboard; others are accessed through full-screen menus. Chapter Contents Getting Started: Lottery Chances ................... Keyboard Math Operations ....................... MATH MATH Operations ......................... MATH NUM (Number) Operations .................. MATH HYP (Hyperbolic) Operations ............
Getting Started: Lottery Chances Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to enter a lottery where 6 numbers will be drawn out of 49. To win, you must pick all 6 numbers (in any order). What is the probability of winning if you buy one ticket? What is the probability of winning if you buy five tickets? 1. Determine the number of combinations possible. On the Home screen, press 49 to enter the total number of items. Press | to display the MATH PRB menu.
Keyboard Math Operations The most commonly used math functions are on the keyboard. Using Lists with Functions Functions that are valid for lists return a list calculated on an element-byelement basis. If two lists are used in the same expression, they must be the same length. + (Add), – (Subtract), … (Multiply), à (Divide) + (addition Ã), – (subtraction ¹), … (multiplication ¯), and à (division ¥) may be used with numbers, expressions, lists, or matrices (Chapter 10).
log, 10^, ln log (logarithm «), 10^ (power of ten y ã10xä), and ln (natural log y ãlnä) may be used with a number, expression, or list. log value, 10^power, ln value e^ e^ (exponential y ãexä) may be used with a number, expression, or list. e^ returns the constant e raised to a power. e^1 returns the value of the constant e. e^power M (Negation) M (negation Ì) returns the negative of a number, expression, list, or matrix (Chapter 10).
MATH MATH Operations To display the MATH MATH menu, press . When you select an item from the menu, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis.
3 (Cube) 3 (cube, MATH MATH item 3) returns the cube of a number, expression, list, or square matrix (Chapter 10). value3 3‡ (Cube Root) 3‡ (cube root, MATH MATH item 4) returns the cube root of a number, expression, or list. 3‡value x‡ (Root) x‡ (root, MATH MATH item 5) returns the nth real root of a number, expression, or list.
nDeriv( nDeriv( (numerical derivative, MATH MATH item 8) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative, and H (optional; if none is specified, 1E.3 is used).
solve( solve( (MATH MATH item 0) returns a solution (root) of expression for variable, given an initial guess, a lower bound, and an upper bound within which a solution is sought (optional, if not specified, lower=.1E99 and upper=1E99). solve(expression,variable,guess) or solve(expression,variable,guess,{lower,upper}) expression is assumed equal to zero. The value of variable in memory will not be updated. guess may be a value or a list of two values.
MATH NUM (Number) Operations To display the MATH NUM menu, press ~. When you select an item from the menu, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis. MATH NUM Menu MATH NUM HYP PRB 1: round( Round 2: iPart Integer part 3: fPart Fractional part 4: int Greatest integer 5: min( Minimum value 6: max( Maximum value round( round( returns a number, expression, list, or matrix rounded to #decimals (9).
int int (greatest integer) returns the largest integer less than or equal to a number, expression, list, or matrix. The value is the same as iPart for nonnegative numbers and negative integers, but one integer less than iPart for negative noninteger numbers. int value min(, max( min( (minimum value) returns the smaller of valueA or valueB or the smallest element in a list. If two lists are compared, it returns a list of the smaller of each pair of elements.
MATH HYP (Hyperbolic) Operations To display the MATH HYP menu, press ~ ~. When you select an item from the menu, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis.
MATH PRB (Probability) Operations To display the MATH PRB menu, press |. When you select an item from the menu, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis. MATH PRB Menu MATH NUM HYP PRB 1: rand Random number generator 2: nPr Number of permutations 3: nCr Number of combinations 4: ! Factorial rand rand (random number) generates and returns a random number greater than 0 and less than 1.
ANGLE Operations To display the ANGLE menu, press y ;. The ANGLE menu displays angle indicators and instructions. When you select an item from the menu, the name is copied to the cursor location. Angle entries are interpreted according to the Radian/Degree MODE setting.
8DMS 8DMS (display as degree/minute/second) displays answer in degree, minute, second format. The MODE setting must be Degree for the TI.82 to interpret answer as degrees, minutes, and seconds. 8DMS is valid only at the end of a line. answer8DMS R8Pr(, R8Pq(, P8Rx(, P8Ry( R8Pr( converts rectangular to polar and returns R, and R8Pq( converts rectangular to polar and returns q, given X and Y rectangular coordinate values.
TEST TEST (Relational) Operations To display the TEST TEST menu, press y :. When you select from the menu, the name is copied to the cursor location. These functions are valid for lists; they return a list calculated on an element-by-element basis.
TEST LOGIC (Boolean) Operations To display the TEST LOGIC menu, press y : ~. When you select from the menu, the name is copied to the cursor location. TEST LOGIC Menu TEST LOGIC 1: and 2: or 3: xor 4: not True if: Both values are nonzero (true) At least one value is nonzero (true) Only one value is zero (false) The value is zero (true) Boolean Operators Boolean operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values.
Chapter 3: Function Graphing This chapter describes function graphing on the TI.82 in detail. It also lays the foundation for using the other graphing features of the TI.82. Chapter Contents Getting Started: Graphing a Circle .................. Defining a Graph ............................... Setting Graph Modes ............................ Defining Functions in the Y= List ................... Selecting Functions ............................. Defining the Viewing WINDOW ....................
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 a circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZOOM Square to adjust the display to make the functions appear as a circle. 1. In Func MODE, press o to display the Y= edit screen.
Defining a Graph To define a graph, you set the modes, enter and select the functions to graph, and define the viewing WINDOW and WINDOW FORMAT. Once you have defined a graph, you can plot, display, and explore it. Steps in Defining a Graph There are six basic steps to defining a graph. You may not need to do all the steps each time you define a graph. The procedures are described in detail on the following pages. 1. Set the MODE to Func graphing. 2. Enter or edit a function in the Y= list. 3.
Setting Graph Modes Pressing z displays the current MODE settings (Chapter 1). The graphing MODE in function graphing must be Func. Checking and Changing Graphing Modes Press z to display the MODE settings. The current settings are highlighted. The TI.82 has four graphing modes. ¦ ¦ ¦ ¦ Func (function graphing) Par (parametric graphing) Pol (polar graphing) Seq (sequence graphing) To graph functions, you must select Func (function graphing). The basics of graphing on the TI.
Defining Functions in the Y= List Pressing o accesses the Y= edit screen, where you enter the functions to graph. You can store up to ten functions in memory at one time. You can graph one or more of these functions at a time. Displaying the Functions in the Y= List Press o to display the Y= edit screen. In the example below, the Y1 and Y2 functions are defined. Defining a New Function To define a new function, enter an expression on the Y= edit screen. 1.
Editing a Function 1. Move the cursor to the function in the Y= list you want to change. 2. Make the changes. You can press ‘ to erase the expression and then enter a new expression. The expression is stored as one of the ten user-defined functions in the Y= list as you enter it. Clearing a Function To clear or erase a function on the Y= edit screen, position the cursor anywhere on the function, and then press ‘. Defining Functions from the Home Screen or a Program 1. Begin on a blank line.
Selecting Functions Only functions that are selected are graphed. Up to ten functions may be selected at one time. Turning a Function “On” or “Off” You select and deselect (“turn on” and “turn off”) functions on the Y= edit screen. The = sign on a selected function is highlighted. To change the selection status of a function: 1. If the Y= edit screen is not displayed, press o to display the functions. 2. Move the cursor to the function whose status you want to change. 3.
Defining the Viewing WINDOW The WINDOW variables determine the boundaries and other attributes of the viewing WINDOW. The WINDOW variables are shared by all graphing modes. TI-82 Viewing WINDOW The viewing WINDOW of the TI.82 is the portion of the coordinate plane defined by Xmin, Xmax, Ymin, and Ymax. The distance between tick marks is defined by Xscl for the X axis and Yscl for the Y axis.
Leaving the WINDOW Edit Screen To leave the WINDOW edit screen: ¦ Select another screen by pressing the appropriate key, such as s or o. ¦ Press y ãQUITä to return to the Home screen. Storing to a WINDOW Variable from the Home Screen or a Program Begin on a blank line. 1. Enter the value you want to store (which can be an expression). 2. Press ¿. 3. Press to display the VARS menu. 4. Select Window... to display the WINDOW variables. 5. Select the WINDOW variable to which you want to store.
Setting WINDOW FORMAT WINDOW FORMAT determines how a graph appears on the display. WINDOW FORMAT settings apply to all graphing modes. Checking WINDOW FORMAT To display the WINDOW FORMAT screen, press p ~. The current settings are highlighted. WINDOW FORMAT RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn Sets rectangular or polar cursor. Sets cursor coordinates on or off. Sets grid off or on. Sets axes on or off. Sets axes label off or on. Changing WINDOW FORMAT 1.
Displaying a Graph Pressing s graphs any functions selected on the Y= edit screen. The current MODE settings apply, and the current values of the WINDOW variables define the viewing WINDOW. Displaying a New Graph Press s to display the graph of the selected function or functions. (Some operations, such as TRACE and the ZOOM CALC operations, display the graph automatically.) As a graph is plotted, the busy indicator is on and X and Y are updated.
Graphing a Family of Curves If you enter a list (Chapter 11) as an element in an expression, the TI.82 plots the function for each value in the list, graphing a family of curves. (In Simul, it graphs all functions for the first element, 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. 3-12 Function Graphing 8203FUNC.
Exploring a Graph with the Free-Moving Cursor While a graph is displayed, you can move the free-moving cursor anywhere on the graph and display the coordinates of any location on the graph. Free-Moving Cursor You can use |, ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. As soon as you press |, ~, }, or †, the cursor moves from the center of the viewing window.
Exploring a Graph with TRACE TRACE moves the cursor from one plotted point to the next along a function, while displaying the cursor coordinates at the bottom of the screen. Beginning a Trace Press r to begin a trace. If the graph is not displayed already, the TI.82 displays it. The cursor is on the first selected function in the Y= list at the middle X value on the screen. The number of the function shows at the upper right of the display.
Moving from Function to Function To trace another selected function on the graph, use † or } to move the cursor to that function. The cursor movement is based on the order of the selected functions in the Y= list, not the appearance of the functions as graphed on the screen. The cursor moves to the new function at the same X value. The function number in the upper right corner of the display changes. Leaving TRACE To leave TRACE: ¦ Select another screen by pressing the appropriate key, such as p or q.
Exploring a Graph with ZOOM Pressing q accesses a menu that allows you to adjust the viewing WINDOW of the graph quickly in a variety of ways. All of the ZOOM commands are accessible from programs. ZOOM Menu ZOOM MEMORY 1: ZBox 2: Zoom In 3: Zoom Out 4: ZDecimal 5: ZSquare 6: ZStandard 7: ZTrig 8: ZInteger 9: ZoomStat Draws box to define viewing WINDOW. Magnifies graph around cursor. Views more of graph around cursor. Sets .1 as dot size. Sets equal sized dots on X and Y axes.
Zoom In, Zoom Out Zoom In magnifies the graph around the cursor location. Zoom Out displays a greater portion of the graph, centered on the cursor location, to provide a more global view. The XFact and YFact settings determine the extent of the zoom. 1. After checking or changing XFact and YFact (page 3.20), select Zoom In from the ZOOM menu. Notice the different cursor. It indicates that you are using a ZOOM instruction. 2.
