Manual / Guide · 1990
TI-81 Guidebook
The guidebook for the TI-81 of 1990, Texas Instruments' first graphing calculator (scanned).
Manual / Guide · 1990
The guidebook for the TI-81 of 1990, Texas Instruments' first graphing calculator (scanned).
| | | TI-81 NS Guidebook ~ ‘| TEXAS INSTRUMENTS 71-87 % (y= J [Ranae} [zoom] (TRACE ] [GRAPH] Sry 5 A-LOCK area] (2) [rome] LJ TEST A STAT B DRAW C_Y-vars QUIT [ MATH [MATRX | [ PREM ] [ VARS } a ABS _D SINTE (cos) TAN-1G tt Le} LS J Leos_] La) (= vo J K L M JEU JLo te lO CIC SOc JE ca] 7 Jt) OFF ui fy} oy ANS 2 ENTRY Cm 2 0 ee XY TEXAS INSTRUMENTS Manual developed by: With contributions by: Tl-81 The staff of Texas Instruments Instructional Communications Brad Christensen Franklin Demana Linda Ferrio Pat Milheron John Powers Tom Prickett Dave Santucci Bert K. Waits Texas Instruments gratefully acknowledges the contributions of Bert K. Waits and Franklin Demana, who provided ideas for some of the applications and examples in this manual. Copyright © 1990, 1992 by Texas Instruments Incorporated. 123456789 Important FCC Information Concerning Radio Frequency Interference ii Introduction Texas Instruments makes no warranty, eitner expressea 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. Inno event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these tmaterials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this equipment. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will not occur in a particular installation. Tf this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures: e Reorient or relocate the receiving antenna. « Increase the separation between the equipment and receiver. « Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. e Consult the dealer or an experienced radio/television technician for help. Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment. This digital apparatus does not exceed the Class B limits for radio noise emissions from digital apparatus set out in the Radio Interference Regulations of the Canadian Department of Communications. Table of Contents This manual describes how to use the TI-81 Graphics Calculator. The first chapter gives general instructions on operating the TI-81. Chapters 2 through 8 describe its Interactive features. Getting Started Chapter 1: Operating the Tl-81 Chapter 2: Math and Test Operations Using this Manual Effectively ............-.56- vii The Keyboard ....... 00... e eee e cece eee e nee 2 The First Steps ........ 0. cece cece teen ee 3 Entering a Calculation .............0 cece eee 4 Continuing a Calculation .............000ee eee 5 Graphing Features .........00::eeeeeeeeereee 6 Defining FunctionstoGraph .... . 7 Checking the Viewing Rectangle . 8 Displayingthe Graph .........+.:.eeee5> . 9 ZoomingInonthe Graph ..........0. cece eens 10 Moving between the Graph and RangeScreens.... 11 Moving the Cursor alongaFunction ............ 12 Using Zoom Box 2.0... ccc cece cece eee eens 14 Other Features .........: cc csseee ee eeeeeeee 16 The Keyboard .......... cc cece cere ee eeeenee 1-2 The Second and Alpha Keys .......... 0020000: 1-3 Turning the TI-81 On and Off...............00. 1-4 Setting the Display Contrast .............0006- 1-5 The Display ....... 0... ccc cece cece cece eens 1-6 The Equation OperatingSystem ............... 1-8 Entering Expressions for Evaluation............ 1-10 Editing Expressions .............00cceeeeeeee 1-12 Setting Modes ......... 00. .cccceeee ene eeeeee 1-14 Entering Numbers in Scientific Notation . . ... 1-17 Selecting fromaMenu ............. 1-18 Storing and Recalling Variable Values . . Last ANSWEF 6... 6. eee eee ee eee e eee ener eens Last Entry... 0... ccc ccc cc eect e ee eee Clearing Expressions and Entries Leaving a Menu or Edit Screen................. Error Conditions. ...........:eeeee eee eens Resetting the TI-81...........0 0. eee eee ee eees The Keyboard Math Functions ...............-+ Using the MATH Menus .............-0005 . Using the MATH (Mathematical) Menu Using the NUM(Number) Menu............ Using the HYP (Hyperbolic) Menu .......... Using the PRB (Probability) Menu .......... Using the TEST (Relational) Menu ........... Using the Relational Operators .............. . Table of Contents (Continued) Chapter 3: Function Graphing Chapter 4: Parametric Graphing Chapter 5: The DRAW Features iv DefiningaGraph....... ccc cece cece cece eee eee Setting Graph Modes ............ Defining Functions in the Y= List . . Selecting Functions ............. Defining the Viewing Rectangle ... DisplayingaGraph ...........-eeeeeereeee . Exploring a Graph with the Free-Moving Cursor .. 3-9 Exploring a Graph with the TRACE Feature ...... 3-10 Exploring a Graph with the ZOOM Features ...... 8-11 Using ZOOMBOX ....... 