ZDecimal ZDecimal replots the functions immediately, updating the WINDOW variables to preset values that set @X and @Y equal to .1 and defining the X and Y value of each pixel as one decimal. Xmin = M4.7 Xmax = 4.7 Xscl = 1 Ymin = M3.1 Ymax = 3.1 Yscl = 1 ZSquare ZSquare replots the functions immediately, redefining the WINDOW based on the current WINDOW variables, but adjusted in only one direction so that @X=@Y. This makes the graph of a circle look like a circle. Xscl and Yscl remain unchanged.
Using ZOOM MEMORY ZPrevious allows you to return to the WINDOW displayed prior to the previous ZOOM. ZoomSto stores the values of the current WINDOW variables to userdefined ZOOM MEMORY variables. ZoomRcl changes the WINDOW to the values stored with ZoomSto. ZOOM MEMORY Menu ZOOM MEMORY 1: ZPrevious 2: ZoomSto 3: ZoomRcl 4: SetFactors… Uses previous viewing WINDOW. Stores user-defined WINDOW. Recalls user-defined WINDOW. Changes Zoom In, Zoom Out factors.
Setting ZOOM FACTORS The ZOOM FACTORS, XFact and YFact, determine the extent of the change for the viewing window created by Zoom In or Zoom Out on a graph. ZOOM FACTORS ZOOM FACTORS 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. Checking XFact and YFact To review the current values of XFact and YFact, select SetFactors... from the ZOOM MEMORY menu.
Using CALC (Calculate) Operations Pressing y ãCALCä (above r) accesses a menu with operations you can use to analyze the current graph functions. You are prompted to specify the function(s), interval, and point. CALCULATE Menu CALCULATE 1: value 2: root 3: minimum 4: maximum 5: intersect 6: dy/dx 7: ‰f(x)dx Calculates function value for given X. Finds root of function. Finds minimum of function. Finds maximum of function. Finds intersection of functions. Finds numeric derivative of function.
root root (CALC item 2) uses solve( (Chapter 2) to find the root (zero or X-intercept) of a function. Selecting good values for the bounds and a guess help it find the correct root and find it more quickly. 1. Select root from the CALC menu. The current graph is displayed, with a prompt to enter Lower Bound. 2. Use † or } to move the cursor to the function for which you want to find the root. 3. Move the cursor to the X value you want for the lower bound of the interval and press Í.
minimum, maximum minimum (CALC item 3) and maximum (CALC item 4) find the minimum or maximum of a function in a specified interval to a tolerance of 1EL5. 1. Select minimum or maximum from the CALC menu. The current graph is displayed. 2. Set Lower Bound, Upper Bound, and Guess as described for root. The result cursor is on the solution and the coordinate values are displayed (even if you have selected CoordOff on the WINDOW FORMAT screen). When you press |, ~, }, or †, the free-moving cursor appears.
dy/dx dy/dx (numerical derivative, CALC item 6) finds the numerical derivative (slope) of a function at a point with H = 1EL3. 1. Select dy/dx from the CALC menu. The current graph is displayed. 2. Move the cursor to the X value at which you want to calculate the derivative and press Í. The result cursor is on the solution and the coordinate values are displayed (even if you have selected CoordOff on the WINDOW FORMAT screen). When you press |, ~, }, or †, the free-moving cursor appears.
Chapter 4: Parametric Graphing This chapter describes how to graph parametric equations on the TI.82. Before doing parametric graphing, you should be familiar with Chapter 3, Function Graphing. Chapter Contents Getting Started: Path of a Ball ..................... Defining and Displaying a Parametric Graph ........... Exploring a Parametric Graph ..................... 4-2 4-3 4-6 Parametric Graphing 4-1 8204PARA.
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 position of a ball kicked at an angle of 60¡ with an initial velocity of 15 meters per second. (Ignore air resistance.) What is the maximum height? When does the ball strike the ground? 1. Press z. Press † † † ~ Í to select Par MODE.
Defining and Displaying a Parametric Graph Parametric equations consist of an X component and a Y component, each expressed in terms of the same independent variable T. They are often used to graph equations over time. Up to six pairs of parametric equations can be defined and graphed at a time. Defining a Parametric Graph The steps for defining a parametric graph are the same as those for defining a function graph. Differences are noted below.
Selecting Parametric Equations Only the selected parametric equations are graphed. The = sign on both components of selected equations is highlighted. You may select any or all of the equations on the parametric Y= edit screen. To change the selection status of a parametric equation, press | to move the cursor onto the = sign on either the X or Y component and press Í. The status on both the X and Y components is changed.
Setting the WINDOW FORMAT Press p ~ to display the current WINDOW FORMAT settings. The formats are shared with the other graphing modes. Displaying a Graph When you press s, the TI.82 plots the selected parametric equations. It evaluates both the X and the Y component for each value of T (from Tmin to Tmax in intervals of Tstep) and then plots each point defined by X and Y. The WINDOW variables define the viewing WINDOW. As a graph is plotted, the TI.82 updates X, Y, and T.
Exploring a Parametric Graph As in Function graphing, three tools are available for exploring a graph: using the free-moving cursor, tracing an equation, and zooming. Free-Moving Cursor The free-moving cursor works in Par graphing just as it does in Func graphing. In RectGC FORMAT, moving the cursor updates and displays (if FORMAT is CoordOn) the values of X and Y. (In PolarGC FORMAT, X, Y, R, and q are updated, and R and q are displayed.
Chapter 5: Polar Graphing This chapter describes how to graph polar equations on the TI.82. Before doing polar graphing, you should be familiar with Chapter 3, Function Graphing. Chapter Contents Getting Started: Polar Rose ..................... Defining and Displaying a Polar Graph ............. Exploring a Polar Graph ....................... 5 -2 5 -3 5 -6 Polar Graphing 5-1 8205POLR.
Getting Started: Polar Rose Getting Started is a fast-paced introduction. Read the chapter for details. The polar equation A sin 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. Press † † † ~ ~ Í to select Pol MODE. Choose the initial settings for the other modes (the choice at the beginning of each line). 2. Press o to display the polar Y= edit screen. Press 8 ˜ 2.5 „ Í to define r1. 3.
Defining and Displaying a Polar Graph Polar equations are defined in terms of the independent variable q. Up to six polar equations can be defined and graphed at a time. Defining a Polar Graph The steps for defining a polar graph are the same as those for defining a function graph. Differences are noted below. Setting Polar Graph Modes Press z to display the MODE settings. To graph polar equations, you must select Pol before you enter WINDOW variables or enter a polar equation.
Setting WINDOW Variables Press p to display the current WINDOW variable values. The WINDOW variables define the viewing WINDOW. The values shown are the standard values in Radian MODE. qmin=0 qmax=6.2831853… qstep=.
Displaying a Graph When you press s, the TI.82 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. As a graph is plotted, the TI.82 updates X, Y, R, and q. Smart Graph applies to polar graphs. Note that the free-moving cursor displays X and Y coordinate values if the WINDOW FORMAT setting is the default RectGC. To see R and q, select PolarGC WINDOW FORMAT.
Exploring a Polar Graph As in function graphing, three tools are available for exploring a graph: using the free-moving cursor, tracing an equation, and zooming. Free-Moving Cursor The free-moving cursor works in Pol graphing just as it does in Func graphing. In RectGC FORMAT, moving the cursor updates and displays (if FORMAT is CoordOn) the values of X and Y. (In PolarGC FORMAT, X, Y, R, and q are updated, and R and q are displayed.
Chapter 6: Sequence Graphing This chapter describes how to graph sequences on the TI.82. Before doing sequence graphing, you should be familiar with Chapter 3, Function Graphing. Chapter Contents Getting Started: Forest and Trees ................... Defining and Displaying a Sequence Graph ............ Exploring a Sequence Graph ...................... 6-2 6-3 6-6 Sequence Graphing 6-1 8206SEQ.
Getting Started: Forest and Trees Getting Started is a fast-paced introduction. Read the chapter for details. A small forest contains 4000 trees. The new forestry plan is that each year 20% of the trees will be harvested and 1000 new trees will be planted. Will the forest disappear? Does it stabilize at a certain number of trees? If so, what is that number? 1. Press z. Press † † † ~ ~ ~ Í to select Seq MODE. Press † ~ Í to select Dot MODE. 2. Press o.
Defining and Displaying a Sequence Graph There are two sequence functions, Un and Vn. Sequence functions can be defined in terms of the independent variable (n) or the prior item in the sequence function (Un-1 or Vn-1). They also can be defined in terms of the prior term in the other sequence function. Defining a Sequence Graph The basic steps for defining a sequence graph are the same as those for defining a function graph. Differences are noted below.
Selecting Sequence Functions Only the selected sequence functions are graphed. On selected functions the = sign is highlighted. You may select one or both of the functions on the sequence Y= edit screen. To change the selection status of a sequence function, press | to move the cursor onto the = sign and press Í. Note: When you enter or edit either function, that function is selected automatically. Setting the WINDOW Variables Press p to display the current WINDOW variable values.
Setting WINDOW FORMAT Press p ~ to display the current WINDOW FORMAT settings. Sequence graphing has one unique format, Time or Web. The other formats are shared with the other graphing modes. PolarGC is ignored in Time FORMAT.
Exploring a Sequence Graph As in Function graphing, three tools are available for exploring a graph: using the free-moving cursor, tracing a function, and zooming. Free-Moving Cursor The free-moving cursor works in Seq graphing just as it does in Func graphing. In RectGC FORMAT, moving the cursor updates and displays (if FORMAT is CoordOn) the values of X and Y. (In PolarGC Web FORMAT, X, Y, R, and q are updated, and R and q are displayed.
Chapter 7: Tables This chapter describes how to use tables on the TI.82. Chapter Contents Getting Started: Roots of a Function ............... Defining the Variables ......................... Defining the Dependent Variable ................. Displaying the Table .......................... 7 -2 7 -3 7 -4 7 -5 Tables 7-1 8207TABL.
Getting Started: Roots of a Function Getting Started is a fast-paced introduction. Read the chapter for details. Evaluate the function Y=X3N2X at each integer between M10 and 10. How many sign changes are there and where do they occur? 1. Press y ãTblSetä to display the TABLE SETUP screen. Press Ì 10 to set TblMin=M10. Leave @Tbl=1. Leave the independent and dependent value settings on Auto. 2. Press o „ 3 (to select 3) ¹ 2 „ to enter the function Y1=X3–2X. 3.
Defining the Variables The independent variable for tables is the independent variable in the current graphing MODE. It is defined on the TABLE SETUP screen. TABLE SETUP Screen To display the TABLE SETUP screen, press y ãTblSetä. TblMin and @Tbl TblMin (table minimum) applies when Indpnt is Auto (when the independent variable is automatically generated). It defines the initial value for the independent variable: X (Func), T (Par), q (Pol), and n (Seq).
Defining the Dependent Variable The selected Yn functions define the dependent variables. You can have as many dependent variables as there are functions in the current graphing MODE. From the Y= Editor Enter the functions to define the dependent variables in the Y= editor. The current graphing MODE is used. In Par, you must define both components of the parametric equation. Only functions that are selected are displayed in the table (Chapter 3).
Displaying the Table The table displays two independent values for up to seven dependent values. Once the table is displayed, you can use |, }, ~, and † to move around and scroll the table, displaying other independent variables and other dependent values. The Table Press y ãTABLEä to display the table screen. The top line displays the name of the independent variable and one or two dependent variables. The bottom line displays the full value of the current cell, as indicated by the rectangular cursor.
Displaying More Independent Values If you selected Indpnt: Auto, you can use } and † to display additional values of the independent variable and the corresponding dependent variables. Note: You can scroll “back” from the value entered for TblMin. As you scroll, TblMin is updated automatically to the value shown on the top line of the table. For example, TblMin=0 and @Tbl=1 generates and displays values of X=0, . . ., 6, but you can press } to scroll backwards and display the table for X=L1, . . ., 5.
Chapter 8: DRAW Operations This chapter describes how to use the DRAW operations of the TI.82. Before using the DRAW operations, you should be familiar with Chapter 3, Function Graphing. Chapter Contents Getting Started: Shading a Graph ................. DRAW DRAW Menu ........................... Drawing Lines ............................... Drawing Horizontal and Vertical Lines ............. Drawing Tangent Lines ........................ Drawing Functions and Inverses .................
Getting Started: Shading a Graph Getting Started is a fast-paced introduction. Read the chapter for details. Shade the area above the function Y=X+1 and below the function Y=X3–8X. 1. Press o to see that all functions are deselected. 2. Press q 6 to reset the graph screen to the standard viewing WINDOW, clear any existing drawings, and display the viewing window. 3. Press y ãDRAWä and press 7 to select Shade(, which is copied to the Home screen. 4.
DRAW DRAW Menu To display the DRAW DRAW menu, press y <. What happens when you select an item from this menu is dependent on whether or not a graph is displayed when you access the menu, as described under each operation. DRAW DRAW Menu 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 Clears all drawn elements. Draws a line between two points. Draws a horizontal line. Draws a vertical line.
Drawing Lines While a graph is displayed, Line( lets you define a line on the graph using the cursor. If a graph is not displayed, the instruction is copied to the Home screen. Directly on a Graph 1. When a graph is displayed, select Line( from the DRAW DRAW menu (item 2). 2. Position the cursor at the beginning point of the line you want to draw. Press Í. 3. Move the cursor to the end point of the line you want to draw. The line is displayed as you move the cursor. Press Í.
Drawing Horizontal and Vertical Lines While a graph is displayed, Horizontal and Vertical let you define lines on the graph using the cursor. If a graph is not displayed, the instruction is copied to the Home screen. Directly on a Graph 1. When a graph is displayed, select Horizontal (item 3) or Vertical (item 4) from the DRAW DRAW menu. 2. A line is displayed that moves as you move the cursor. Position the cursor where you want to draw the line. Press Í. The line is drawn on the graph.
Drawing Tangent Lines While a graph is displayed, you can draw the tangent line of a function at a specified point using the cursor. If a graph is not displayed, the instruction is copied to the Home screen. Directly on a Graph 1. When a graph of selected functions is displayed, select Tangent( from the DRAW DRAW menu (item 5). 2. Use † and } to move the cursor to the function for which you want to draw the tangent line. 3.
Drawing Functions and Inverses DrawF (draw function) draws a function on the current graph. DrawInv (draw inverse) draws an inverse of a function on the current graph. Both instructions must be entered on the Home screen or in the program editor. Drawing a Function DrawF (draw function) (DRAW DRAW item 6) is not an interactive operation. It draws expression as a function in terms of X on the current graph. DrawF expression For example, if Y1=.
Shading Areas on a Graph Shade( shades the area on a graph that is both below one specified function and above another, between two X values. The instruction must be entered on the Home screen or in the program editor. Shading a Graph Shade( (DRAW DRAW item 7) is not an interactive operation. It 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.
Drawing Circles While a graph is displayed, Circle( lets you define a circle on the graph using the cursor. If a graph is not displayed, the instruction is copied to the Home screen. Directly on a Graph 1. When a graph is displayed, select Circle( from the DRAW DRAW menu (item 9). 2. Position 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. The circle is drawn on the graph. To continue to draw circles, repeat steps 2 and 3.
Placing Text on a Graph While a graph is displayed, Text( lets you place text on it. If a graph is not displayed, the instruction Text( is copied to the Home screen. Directly on a Graph 1. When a graph is displayed, select Text( from the DRAW DRAW menu. 2. Position the cursor where you want the text to begin. 3. Type the characters. You may enter TI.82 functions and instructions. The font is proportional, so the exact number of characters you can place is variable.
Using Pen to Draw on a Graph While a graph is displayed, Pen lets you draw directly on the graph with the cursor. Using Pen Pen draws directly on a graph. It is not accessible from the Home screen or a program. 1. When a graph is displayed, select Pen from the DRAW DRAW menu (item A). 2. Position the cursor where you want to begin drawing. Press Í to turn the pen on. 3. As you move the cursor, it draws on the graph, turning on each point that the cursor crosses. 4. Press Í to turn the pen off.
Drawing Points To display the DRAW POINTS menu, press y < ~. What happens when you select an item from this menu is dependent on whether or not a graph is displayed when you access the menu, as described under each operation. DRAW POINTS Menu DRAW POINTS STO 1: Pt-On( 2: Pt-Off( 3: Pt-Change( 4: Pxl-On( 5: Pxl-Off( 6: Pxl-Change( 7: pxl-Test( Turn on a point. Turn off a point. Toggle a point on or off. Turn on a pixel. Turn off a pixel. Toggle a pixel on or off. Return 1 if pixel is on, 0 if off.
Drawing Pixels The Pxl (pixel) operations let you turn on, turn off, or reverse a pixel (a dot) on the graph using the cursor. The instruction must be entered on the Home screen or in the program editor. TI.82 Pixels Turning Pixels On and Off The pixel instructions are not interactive. Pxl.On( (pixel on) (DRAW POINTS item 9) turns on the pixel at (row,column), where row is an integer between 0 and 62 and column is an integer between 0 and 94. Pxl.On(row,column) Pxl.Off(row,column) Pxl.
Storing and Recalling Graph Pictures Press y < | to display the DRAW STO menu. You can store an image of the current display and superimpose that image onto a displayed graph at a later time from the Home screen or a program. DRAW STO Menu DRAW POINTS STO 1: StorePic 2: RecallPic 3: StoreGDB 4: RecallGDB Store the current picture. Recall a saved picture. Store the current graph database. Recall a saved graph database.
Storing and Recalling Graph Databases A graph database is the set of elements that define a particular graph. The graph can be recreated from these elements. You can store up to six graph databases and recall any of them to recreate a graph at a later time. Graph Databases The elements of a graph database are: ¦ Graphing MODE. ¦ WINDOW variables and WINDOW FORMAT. ¦ All functions in the Y= list, and whether they are selected.
Clearing a Drawing All points, lines, and shading drawn on a graph with DRAW operations are temporary. They remain only until you execute a ClrDraw (clear drawing) instruction or a change prompts Smart Graph to replot the graph, at which time all drawn elements are erased. When a Graph is Displayed To clear drawings from the currently displayed graph, select ClrDraw from the DRAW DRAW menu (item 1). The current graph is plotted and displayed immediately with no drawn elements.
Chapter 9: Split Screen On the TI.82, you can simultaneously display a graph (including a stat plot) and an editor such as the Home screen, Y= editor, list editor, or table editor. Chapter Contents Getting Started: Polynomial Coefficients ............ Using Split Screen ............................ 9-2 9-3 Split Screen 9-1 8209SPLT.
Getting Started: Polynomial Coefficients Getting Started is a fast-paced introduction. Read the chapter for details. Use the split screen capability to explore the behavior of the graph of a polynomial as the coefficients change. 1. In Func MODE, press o to display the Y= screen. Press .1 „ 3 (to select 3) ¹ 2 „ Ã 6 Í to enter the polynomial .1X3N2X+6. 2. Press z to enter display the MODE screen. Press † † † † † † ~ Í to set the screen to Split. 3. Press q 6 (to select ZStandard). The TI.
Using Split Screen Once you have selected split screen, it remains in effect until you change it. A split-screen display may be replaced temporarily by a full-screen display. When you press a key in split-screen MODE, the cursor automatically moves to the correct half of the display for that key. Setting Screen MODE To change the screen MODE from FullScreen to Split or vice versa, you must use the MODE screen. Split Screen: Top The top half displays the graph screen (any MODE).
TI-82 Pixels DRAW Pixels Instructions The maximum value of row is 30 in the Pxl-On(, Pxl-Off(,and Pxl-Change( instructions and the pxl-Test( function when MODE is Split. Pxl-On(row,column) DRAW Text Instruction The maximum value of row is 25 in the Text( instruction when MODE is Split. Text(row,column,"text") PRGM Output Instruction The maximum value of row is 4 in the Output( instruction when MODE is Split.
Chapter 10: Matrices This chapter describes the matrix features of the TI.82. The TI.82 can store up to five matrices. A matrix, depending on available memory, may have up to 99 rows or columns. Chapter Contents Getting Started: Systems of Linear Equations ........ 10-2 Defining a Matrix ............................ 10-4 Viewing Matrix Elements ....................... 10-5 Editing Matrix Elements ....................... 10-6 About Matrices .............................. 10-8 Matrix Math Functions ........
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.82, you can solve a system of linear equations by entering the coefficients as elements in a matrix and then using the matrix row operations to obtain the reduced row echelon form. 1. Press . Press ~ ~ to display the MATRX EDIT menu. Press 1 to select ãAä to edit matrix ãAä. 2. Press 2 Í 4 Í to define a 2×4 matrix.
6. Press y ãQUITä to return to the Home screen. Begin on a blank line. Press ~ to display the MATRX MATH menu. Press † until the bottom items on the menu are shown, then select …row+( (item A). …row+( is copied to the Home screen. 7. Press Ì 2 ¢. Press 1 (to select ãAä from the MATRX NAMES menu). Press ¢ 1 ¢ 2 ¤ Í. This multiplies row 1 by L2 and adds it to row 2. The resulting matrix is displayed and stored in Ans. The value of ãAä is not changed. 8. Press ~ to display the MATRX MATH menu.
Defining a Matrix A matrix is a two-dimensional array. You can display, enter, or edit a matrix in the matrix editor. The TI.82 has five matrix variables: ãAä, ãBä, ãCä, ãDä, or ãEä. You can define a matrix directly in an expression. Selecting a Matrix To define or display a matrix in the editor, you first must select the name of the matrix. 1. Press ~ ~ to display the MATRX EDIT menu. 2. Select the matrix you want to define (either ãAä, ãBä, ãCä, ãDä, or ãEä). The MATRX EDIT screen appears.
Viewing Matrix Elements After the dimensions of the matrix are set, the matrix can be viewed and values can be entered into the matrix elements. In a “new” matrix, all values are zero. Displaying Matrix Elements 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. The full value of the current element (indicated by the rectangular cursor) is shown on the bottom line. An 8×4 matrix is shown.
Editing Matrix Elements The matrix editor has two “contexts,” viewing and editing. The current context determines the result of a keystroke. Viewing a Matrix In viewing context, you can move quickly from one matrix element to the next. The full value of the current element is displayed on the bottom line. Viewing Context Keys | or ~ Moves the rectangular cursor within the current row. † or } Moves the rectangular cursor within the current column. On the top row, } moves cursor to the column dimension.
Editing a Matrix Element In editing context, an edit cursor is active on the bottom line, and you can change the value of the current matrix element. 1. Use the cursor-movement keys to move the cursor to the matrix element you want to change. 2. Switch to editing context by pressing Í, ‘, or an entry key. 3. Change the value of the matrix element. You may enter an expression (which is evaluated when you leave the editing context) for the value.
About Matrices On the Home screen or in a program, you can use, enter, store, and display matrices. Using a Matrix in an Expression To use a matrix in an expression, you may: ¦ Copy the name from the MATRIX NAMES menu. ¦ Recall the contents of the matrix into the expression with y [RCL] (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. 1.