0c cece cece cence eene 3-12 Using ZoomIn......... cece e cece eee eaee 3-13 Using Zoom Out........ see eee eeeeeeees 3-14 Setting Zoom Factors ...... beeen ence ee eee 3-15 Using Other ZOOM Features .......--.ss-eee eee 3-16 Using RANGE Variables .........+0...2eeeeeee 3-17 Using the Y-VARS Menu ............ceeeeeeuee 3-18 Example: Graphing a Circle ........--sseeeeeee 3-20 Defining and Displaying a ParametricGraph...... 4-2 Exploring a ParametricGraph ...........-2000 Example: Simulating Motion ........ Example: Graphing a Polar Equation Example: Graphing a Parametric Equation....... 4-8 The DRAW Menu.........-.+++ seen ee ee eeeeee 5-2 General Notes about the DRAW Instructions ..... 5-3 Clearing DrawingsonaGraph .............045- DrawingaLine ..........eeeeeee Drawinga Point ....... eee Drawing a Function oer Shading an AreaonaGraph....... Example: Shading the Area between Two FUnctions.... 0.00. cece cece creer ence nee 5-10 Chapter 6: Using Matrices Chapter 7: Performing Statistical Calculations Chapter 8: Programming The MATRX (Matrix) Menus................+-- 6-2 Defining a Matrix 2.0.0.0... . ccc eee e cece eee 6-3 Entering and Editing Matrix Elements .......... 6-4 Notes about Using Matrices ...... : - 6-5 Matrix Math Functions. . - 6-6 Using the Row Operations se eeeee eee . 6-8 Storing and Recalling a Matrix Element ......... 6-10 Storing and Recalling a Matrix Dimension........ 6-1 Example: Reducing a Matrix ............-..005 6-12 The STAT (Statistics) Menus ................... 7-2 Setting Up a Statistical Analysis................ 7-3 Entering and Editing Data ...............00005 7-4 Sorting Data 0.0.0.0... cece cece e erect eee 7-6 Calculating One-Variable Statistics ............. 7-7 Calculating Two-Variable Statistics ............. 7-8 Statistical Results Variables . . . « 7-10 Drawing Statistical Data....... 7-14 Storing and Recalling a Data Value ........ . 7-16 Example: Analyzing One-Variable Statistics ...... 7-17 Example: Analyzing Two-Variable Statistics ...... 7-18 The PRGM (Program) Menus ..............0.4. 8-2 General Notes about Programming ............. 8-3 Enteringa Program ..........-.ceeseeeeeeeee Editinga Program. ..........-. 0 cece e cree ceee Executing a Program ...........:eeeeeseeeeee Erasinga Program ..........0. cs eeeeeseeeeee Accessing the Programming Instructions Menus. . . The Control Instructions ....... The Input/Output Instructions. Sample Program ......... 0. ce cece cece ween Calling Other Programs (The Execute Instructions) 8-16 Setting Modes froma Program...............04 8-18 Table of Contents (Continued) Chapter 9: Applications Appendix A: Commands Appendix B: Reference Information Index Solving a System of Linear Equations ........... 9-2 Solving a System of Nonlinear Equations ........ 9-3 Graphing a Piecewise Function ...............- 9-4 Exploring End Behavior of aRational Function ... 9-5 Analyzing Statistical Data Graphically .......... 9-6 Determining Maximum Volume of anOpenBox ... 9-7 Simulating Motion with Parametric Equations .... 9-8 Graphing the Inverse of aFunction ............- 9-10 Graphing the Unit Circle and TrigonometricCurves 9-11 Program: Numerical Solve Routine ............. 9-12 Program: Numerical Integration ..............- 9-14 Program: Building a Table of Function Values .... . 9-16 Program: Plotting the Derivative............... 9-18 Program: Guess the Coefficients ............... 9-20 Table of Commands............ 0c eect e eens A-2 Battery Information ...............0 020s eeeee B-2 Accuracy Information .............. . B-3 Error Conditions......... Shee e eee ve. Bd InCase of Difficulty .............. 0. cece eee ee B-7 Support and Service Information ............ B-8 Warranty Information ..............0.0005 B-9 Using this Manual Effectively The structure of the TI-81 manual and the design of Its pages can help you quickly find the Information you need. Consistent presentation techniques are used throughout the manual to make It easy to use. Structure of the Manual Page-Design Conventions The manual contains sections that teach you how to use the calculator. © Getting Started is a fast-paced introduction to several important features of the TI-81. © Chapter 1 describes general operation and lays the foundation for Chapters 2 through 8. e Chapters 2 through 8 describe specific functional areas of the TI-81—one per chapter, with short examples showing how to use some of the features described in the chapter. Chapter 9 contains application examples that incorporate features from different functional areas of the calculator. These examples can help you see how commands, functions, and instructions work together to accomplish meaningful tasks, When possible, units of information are presented