Displaying a Matrix To display the contents of a matrix on the Home screen, copy the name from the MATRX NAMES menu and press Í. If all of a matrix answer does not fit in the display, as indicated by ellipsis marks in the left or right column or # or $ in the right column, use ~, |, †, and } to display the rest of the matrix. Copying One Matrix to Another To copy a matrix, store it to another matrix. (Access the names on the MATRX NAMES menu.
Matrix Math Functions You can use many of the math functions on the keyboard, MATH MATH menu, and the MATH NUM menu with matrices. However, the dimensions must be appropriate. + (Add), – (Subtract) To add (Ã) or subtract (¹) matrices, the dimensions must be the same. The answer is a matrix in which the elements are the sum or difference of the individual elements.
round( round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals. If #decimals is omitted, the elements are rounded to 10 digits. round(matrix,#decimals) round(matrix) -1 (Inverse) Use the -1 function (—) to invert a matrix (^M1 is not valid). matrix must be square. The determinant cannot equal zero. matrix-1 Powers To raise a matrix to a power, matrix must be square. You may use 2, 3, or ^n (n between 0 and 255).
MATRX MATH Operations Pressing ~ accesses the matrix math operations on the MATRX MATH menu. MATRX MATH Menu NAMES MATH 1: det 2: T 3: dim 4: Fill( 5: identity 6: randM( 7: augment( 8: rowSwap( 9: row+( 0: …row( A: …row+( EDIT Calculates the determinant. Transposes the matrix. Returns the matrix dimension. Fills all elements with a constant. Returns the identity matrix. Returns a random matrix. Augments two matrices. Swaps two rows of a matrix. Adds two rows, stores in second row.
Creating a Matrix with dim dim (MATRIX MATH item 3) is used with ¿ to create new matrixname of dimensions rows × columns with all elements equal to zero. {rows,columns}!dim matrixname Redimensioning a Matrix with dim dim is used with ¿ to redimension existing matrixname to dimensions rows × columns. The elements in the old matrixname that are within the new dimensions are not changed. Any additional elements that are created are zeros.
augment( augment( (MATRIX MATH item 7) concatenates matrixA and matrixB. The number of rows in matrixA must equal the number of rows in matrixB. augment(matrixA,matrixB) Row Operations The row operations, which can be used in an expression, do not change matrix in memory. All row numbers and values can be entered as expressions. rowSwap( rowSwap( (MATRIX MATH item 8) returns a matrix. It swaps rowA and rowB of matrix.
Chapter 11: Lists This chapter describes the list features of the TI.82. The TI.82 can store up to six lists. A list, depending on available memory, may have up to 99 elements. Chapter Contents Getting Started: Generating a Sequence ............ About Lists ................................. LIST OPS Operations .......................... LIST MATH Operations ......................... 11-2 11-3 11-6 11-9 Lists 11-1 8211LIST.
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 1àN2 and display in fractional form. 1. Begin on a blank line on the Home screen. Press y ãLISTä to display the LIST OPS menu. 2. Press 5 to select seq(. The function name is copied to the cursor location on the Home screen. 3. Press 1 ¥ ƒ A ¡ ¢ ƒ A ¢ 1 ¢ 8 ¢ 1 ¤ ¿ y ãL1ä. Press Í to generate the list and store it in L1.
About Lists The TI.82 has six list variables in memory: L1, L2, L3, L4, L5, and L6. On the Home screen or in a program, you can use, enter, store, and display lists. The list names are on the keyboard. Using a List in an Expression To use a list in an expression, you may: ¦ Use the name of the list (L1, L2, L3, L4, L5, or L6). ¦ Enter the list directly (see below).
Displaying a List To display the contents of a list on the Home screen, enter the name of the list and press Í. If all of a list answer does not fit in the display on the Home screen, as indicated by ellipsis marks in the left or right column, use ~ and | to display the rest of the list. 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.
Notes about Using Math Functions with Lists A list can be used to input several values for certain functions. (Other chapters and Appendix A state if a list is valid.) The function is evaluated for each element in the list, and a list is returned. ¦ If a list is used with a function, the function must be valid for every element in the list, except in graphing. (In graphing, an invalid element in a list, such as M1 in ‡{1,0,M1}, is simply ignored.) ) This returns an error.
LIST OPS Operations Pressing y 9 accesses the list operations on the LIST OPS menu. LIST OPS Menu OPS MATH 1: SortA( 2: SortD( 3: dim 4: Fill( 5: seq( Sorts lists in ascending order. Sorts lists in descending order. Accesses the list dimension. Fills all elements with a constant. Creates a sequence. Note: dim and Fill( are the same as dim and Fill( on the MATRX MATH menu. SortA( and SortD( are the same as SortA( and SortD( on the STAT EDIT menu.
Accessing List Dimensions with dim dim (dimension) returns the length (number of elements) of list. dim list Creating a List with dim dim is used with ¿ to create new listname with dimension length. The elements are zeros. length!dim listname Redimensioning a List with dim dim is used with ¿ to redimension existing listname to dimension length. ¦ The elements in the old listname that are within the new dimension are not changed. ¦ Any additional elements that are created are zeros.
Fill( Fill( (LIST OPS item 4) stores value to each element in listname. Fill(value,listname) seq( seq( (sequence, LIST OPS item 5) returns a list in which each element is the value of expression, evaluated at increments for variable from begin to end. seq(expression,variable,begin,end,increment) variable need not be defined in memory. increment can be negative. seq( is not valid in the expression. Un or Vn is not valid in expression. To generate a sequence from Un or Vn, use Un(nstart,nstop,nstep).
LIST MATH Operations Pressing y 9 ~ accesses the list math operations on the LIST MATH menu. LIST MATH Menu OPS MATH 1: min( 2: max( 3: mean( 4: median( 5: sum 6: prod 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 all elements in list. Returns product of all elements in list. Note: min( and max( are the same as min( and max( on the MATH NUM menu.
sum sum (summation, LIST MATH item 5) returns the sum of the elements in list. sum list prod prod (LIST MATH item 6) turns product of the elements of list. prod list Sums and Products of Numeric Sequences You can combine sum or prod with seq( to obtain: upper G expression(x) x=lower upper ∏ expression(x) x=lower To evaluate G 2 (N–1) from N=1 to 4: 11-10 Lists 8211LIST.
Chapter 12: Statistics This chapter describes the tools for analyzing statistical data on the TI.82. These include entering lists of data, calculating statistical results, fitting data to a model, and plotting data. Chapter Contents Getting Started: Building Height and City Size ........ 12-2 Setting Up a Statistical Analysis .................. 12-9 Viewing List Elements ......................... 12-10 Editing List Elements ......................... 12-11 STAT EDIT Menu .............................
Getting Started: Building Height and City Size Getting Started is a fast-paced introduction. Read the chapter for details. Determine a linear equation to fit the data below. Enter and plot the data and determine the best line, then predict how many buildings of more than 12 stories you would expect to find in a city of 300,000 people. Begin by entering the data in the STAT list editor and sorting it.
5. Press ~ to move to the first element of list L2. 6. Press 4 Í 31 Í 42 Í 9 Í 20 Í 55 Í 73 Í to enter the elements of L2. 7. You can sort the data by size of city. Press … 2 (to select SortA(, which is copied to the Home screen) y ãL1ä (to select the independent list) ¢ y ãL2ä (to select the dependent list) ¤ Í. 8. The lists have been updated in memory. Press … 1 to use the STAT list editor to display the lists. Statistics 12-3 8212STAT.
After entering and sorting the data, set up the statistical calculations, then perform the calculations, storing the equations in the Y= list. 9. Press … ~ to display the STAT CALC menu. 10. Press 3 (to select SetUp...). The SET UP CALCS screen appears. Xlist for 2-Var should be L1; Ylist should be L2; and Freq should be 1. 11. Press … ~ 4 (to select Med.Med). The instruction is copied to the Home screen. Press Í to calculate a line fitting the data using the SET UP CALCS settings.
13. Press 5 (to select Statistics...) and ~ ~ to display the VARS EQ menu. 14. Press 7 (to select RegEQ). The regression equation for the current model equation (which was calculated using Med.Med) is copied to Y1. 15. Press … ~ 5 (to select LinReg(ax+b)). The instruction is copied to the Home screen. Press Í to calculate the least-squares linear regression. 16. Press o (to display the Y= editor) Í (to move to Y2) (to display the VARS menu) 5 (to select Statistics...
To plot statistical data, you must enter the data in lists and then define the plot. If you have done calculations to fit the data to one or more models and stored the resulting equations in the Y= list, the data and the equations can be shown and traced simultaneously. 17. Press y ãSTAT PLOTä to display the STAT PLOTS screen. 18. Press 1 (to display the Plot1 screen). Press Í to turn Plot1 On. Leave Type as a scatter plot, Xlist as L1, and Ylist as L2 and Mark as a ›. 19. Press q 9 (to select ZoomStat).
You can enter expressions to define lists in the STAT list editor. For example, you can define predicted values and residuals. 21. To tell which line better fits the data, look at the residuals for both models. Press … 1 to display the STAT list editor. Press ~ ~ } to move the cursor onto the name L3. Press y ãY-VARSä 1 (to select Function...) 1 (to select Y1) £ y ãL1ä ¤. This defines L3 as the values predicted by the Med.Med line. 22. Press Í to store the values in L3. 23. To store the residuals for Med.
You can use the TI.82 to compare different models on the same data set. 26. Press y ãSTAT PLOTä. Press 1 to select Plot1. Press ~ Í to turn the plot off. Press y ãSTAT PLOTä. Press 2 to select Plot2. Press Í to turn the plot on. Press † † Í to define Xlist as L1. Press † ~ ~ ~ Í to define Ylist as L4. Leave Mark as ›. 27. Press y ãSTAT PLOTä. Press 3 to select Plot3. Press Í to turn the plot on. Press † † Í to define Xlist as L1. Press † ~ ~ ~ ~ ~ Í to define Ylist as L6. Press † ~ Í to define Mark as +.
Setting Up a Statistical Analysis The data for statistical analyses is stored in lists. The TI.82 has six list variables in memory that you can use in stat calculations. Several types of statistical analyses are available. Steps 1. Enter the stat data in list(s) (pages 12.9 through 12.12). 2. Set up statistical calculations (page 12.13). 3. Calculate the statistical variables or fit the data to a model (page 12.14 through 12.17). 4. Plot the data (page 12.18 through 12.21).
Viewing List Elements The STAT list editor has two “contexts,” viewing and editing. The current context determines the result of a keystroke. Viewing Context Keys In viewing context, you can move quickly from one list element to the next. The full value of the current element is displayed on the bottom line. | or ~ Moves the rectangular cursor within the current row. † or } Moves the rectangular cursor within the current column.
Editing List Elements In the editing context, an edit cursor is active on the bottom line, and you can change the value of the current list element. You can also move onto the list name and edit the entire list at once. Editing Context Keys | or ~ Moves the edit cursor within the value. ‘ Clears the value on the bottom line. Any entry character Copies the character to the location of the edit cursor on the bottom line. If it is the first character typed, the value on the bottom line is cleared.
STAT EDIT Menu Pressing … accesses the STAT list editor and several instructions for use with lists. STAT EDIT Menu EDIT CALC 1: Edit… 2: SortA( 3: SortD( 4: ClrList Displays list editor (page 12.9). Sorts list in descending order. Sorts list in ascending order. Deletes all elements of list. Note: SortA( and SortD( are the same as SortA( and SortD( on the LIST OPS menu. SortA(, SortD( SortA( (sort ascending) and SortD( (sort descending) have two uses.
Statistical Analysis Pressing … ~ accesses the STAT CALC menu, where you set up and perform statistical calculations. The TI.82 can analyze one-variable or two-variable statistics. Both can have associated frequencies. STAT CALC Menu EDIT CALC 1: 1-Var Stats 2: 2-Var Stats 3: SetUp… 4: Med-Med 5: LinReg(ax+b) 6: QuadReg 7: CubicReg 8: QuartReg 9: LinReg(a+bx) 0: LnReg A: ExpReg B: PwrReg Calculates 1-variable statistics. Calculates 2-variable statistics. Defines lists to use in calculations.
Statistical Variables The statistical variables are calculated as indicated below. Some are displayed when 1-Var Stats or 2-Var Stats are calculated. You can access these variables for use in expressions through the Statistics... menus. If a list is edited or the type of analysis is changed, all statistical variables are cleared.
Types of Statistical Analysis The SET UP CALCS settings are used for statistical analyses. You can override SET UP CALCS settings by specifying the name(s) of the list(s) and frequency after the statistical calculation instruction (Appendix A). 1-Var Stats 1-Var Stats (one-variable statistics, STAT CALC item 1) calculates statistical variables as indicated on the previous page.
LinReg (a+bx) LinReg (a+bx) (linear regression, STAT CALC item 9) fits the data to the model equation y=a+bx using a least-squares fit and x and y. It displays a (y-intercept), b (slope), and r (correlation coefficient). LnReg LnReg (logarithmic regression, STAT CALC item 0) fits the data to the model equation y=a+b ln(x) using a least-squares fit and transformed values ln(x) and y. It displays a, b, and r (correlation coefficient).
Statistical Analysis in a Program You can enter statistical data, calculate statistical results, and fit data to models from a program. Entering Stat Data Enter statistical data into lists directly (Chapter 11). Statistical Calculations 1. On a blank line in the program editor, select the type of calculation from the STAT CALC menu. 2. You can enter the names of the lists to use in the calculation or use the lists defined in SET UP CALCS. Note: You cannot access SET UP CALCS from the program editor.
Statistical Plotting You can plot statistical data that you have entered in lists. The types of plots available include scatter plots, x-y lines, box-and-whisker plots, and histograms. You can define up to three plots at a time. Steps 1. Enter the stat data in list(s) (page 12.9 through 12.12 and Chapter 11). 2. Set up statistical calculations (page 12.13) and calculate the statistical variables or fit the data to a model (page 12.14 through 12.17), if desired. 3.
Boxplot Boxplot plots one-variable data. The whiskers on the plot extend from the minimum data point in the set (minX) to the first quartile (Q1) and from the third quartile (Q3) to the maximum point (maxX). The box is defined by Q1, the median (Med), and Q3. (page 12.14) Box plots ignore Ymin and Ymax, but are plotted with respect to Xmin and Xmax. When two box plots are plotted, the first plots in the middle and the second plots in the bottom.
Defining the Plots 1. Press y ãSTAT PLOTä. The STAT PLOTS screen shows the current plot definitions. 2. Select the plot to define (Plot1, Plot2, or Plot3). 3. If you wish to plot the statistical data immediately, select On. You can define a plot at any time and leave it Off. The definition will be available in the future. 4. Select the type of plot. The options change appropriately: ¦ ¦ ¦ ¦ Scatter: xyLine: Boxplot: Histogram: Xlist Xlist Xlist Xlist Ylist Ylist Mark Mark Freq Freq 5.
Turning Plots Off or On PlotsOff and PlotsOn allow you to turn stat plots on or off from the Home screen or a program. Used without plot#, they turn all plots on or all plots off. Used with plot#, they turn specific plots on or off. PlotsOff or PlotsOn PlotsOff plot#,plot#, . . . PlotsOn plot# For example, PlotsOff:PlotsOn 3 turns all plots off and then turns Plot3 on. Defining the Viewing WINDOW Stat plots are displayed on the current graph.
Statistical Plotting in a Program You may define a plot, select or deselect a plot, and display a plot from a program Stat Plots To display a stat plot, you may define the plot(s), then turn on the plot(s), and then display the graph. (If you do not define the plot, the current definitions are used). For example: Defining a Stat Plot 1. Begin on a blank line in the program editor. Press y ãSTAT PLOTä to display the STAT PLOTS menu. 2. Select the plot to define.
Chapter 13: Programming This chapter describes specific programming instructions and how to enter and execute programs on the TI.82. Chapter Contents Getting Started: Family of Curves ................. 13-2 About TI.82 Programs ......................... 13-4 Creating and Executing Programs ................ 13-5 Editing Programs ............................ 13-6 PRGM CTL (Control) Instructions ................. 13-7 PRGM I/O (Input/Output) Instructions .............. 13-13 Calling Other Programs ..........
Getting Started: Family of Curves Getting Started is a fast-paced introduction. Read the chapter for details. A program is a set of commands that can be executed sequentially, as if they had been entered from the keyboard. Write a simple program to graph the family of curves 2 sin X, 4 sin X, and 6 sin X. 1. Press ~ ~ to display the PRGM NEW menu. 2. Press Í (to select Create New...). Type S I N E S as the name of the program (the keyboard is in ALPHA-LOCK), and press Í.
7. Press y ãQUITä to return to the Home screen. 8. Press to display the PRGM menu. 9. Select SINES. The instruction prgmSINES is copied to the Home screen. 10. Press Í to execute the instruction. The three curves are graphed immediately, then the dotted “pause” indicator appears in the upper right of the display to indicate that the program will not resume execution until you press Í. 11. Use |, }, ~, and † to trace the curves. 12. When you are done tracing, press Í. The program continues.
About TI-82 Programs Most features of the TI.82 are accessible from programs. Programs can access all variables and named items. The number of programs that the TI.82 can store is limited only by available memory. Notes about Programs On the TI.82, programs are identified by names, up to eight characters, beginning with a letter. A program consists of a series of program commands, which begin with a : (colon). A program command can be an expression or an instruction. The TI.
Creating and Executing Programs The program editor is accessed by pressing and then choosing to create a new program or edit an existing program. Creating a New Program 1. Press ~ ~ to display the PRGM NEW menu. Select Create New. 2. Enter the name you want for the program (the keyboard is in ALPHA-LOCK), followed by Í. The name may have one to eight characters (A-Z, 0-9, q) and must begin with a letter. 3. Enter the program instructions (page 13.6). Editing a Program 1.
Editing Programs In general, anything that can be executed from the Home screen can be included in a program, and vice versa. A program command always begins with a colon. Entering Program Commands A colon indicates the beginning of each program command. To enter more than one instruction on a line, separate them with a colon (Chapter 1), just as on the Home screen. Press Í to indicate the end of a command line.
PRGM CTL (Control) Instructions The PRGM CTL (program control) instructions can be accessed only from within the program editor (press ). They direct the flow within 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 copied to the cursor location.
If-Then Then following an If executes a group of commands if condition is true (nonzero). End identifies the end of the group. (PRGM CTL item 2) :If condition :Then :command if true :command if true :End :command If-Then-Else Else following If-Then executes a group of commands if condition is false (zero). End identifies the end of the group.
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. If condition is false (zero), the program executes the commands following End. While instructions can be nested.
Pause Pause suspends execution of the program so you can see answers or graphs. During the pause, the dotted pause indicator displays. Press Í to resume execution. (PRGM CTL item 8) ¦ Pause with no value temporarily pauses the program. If the instruction DispGraph or Disp has been executed, then the appropriate screen is displayed. ¦ Pause value displays value, which can be scrolled, on the current Home screen. Lbl, Goto Lbl (label) and Goto (go to) are used together for branching.
Menu( Menu( sets up branching within a program. If Menu( is encountered during execution, the menu screen is displayed with the specified menu items, the dotted-bar pause indicator displays, and execution pauses until a menu selection is made. (PRGM CTL item C) The menu title is enclosed in ", followed by up to seven pairs of menu items (text enclosed between " marks to display as the menu selection and the label to which to branch if that selection is made). Menu("title","text1",label1,"text2",label2, . .
Return Return quits the subroutine and returns to the calling program (page 13.18), even if encountered within nested loops. (Any loops are ended.) There is an implied Return at the end of any program called as a subroutine. Within the main program, it stops execution and returns to the Home screen. (PRGM CTL item E) Stop Stop stops execution of a program and returns you to the Home screen. (PRGM CTL item F) 13-12 Programming 8213PROG.
PRGM I/O (Input/Output) Instructions The PRGM I/O (program input/output) instructions can be accessed only from within the program editor (press ~). They control input to and output from a program during execution. They allow you to enter values and display answers during program execution. PRGM I/O Menu CTL I/O EXEC 1: Input 2: Prompt 3: Disp 4: DispGraph 5: DispTable 6: Output( 7: getKey 8: ClrHome 9: ClrTable 0: PrintScreen A: Get( B: Send( Enter value or use free-moving cursor.
Disp ¦ Disp (display) with no value displays the Home screen. ¦ Disp with one or more values displays text and values. Displaying the Home Screen Disp with no value displays the Home screen. Disp Displaying Values and Messages Disp with one or more values displays the value of each. Disp value,value,value... ¦ If value is an expression, it is evaluated and then displayed on the right of the following line according to the current MODE settings.
Prompt During execution Prompt displays each variable, one at a time, followed by =?. Enter a value and then press Í for each variable. The values are stored, and the program resumes execution. (PRGM I/O item 2) Prompt variableA,variableB, . . . For example, Prompt Xmin,Xmax,Ymin,Ymax allows the user to enter values for the viewing WINDOW. If an expression is entered in response to Prompt, the expression is evaluated and then stored. Yn and other Y= functions are not valid with Prompt.
getKey getKey returns a number corresponding to the last key pressed, according to the diagram below. If no key has been pressed, it returns 0. getKey can be used inside loops to transfer control; for example, to create video games. (PRGM I/O item 7) Note: You can press É at any time to act as a break during execution (page 13.4). 13-16 Programming 8213PROG.
ClrHome ClrHome (clear Home screen) clears the Home screen during execution and places the cursor in the upper left corner, but program execution does not pause unless Pause is encountered. (PRGM I/O item 8) ClrTable ClrTable (clear table) clears the table in the table editor during execution and places the cursor in the upper left corner, but program execution does not pause unless Pause is encountered.
Calling Other Programs On the TI.82, any 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. Calling a Program from Another Program To call one program from another, begin on a blank line in the program editor and do one of the following: ¦ Press | to display the PRGM EXEC menu and select the name of the program. prgm and the name are copied to the current cursor location.
Chapter 14: Applications This chapter contains application examples that incorporate features described in the preceding chapters. Several of the examples use programs. Chapter Contents Left-Brain, Right-Brain Test Results ............... 14-2 Speeding Tickets ............................. 14-4 Buying a Car, Now or Later? .................... 14-5 Graphing Inequalities ......................... 14-6 Solving a System of Nonlinear Equations ........... 14-7 Program: Sierpinski Triangle ....................
Left-Brain, Right-Brain Test Results An experiment found a significant difference between the ability of boys and girls to identify objects held in their left hands (which are controlled by the right side of the brain) versus their right hands (which are controlled by the left side of the brain). The TI Graphics team decided to conduct a similar test for adult men and women. Problem 30 small objects were chosen.
6. Press q 9 (to select ZoomStat). This adjusts the viewing WINDOW and displays the box plots for the women’s results (left on top). 7. Press r and examine minX, Q1, Med, Q3, and maxX for each plot. What is the median for the left hand? For the right hand? Does it appear that the women guessed correctly more often with the left or right hand? 8. Examine the men’s results. Press y ãSTAT PLOTä and redefine Plot1 to use L3 and Plot2 to use L4. Press r. What difference do you see between the plots? 9.
Speeding Tickets The fine for speeding in your area is 50 plus 5 per kilometer per hour over the limit for the first 10 kilometers, plus 10 per kilometer per hour for the next 10 kilometers, plus 20 per kilometer thereafter. Graph the piecewise function that describes the cost of the ticket in a 45-kilometer-per-hour zone.
Buying a Car, Now or Later? You have identified the car you would like to buy, which costs 8,000. You can afford payments of 250 per month. You can either borrow the money at 10% annual interest (compounded monthly) and buy the car now, or invest the payments at 6% and pay cash for the car later. How long will it take to pay for the car each way? Procedure 1. Press z. Select the default MODE settings. Press y [STAT PLOT] and turn off all stat plots. 2.
Graphing Inequalities Examine the inequality .4X 3–3X+5<.2X+4 graphically. Use the TEST functions 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 MODE settings. Press y [STAT PLOT] and turn off all stat plots. 2. Press o. Turn off all functions. Enter the left side of the inequality as Y4 and the right side as Y5. Y4=.4X3–3X+5 Y5=.2X+4 3. Enter the statement of the inequality as Y6.
Solving a System of Nonlinear Equations Solve the equation X 3–2X=2cosX graphically. Stated another way, solve the system of two equations and two unknowns: Y=X 3–2X and Y=2cosX. Use the ZOOM factors to control the decimal places displayed on the graph. Procedure 1. Press z. Select the default MODE settings. Press y [STAT PLOT] and turn off all stat plots. Press o. Turn off all functions and enter the functions Y7=X3–2X and Y8=2cos X. 2. Press q and select ZDecimal.
Program: Sierpinski Triangle This program creates a drawing of a famous fractal, the Sierpinski Triangle, and stores the drawing in a picture. 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 N1à3 :Then :.5X!X :.5Y!Y :End :If 1à3
Cobweb Attractors Using Web WINDOW FORMAT, you can identify points with attracting and repelling behavior in sequence graphing. Procedure 1. Press z. Select Seq. Press p ~. Select Web and the defaults. Press y [STAT PLOT] and turn off all stat plots. 2. Press o. Enter the sequence. (Un-1 is on the keyboard.) Un=KUn-1(1–Un-1) 3. Press y ãQUITä to return to the Home screen and store 2.9 to K. 4. Press p. Set the WINDOW variables. UnStart = .
Program: Guess the Coefficients This program graphs the function A sin BX with random integer coefficients between 1 and 10. You then try to guess the coefficients and graph your guess as C sin DX. The program continues until your guess is correct.
The Unit Circle and Trigonometric Curves You can use the parametric graphing feature of the TI.82 to show the relationship between the unit circle and any trigonometric curve. Problem Graph the unit circle and the sine curve to demonstrate graphically the relationship between them. Any function that can be plotted in function graphing can be plotted in parametric graphing by defining the X component as T and the Y component as F(T). Solution 1. Press z. Select Radian, Par, and Simul. 2. Press p.
Ferris Wheel Problem Use two pairs of parametric equations to describe two objects in motion, a person on a ferris wheel and a ball thrown to that person. Determine when the two objects are closest. Problem The ferris wheel has a diameter of 20 meters (d) and is rotating counterclockwise at a rate of one revolution every 12 seconds (s).
5. Press s to graph the equations and watch closely as they are plotted. Notice that the ball and the passenger on the ferris wheel appear to be closest near where the paths cross in the upper right quadrant of the ferris wheel. 6. 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 7. Press r.
Reservoir Problem On the TI.82, parametric graphing can be used to animate a process, providing valuable insight into dynamic problems such as water flow out of a reservoir. Problem A new park has a series of waterfalls, fountains, and pools (reservoirs). The height of one of the reservoirs is 2 meters. Several holes of relatively small diameter will be drilled in the side to make streams of water that fall into the next pool.
4. Repeat step 3 to create three more pairs of equations using the heights 1.00, 1.50, and 1.75 meters. 5. Press p. Set the viewing WINDOW. Tmin = 0 Tmax = ‡(4à9.8) Tstep = .01 Xmin = 0 Xmax = 2 Xscl = .5 Ymin = 0 Ymax = 2 Yscl = .5 6. Press q and select ZSquare. ZSquare adjusts the WINDOW variables to include the viewing WINDOW you specified, while providing a realistic (proportional) visual representation of the water jets. It then graphs the trajectories of the water jets from the 5 chosen heights.
Predator-Prey Model Use sequence graphing on the TI.82 to explore the well-known predator-prey model in biology. Determine the numbers of rabbits and wolves that maintain population equilibrium in a certain region. Problem R M K W G D = = = = = = Number of rabbits. Growth rate of rabbits if there are no wolves. Rate at which wolves can kill rabbits. Number of wolves. Growth rate of wolves if there are rabbits. Death rate of wolves if there are no rabbits.
5. Enter the program: PROGRAM:ORBIT :ClrDraw:FnOff :PlotsOff :Dot :Un(1,99,1)!L1 :Vn(1,99,1)!L2 :Un(100,198,1)!L3 :Vn(100,198,1)!L4 :Un(199,297,1)!L5 :Vn(199,297,1)!L6 :min(L1)-10!Xmin :max(L1)+10!Xmax :10!Xscl :min(L2)-10!Ymin :max(L2)+10!Ymax :10!Yscl :For(I,1,99) :Pt-On(L1(I),L2(I)) :End :For(I,1,99) :Pt-On(L3(I),L4(I)) :End :For(I,1,99) :Pt-On(L5(I),L6(I)) :End 6. Execute prgmORBIT, which shows the cycle of the numbers of rabbits (X axis) and wolves (Y axis) over 297 periods.
Fundamental Theorem of Calculus The TI.82 can graph functions that are defined by integrals or derivatives, using the functions fnInt( and nDeriv( from the MATH MATH menu. Problem 1 Demonstrate graphically that x F(x) = ‰1 1àt dt = ln(x), x>0 and that x Dx [ ‰1 1àt dt ] = 1àx Procedure 1 1. Press z. Select Simul and the default MODE settings. Press o and turn off all functions. Press y [STAT PLOT] and turn off all stat plots. 2. Press p. Set the viewing WINDOW. Xmin = .
Problem 2 Explore the functions defined by x y= ‰.2 t2 dt, x ‰0 t 2 dt, and x ‰2 t2 dt Procedure 2 1. Press o. Turn off all functions. On the TI.82, the three functions above can be defined simultaneously using a list. Y5=fnInt(T2,T,{M2,0,2},X) 2. Press z. Select Sequential. 3. Press q 6 to select ZStandard. 4. Press r. Notice that the functions appear identical, but shifted vertically by a constant. 5. Press o. Enter the numerical derivative of Y5. Y6=nDeriv(Y5,X,X) 6. Press r.
Finding the Area between Curves Find the area of the region bounded by: f(x) = 300 x à (x2 + 625) g(x) = 3 cos .1 x x = 75 Procedure 1. Press z. Select the default MODE settings. Press o and turn off all functions. Press y [STAT PLOT] and turn off all stat plots. 2. Press p. Set the viewing WINDOW. Xmin = 0 Xmax = 100 Xscl = 10 Ymin = M5 Ymax = 10 Yscl = 1 3. Press o. Enter the upper and lower functions. Y1=300Xà(X2+625) Y2=3cos .1X 4. Press y ãCALCä and select intersection. The graph is displayed.
Chapter 15: Memory Management This chapter describes how to manage memory on the TI.82. To increase the amount of memory available for use, occasionally you may want to delete from memory items that you are no longer using. You also can reset the calculator, erasing all data and programs. Chapter Contents Checking Available Memory ..................... 15-2 Deleting Items from Memory .................... 15-3 Resetting the TI.82 ........................... 15-4 Memory Management 15-1 8215MEM.
Checking Available Memory The MEMORY Check RAM screen displays the total amount of available memory and the amount of memory used by each variable type. This allows you to determine the amount of memory available for new items such as programs and the amount used by old items that you no longer need. Displaying the MEM FREE Screen 1. Press y ãMEMä to display the MEMORY screen. 2. Select Check RAM.... The number of bytes used by each variable type is shown on the right. 3.
Deleting Items from Memory You can delete the contents of any variable (real number, list, matrix, Y= function), program, picture, or graph database from memory to increase available memory. Deleting an Item 1. Press y ãMEMä to display the MEMORY screen. 2. Select Delete.... 3. Select the type of item that you want to delete. (If you select All..., a list of all items is displayed.) A screen appears listing all variables of that type and the amount used by each. For example, if you select List...
Resetting the TI-82 Resetting the TI.82 restores memory to the factory settings, including deleting the contents of all variables and programs and resetting all system variables to the original settings. Because you can increase available memory by deleting individual items, you should rarely need to reset the TI.82. Resetting 1. Press y ãMEMä to display the MEMORY screen. 2. Select Reset.... 3. Make the appropriate menu selection: ¦ To go to the Home screen without resetting memory, select No.
Chapter 16: Communication Link The TI.82 has a port to let you communicate with another TI.82, with a compatible device such as a CBL 2é /CBLé or CBRé, or with a PC or Macintoshë. This chapter describes how to communicate with another TI.82. Chapter Contents Getting Started: Sending Variables ................ TI.82 LINK .................................. Selecting Items .............................. Transmitting Items ........................... Receiving Items .............................
Getting Started: Sending Variables Getting Started is a fast-paced introduction. Read the chapter for details. Create and store a variable and a random matrix and then transfer them to another TI.82. 1. On the Home screen, press 5 ¥ 3 ¿ ƒ Q Í. 2. Press ~ 6 (to select randM(). Press 3 ¢ 3 ¤ ¿ 1 (to select ãAä) Í to store a random matrix into ãAä. 3. Connect the calculators together with the cable. 4. On the receiving unit, press y ãLINKä ~ to display the RECEIVE menu. Press 1 (to select Receive).
TI-82 LINK The TI.82 communication capability lets you share variables and programs or entire memory backup with another TI.82 or with a personal computer. You can print TI.82 screens on a printer connected to a computer. Linking to Another TI-82 The software for one TI.82 to communicate with another is built into the TI.82. The instructions are in this chapter. Note: You cannot transmit items between the TI.82 and the TI.85 or TI.86. You can transmit some items between the TI.82 and the TI.83.
Selecting Items You can send individual items (variables), all items, or a memory backup from one TI.82 to another. To transmit from the TI.82, you first select what you want to send. The transmission does not begin until you select from the TRANSMIT menu.
Selecting Items to Send 1. Press y ãLINKä to display the LINK SEND menu. 2. For convenience, you can display the individual items with all of them selected, none of them selected, or the ones from the last transmission selected. ¦ SelectAll+ displays with all items selected. ¦ SelectAll– displays with no items selected. ¦ SelectCurrent reselects all currently selected items (page 16.6). The SELECT screen is displayed where you may continue to select or deselect individual items.
Transmitting Items Once you have selected what to send and the receiving unit is ready, you can begin transmitting. For easy distribution of items to several TI.82 units, current items remain selected in both the sending and receiving unit. It is easy to transmit the items again. Transmitting Items After you have selected the items you want to send, press ~ to move the cursor to TRANSMIT and display the TRANSMIT menu. Be sure that the receiving unit is set to Receive (page 16.7).
Receiving Items Items are not transmitted until the receiving unit is ready. If the receiving unit already has a variable with that name, you have the opportunity to overwrite it, skip it, or save it to a new name. Receiving Unit When you select Receive from the LINK RECEIVE menu, the busy indicator and the message Waiting... is displayed and the receiving unit is ready to receive transmitted items. The receiving unit displays the name and type of each item as it is accepted.
Backing Up Memory Backup transmits all items in memory to the receiving unit. Memory Backup To copy the exact contents of memory in the sending unit to the memory of the receiving unit, put the other unit in Receive mode and select Backup from the LINK menu. ¦ Select Transmit to begin transmission. ¦ Warning: Backup overwrites the memory in the receiving unit and all information in the memory of the receiving unit is lost. If you do not want to do a backup, select Quit to return to the LINK menu.
Appendix A: Tables This appendix provides a list of all the TI.82 functions that you can use in expressions and all the TI.82 instructions that you can use on the Home screen and in programs. Appendix Contents Table of Functions and Instructions ............... A-2 Menu Map ................................. A-22 Table of Variables ............................ A-28 Tables A-1 8299APPA.
Table of Functions and Instructions Functions (F) return a value, list, or matrix and can be used in an expression; instructions (I) initiate an action. Some, but not all, have arguments. † indicates that the instruction is available only in the program editor. Returns absolute value of value. (F) Returns absolute value of abs list list elements. (F) Returns matrix of abs matrix absolute values of matrix elements. (F) Addition: valueA+valueB Returns valueA plus valueB.
ClrHome † I/O áClrHomeâ 13.17 … EDIT Clears all values from listA, listB, . . . (I) áClrListâ 12.12 Clears all values from † I/O áClrTableâ 13.17 table. (I) Sets connected line † z áConnectedâ 1.11 graphing format. (I) Does not display cursor † p FORMAT áCoordOffâ 3.10 coordinate values. (I) Displays cursor † p FORMAT áCoordOnâ 3.10 coordinate values. (I) ™ Returns cosine of value. 2.3 (F) ™ Returns cosine of list 2.3 elements. (F) y ãcos.1ä Returns arccosine of value. (F) 2.
CubicReg CubicReg Xlist,Ylist CubicReg Xlist,Ylist,Flist value8Dec Fits data to cubic model using lists from SET UP CALCS. (I) Fits Xlist and Ylist to cubic model. (I) Fits Xlist and Ylist to cubic model with frequency Flist. (I) Displays value as decimal. (I) list8Dec Displays list as decimal. (I) matrix8Dec Degree Degree notation: angle¡ DependAsk DependAuto det matrix dim list dim matrix length!dim listname {row,col}!dim matrixname Disp Displays matrix as decimal. (I) Sets degree MODE.
Division: valueAàvalueB Division: listàvalue Division: valueàlist Division: listAàlistB answer8DMS Dot Returns valueA divided by valueB. (F) Returns list elements divided by value. (F) Returns value divided by list elements. (F) Returns listA elements divided by listB elements. ¥ (F) 2.3 y ãANGLEä á8DMSâ 2.14 † z áDotâ 1.11 y ãDRAWä DRAW áDrawFâ 8.7 y ãDRAWä DRAW áDrawInvâ Displays answer in DMS format. (I) Sets dot graphing format.
Exponent: valueEexponent Exponent: listEexponent Returns value times 10 to y ãEEä the exponent. (F) Returns list elements time y ãEEä 10 to the exponent. (F) 1.7 1.7 Exponent: matrixEexponent Returns matrix elements times 10 to the exponent. y ãEEä 1.7 (F) ExpReg ExpReg Xlist,Ylist ExpReg Xlist,Ylist,Flist Factorial: value! Factorial: list! Fill(value,matrixname) Fits data to exponential model using lists from SET UP CALCS. (I) Fits Xlist and Ylist to exponential model.
fMin(expression,variable, lower,upper) fMin(expression,variable, lower,upper,tolerance) Returns value of variable MATH áfMin(â where minimum of expression occurs, between lower and upper. Tolerance is 1EL5. (F) Returns value of variable MATH áfMin(â where minimum of expression occurs, between lower and upper, with specified tolerance.
fPart matrix value8Frac list8Frac matrix8Frac FullScreen Func Get(variable) getKey Goto label Greater than: valueA>valueB Greater than: listA>listB Greater than or equal: valueA‚valueB Greater than or equal: listA‚listB GridOff GridOn Horizontal Y identity dim Returns fractional part of each matrix element. (F) Displays value as most simplified fraction. (I) Displays list elements as most simplified fractions. NUM áfPartâ 10.11 MATH á8Fracâ 2.5 MATH á8Fracâ (I) 11.
If condition:commandA :commands If condition :Then:commands:End If condition :Then:commands :Else:commands:End IndpntAsk IndpntAuto Input Input variable Input "string",variable int value int list int matrix Inverse: valueM1 Inverse: listM1 Inverse: matrixM1 iPart value iPart list iPart matrix IS>(variable,value) :commandA :commands If condition = 0 (false), skips commandA. (I) Executes commands from Then to End if condition = 1 (true).
† p FORMAT áLabelOffâ 3.10 † p FORMAT LabelOn áLabelOnâ 3.10 † CTL áLblâ Lbl label 13.10 y ãTESTä TEST Less than: valueA
LnReg Xlist,Ylist,Flist log value log list max(valueA,valueB) max(list) max(listA,listB) mean(list) mean(list,Flist) Med.Med Med.Med Xlist,Ylist Med.Med Xlist,Ylist,Flist median(list) median(list,Flist) Menu("title","text",label, "text",label, . . .) min(valueA,valueB) min(list) min(listA,listB) Fits Xlist and Ylist to logarithmic model with frequency Flist. (I) Returns logarithm of value. (F) Returns logarithm of list elements. (F) Returns larger of valueA and valueB.
Minute notation: degrees'minutes'seconds' Multiplication: valueA…valueB Multiplication: value…list Multiplication: list…value Multiplication: listA…listB Multiplication: value…matrix Multiplication: matrixA…matrixB items nCr number nDeriv(expression, variable,value) nDeriv(expression, variable,value,H) Negation: Mvalue Interprets angle as degrees, minutes, and seconds. (F) Returns valueA times valueB. (F) Returns value times each list element. (F) Returns each list element times value.
Normal not value Not equal: valueAƒvalueB Not equal: listAƒlistB Not equal: matrixAƒmatrixB items nPr number 1.Var Stats 1.Var Stats Xlist 1.Var Stats Xlist,Flist valueA or valueB Output(line,column,"text") Output(line,column,value) Sets normal display MODE. (I) Returns 0 if value is ƒ 0. † z áNormalâ 1.10 y ãTESTä LOGIC ánotâ 2.16 (F) y ãTESTä TEST Returns 1 if valueA ƒ valueB. Returns 0 if áƒâ valueA = valueB. (F) 2.15 Returns 1 if listA element y ãTESTä TEST ƒ listB element.
Par Pause Pause value Plot#(type,Xlist,Ylist,mark) Plot#(type,Xlist,Flist) PlotsOff PlotsOff plot#,plot#, . . . PlotsOn PlotsOn plot#,plot#, . . . Pol PolarGC Power of ten: 10^value Power of ten: 10^list Powers: value^power Powers: list^power Powers: value^list Powers: matrix^power prgmname PrintScreen Sets parametric graphing MODE. (I) Suspends program execution until Í is pressed. (I) Displays value, suspends program execution until Í is pressed.
prod list Prompt varA,varB, . . . P8Rx(R,q) P8Ry(R,q) Pt.Change(X,Y) Pt.Off(X,Y) Pt.On(X,Y) PwrReg PwrReg Xlist,Ylist PwrReg Xlist,Ylist,Flist Pxl.Change(row,column) Pxl.Off(row,column) Pxl.On(row,column) pxl.Test(row,column) QuadReg QuadReg Xlist,Ylist QuadReg Xlist,Ylist,Flist y ãLISTä MATH áprodâ 11.10 † I/O áPromptâ 13.15 y ãANGLEä áP8Rx(â 2.14 y ãANGLEä áP8Ry(â 2.14 y ãDRAWä POINTS áPt-Change(â 8.12 y ãDRAWä POINTS Erases point at (X,Y). (I) áPt-Off(â 8.
QuartReg QuartReg Xlist,Ylist QuartReg Xlist,Ylist,Flist angler Radian Fits data to quartic model using lists from SET UP CALCS. (I) Fits Xlist and Ylist to quartic model. (I) Fits Xlist and Ylist to quartic model with frequency Flist. (I) Interprets angle as radians. (F) Sets radian MODE. (I) … CALC áQuartRegâ 12.15 … CALC áQuartRegâ … CALC áQuartRegâ 12.15 12.15 y ãANGLEä árâ 2.13 † z áRadianâ 1.
round(list,#decimals) round(matrix) round(matrix,#decimals) rowSwap(matrix,rowA, rowB) row+(matrix,rowA,rowB) …row(value,matrix,row) Returns list elements rounded to #decimals (9). (F) Returns matrix elements rounded to 10 digits. (F) Returns matrix elements rounded to #decimals. (F) Returns matrix with rowA of matrix swapped with rowB. (F) Returns matrix with rowA of matrix added to rowB and stored in rowB. (F) Returns matrix with row of matrix multiplied by value and stored in row. NUM áround(â 2.
Shade area above lowerfunc and below upperfunc. (I) Shade area above Shade(lowerfunc, upperfunc,resolution) lowerfunc, below upperfunc with 1
solve(expression,variable, guess,{lower,upper}) SortA(listname) SortA(listnameI, listnameD,listnameD,...) SortD(listname) SortD(listnameI, listnameD,listnameD,...) Split Square root: ‡value Square root: ‡list Squaring: value2 Squaring: list2 Squaring: matrix2 Stop MATH ásolve(â Solves expression for variable using guess (a number or 2-element list), between lower and upper. 2.8 (F) Sorts listname elements y ãLISTä OPS áSortA(â 11.6 in ascending order.
Subtraction: listA–listB Subtraction: matrixA–matrixB sum list tan value tan list tanM1 value tanM1 list Tangent(expression,value) tanh value tanh list tanhM1 value tanhM1 list Text(row,column,valueA, valueB . . .) Subtracts listB elements from listA elements. (F) Subtracts matrixB elements from matrixA elements. (F) Returns sum of elements of list. (F) Returns tangent of value. ¹ 2.3 ¹ 10.10 y ãLISTä MATH ásumâ 11.10 š 2.3 (F) š Returns tangent of list 2.3 elements.
2-Var Stats 2-Var Stats Xlist,Ylist 2-Var Stats Xlist,Ylist,Flist Vertical X Web While condition :commands:End valueA xor valueB ZBox ZDecimal ZInteger Zoom In Zoom Out ZoomRcl ZoomSto ZoomStat ZPrevious ZSquare ZStandard ZTrig Performs two-variable analysis using lists from SET UP CALCS menu. (I) Performs two-variable analysis using Xlist and Ylist. (I) Performs two-variable analysis using Xlist and Ylist with frequency Flist. (I) Draws vertical line at X. (I) Sets sequence graphs to to trace as webs.
TI-82 Menu Map Menus begin in the upper left of the keyboard. Default values are shown. o ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ (Func MODE) Y1= Y2= Y3= Y4= ... Y9= Y0= (Par MODE) X1T= Y1T= X2T= Y2T= ...
y ãCALCä ÚÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ (Par MODE) CALCULATE 1:value 2:dy/dx 3:dy/dt 4:dx/dt (Func MODE) CALCULATE 1:value 2:root 3:minimum 4:maximum 5:intersect 6:dy/dx 7:‰f(x)dx (Pol MODE) CALCULATE 1:value 2:dy/dx 3:dr/dq (Seq MODE) (Time FORMAT) CALCULATE 1:value y ãTblSetä ÚÄÄÄÙ y ãTblSetä ÚÄÄÄÄÙ z ÚÙ TABLE SETUP TblMin=0 @Tbl=1 Indpnt: Auto Ask Depend: Auto Ask (PRGM editor) TABLE SETUP Indpnt: Auto Ask Depend: Auto Ask Normal Sci Eng Float 0123456789 Radian Degree Func Par P
y ãLISTä ÚÄÄÁÄÄÄÄÄÄÄÄÄÄ¿ OPS 1:SortA( 2:SortD( 3:dim 4:Fill( 5:seq( MATH 1:min( 2:max( 3:mean( 4:median( 5:sum 6:prod ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿ MATH 1:8Frac 2:8Dec 3:3 4:3‡ 5:x ‡ 6:fMin( 7:fMax( 8:nDeriv( 9:fnInt( 0:solve( NUM 1:round( 2:iPart 3:fPart 4:int 5:min( 6:max( HYP 1:sinh 2:cosh 3:tanh 4:sinh -1 5:cosh-1 6:tanh-1 PRB 1:rand 2:nPr 3:nCr 4:! y ãTESTä ÚÄÄÄÄÁÄÄÄÄÄÄÄÄ¿ LOGIC 1:and 2:or 3:xor 4:not TEST 1:= 2:ƒ 3:> 4:‚ 5:< 6: ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿ NAMES 1:[A] 2:[B] 3:[
ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ EXEC 1:name 2:name 3:name ... EDIT 1:name 2:name 3:name ... New 1:Create New ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ (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 (PRGM editor) I/O 1:Input 2:Prompt 3:Disp 4:DispGraph 5:DispTable 6:Output( 7:getKey 8:ClrHome 9:ClrTable 0:PrintScreen A:Get( B:Send( (PRGM editor) EXEC 1:name 2:name 3:name ...
ÚÙ VARS 1:Window… 2:Zoom… 3:GDB… 4:Picture… 5:Statistics… 6:Table… ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄ (Window…) X/Y 1:Xmin 2:Xmax 3:Xscl 4:Ymin 5:Ymax 6:Yscl 7:@X 8:@Y 9:XFact 0:YFact (Window…) T/q 1:Tmin 2:Tmax 3:Tscl 4:qmin 5:qmax 6:qstep (Window…) U/V 1:UnStart 2:VnStart 3:nStart 4:nMin 5:nMax (Zoom…) ZX/ZY 1:ZXmin 2:ZXmax 3:ZXscl 4:ZYmin 5:ZYmax 6:ZYscl (Zoom…) ZT/Zq 1:ZTmin 2:ZTmax 3:ZTscl 4:Zqmin 5:Zqmax 6:Zqstep ÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄ (Zoo
y ãY-VARSä ÚÄÄÙ Y-Vars 1:Function… 2:Parametric… 3:Polar… 4:Sequence… 5:On/Off… y ãY-VARSä ÚÄÄÄÄÁÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿ (Function…) FUNCTION 1:Y1 2:Y2 3:Y3 4:Y4 ... 9:Y9 0:Y0 (Parametric…) PARAMETRIC 1:X1T 2:Y1T 3:X2T 4:Y2T ...
Table of Variables The variables listed below are used by the TI.82 in various ways. Some have restrictions on their use. User Variables The variables A through Z and q are defined as real numbers. You may store to them. However, the TI.82 can update X, Y, R, q, and T during graphing, so you may wish to avoid using these variables for nongraphing activities. The variables L1 through L6 are defined as lists. You cannot store another type of data to them.
Appendix B: Reference Information This appendix provides supplemental information that may be helpful as you use the TI.82. It includes procedures that may help you correct problems with the calculator. Appendix Contetns Battery Information ............................ B-2 In Case of Difficulty ............................ B-4 Accuracy Information .......................... B-5 Error Conditions .............................. B-7 Support and Service Information ...................
Battery Information The TI.82 uses two types of batteries: four AAA alkaline batteries and a lithium battery as a backup for retaining memory while you change the AAA batteries. When to Replace the Batteries As the batteries run down, the display begins to dim (especially during calculations), and you must adjust the contrast to a higher setting. If you find it necessary to set the contrast to a setting of 8 or 9, you will need to replace the batteries soon.
Replacing the Batteries 1. Turn off the calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the calculator. Turn the back of the calculator toward you. 2. Hold the calculator upright. Place your thumb on the oval indentation on the battery cover. Push down and toward you to slide the cover about ¼ inch (6 mm). Lift off the cover to expose the battery compartment. Note: To avoid loss of information stored in memory, you must turn off the calculator.
In Case of Difficulty If you have difficulty operating the calculator, the following suggestions may help you to correct the problem. Handling a Difficulty 1. If an error occurs, follow the procedure on page 1.22. Refer to the more detailed explanations about specific errors beginning on page B.6, if necessary. 2. If you cannot see anything on the display, follow the instructions on page 1.3 to adjust the contrast. 3. If the cursor is a checker-board pattern, memory is full. Press y ãMEMä Delete...
Accuracy Information To maximize accuracy, the TI.82 carries more digits internally than it displays. Computational Accuracy Values in memory are stored using up to 14 digits with a 2-digit exponent. ¦ You can store a value in the WINDOW variables using up to 10 digits (12 digits for Xscl, Yscl, Tstep, and qstep). ¦ When a value is displayed, the displayed value is rounded as specified by the MODE setting (Chapter 1), with a maximum of 10 digits and a 2digit exponent.
Function Limits Function Range of Input Values sin x, cos x, tan x 0 | x | < 10 12 (radian or degree) arcsin x, arccos 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.
Error Conditions When the TI.82 detects an error, it displays ERR:message and the error menu. The general procedure for correcting errors is described on page 1.22. Each error type, including possible causes and suggestions for correction, are shown below. ARGUMENT A function or instruction does not have the correct number of arguments. See Appendix A and the appropriate chapter. BAD GUESS ¦ For a CALC operation, Guess must be between Lower Bound and Upper Bound.
DIVIDE BY 0 ¦ You are attempting to divide by zero. This error does not occur during graphing. The TI.82 allows for undefined values on a graph. ¦ You are attempting a linear regression with a vertical line. DOMAIN ¦ The argument to a function or instruction is out of the valid range. See Appendix A and the appropriate chapter. This error does not occur during graphing. The TI.82 allows for undefined values on a graph.
LABEL The label in the Goto instruction is not defined with a Lbl instruction in the program. MEMORY There is insufficient memory in which to perform the desired command. You must delete item(s) from memory (Chapter 15) before executing this command. Recursive problems, such as A=A+2:A, display this error. Interrupting an If/Then, For, While, or Repeat loop with a Goto that branches out of the loop can also cause this error, because the End statement that terminates the loop is never reached.
SINGULARITY expression in the solve( function 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 and/or the initial guess. STAT You are attempting 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. Freq, when used, must be an integer ‚ 0.
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.
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.
Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction.
Index -Aa variable, 12-14 to 12-16, A-28 ãAä matrix, 10-4, 10-8, 10-9, A-28 abs, 2-4, 10-10, A-2 Absolute value, 2-4, 10-10, A-2 Accuracy, 3-13, B-4, B-5 Addition: +, 2-3, 10-10, A-2 ALPHA, ALPHA-LOCK, 1-8 and, 2-16, A-2 Angle entry indicators (¡, r, '), 2-13 ANGLE menu, 2-13, 2-14 Angle MODE, 1-11 Ans, 1-16, 13-4 Antilogs, 2-4 APD, 1-2 Applications Area between curves, 14-20 Box with lid, 6 to 13 Building height, 12-2 to 12-8 Buying a car, 14-5 Cobweb, 14-9 Compound interest, 4 to 5, 14-5 Family of curves
- C (Cont.) Clearing (Cont.) display, 1-8 drawing, 8-16 expression, 1-8 Home screen, 1-8 list, 12-10 to 12-12 matrix, 10-6, 10-7 menu, 2, 1-17 table, 7-6 ClrDraw, 3-24, 8-3, 8-16, A-2 ClrHome, 13-13, 13-15, 13-17, A-3 ClrList, 12-12, A-3 ClrTable, 7-6, 13-13, 13-17, A-3 Cobweb graph.
- D (Cont.
- F (Cont.) For(, 13-7 to 13-9, A-7, B-8 FORMAT.
- I (Cont.
- M (Cont.) Menus (Cont.
- P (Cont.
-SScatter plot, 12-18, 12-20 to 12-22 Sci MODE, 1-7, 1-9, 1-10, A-17 Scientific notation, 1-7, 1-9, 1-10, A-17 2nd, 1-8 SELECT (LINK) screen, 16-5 SelectAll+, SelectAll-, 16-5 SelectCurrent, 16-5 Selecting from a menu, 2, 1-17 Selecting functions, 1-19 Send(, 13-13, 13-17, A-17 Sending, 16-1 to 16-8 Seq, 1-9, 1-11, 3-4, 6-3, 7-3, A-17 seq(, 6-5, 11-2, 11-6, 11-8, 11-10, A-17, B-7 Sequence generating, 6-5, 11-2, 11-6, 11-8, 11-10, A-17 graphing, 1-19, 6-1 to 6-6 product, 11-10 sum, 11-10 Sequential, 1-9, 1-
-TT (transpose), 10-12, A-20 -Vvalue, 3-21, 4-6, 5-6 T variable, 4-5, 4-6, 7-3, A-28 Variables, x, 1-12, 1-13, A-28 Tables, 7 to 9, 7-1 to 7-6 TABLE SETUP screen, 7-2, 7-3, 9-3 Table variables, 1-19 tan, tan–1, 2-3, A-20, B-5 Tangent(, 8-3, 8-6, A-20 Tangent line, 8-6 tanh, tanh–1, 2-11, A-20, B-5 TblMin, 1-19, 7-2, 7-3, 7-5, 12-4, 12-5 TEST menu, 2-15 TEST LOGIC menu, 2-16 Text(, 8-3, 8-10, 9-4, A-20 Then, 13-7, 13-8, A-20 q variable, 4-6, 5-5, 5-6, 7-3, A-28 qmax, qmin, 5-4, 5-5, 5-6, B-4, B-9 qstep,
-Yw, 12-14, A-28 Y, 3-8, 4-5, 4-6, 5-5, 5-6, 6-5, 6-6, A-28, B-4 Y-VARS menu, 1-19 Yn, 1-19, 3-5 to 3-7, 13-15, A-28 y1, y2, y3, 12-14, 12-15, A-28 YnT functions, 1-19, A-28 Y= editor, 1-19, 3-5 to 3-7, 4-3, 5-3, 6-3, 7-4, A-28 @Tbl, 7-2, 7-3, 7-6 @X, @Y, 3-9, 3-18, A-28, B-4 H, 2-7, 3-24 sx, sy, 12-14, A-28 G (VARS) menu, 1-19, 12-14 Gx, Gy, Gx2, Gy2, Gxy, 12-14, A-28 q, 4-6, 5-5, 5-6, 7-3, A-28 qmax, qmin, 5-4, 5-5, 5-6, B-4, B-9 qstep, 5-4, 5-5, 5-6, B-4, B-9 Y= functions.