ona single page or on two facing pages. Several page-design elements help you find information quickly. ¢ Page headings—The descriptive heading at the top of the page or two-page unit identifies the subject of the unit. © General text—Just below the page heading, ashort section of bold text provides general information about the subject covered in the unit. ¢ Left-column subheadings—Each subheading identifies a specific topic or task related to the page or unit subject. © Specific text—The text to the right of a subheading presents detailed information about that specific topic or task. The information may be presented as paragraphs, numbered procedures, bulleted lists, or illustrations, © Page “footers”—The bottom of each page shows the chapter name, chapter number, and page number. Using this Manual Effectively (Continued) information- Several conventions are used to present information mapping concisely and in an easily referenced format. Conventions ¢ Tables and charts—Sets of related information are presented in tables or charts for quick reference. e Numbered procedures—A procedure is a sequence of steps that performs a task. In this manual, each step is numbered in the orderin which you must perform it. No other text in the manual is numbered; therefore, when you see numbered text, you know you must perform the steps sequentially. ¢ “Bulleted” lists—If several items have equal importance, or if you may choose one of several alternative actions, this manual precedes each item witha “bullet” () to highlight it—like this list you are reading now. ReferenceAids Several techniques have been used to help you look up specific information when you need it. These include: e Acomplete table of contents at the front of the manual, listing the page headings in each chapter. e Achapter table of contents on the first page of each chapter. e Analphabetical table of commands in Appendix A, showing their correct formats, the key and menu sequences for accessing them, and page references for more information. ¢ Atable of error codes in Appendix B, showing the codes and their meanings, with problem-handling information. e Analphabetical index at the back of the manual, listing tasks and topics you may need to look up. viii Do this first! Getting Started The Getting Started section takes you through several examples to Introduce you to some of the principal operating and graphing features of the TI-81. You can save time and effort by completing these examples first. Contents The Keyboard ......... 0... cece eee eenee 2 The First Steps ....... 0... cece eee ee eee 3 Enteringa Calculation ...........cceee eens 4 Continuing a Calculation ................0. 5 Graphing Features ........ 0... c eee eeeeeee 6 Defining FunctionstoGraph ............... 7 Checking the Viewing Rectangle ............ 8 DisplayingtheGraph ........ 9 ZoomingInontheGraph ..............0005 10 Moving between the Graph and Range Screens..... 11 Moving the Cursor along a Function..... eee eeenes 12 Using Zoom Box 14 Other Features 16 Getting Started 1 The Keyboard The keys of the TI-81 are grouped by color and physical layout to allow easy location of the key you need. The keys are divided into four zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys. The Zones of the 7 ~ Keyboard ‘TEXAS INSTRUMENTS TI-81 » Ln 4 Graphing—{_ 2S _ A ~ a ae YvaRg_ QUIT Advanced [MATH] [waTAK) [pnw] [VARS] (cLeAR] unctions —{ ass D SINTE COS-'F TANTG vd rn K L uw moje 10% ON Scfentific __| C2 = — aa = Calculat ical esis es = a \ Editing —— Graphing Keys = These keys are most frequently used to access the interactive graphing features of the TI-81. Editing Keys These keys are most frequently used for editing expressions and values. Advanced These keys are used to access the advanced functions of Function Keys the TI-81. Scientific These keys are used to access the capabilities of a Calculator Keys standard scientific calculator. 2 Getting Started The First Steps Before beginning these sample problems, follow the steps on this page to ensure that the TI-81 is reset toits factory settings. (Resetting the TI-81 erases alt previously entered data.) 1. Press [ON] to turn the calculator on. ee § T U (ALY [Bl_Z re} 7) OFF &} u > CICICS 2. Press [2nd] and then press [+]. (Pressing accesses the function printed to the left above the next key that you press. RESET is the second function of [+].) The TI-81 displays the RESET menu. io tReset Butes Avail 246) 8. Press [2] to select <Reset>, the second item in the RESET menu. The display shows the message Memcleared. Press toclear the screen. If you need to adjust the display contrast, press and then press [4] (to make the display darker) or Ly] (to make the display lighter). GettingStarted 3 Entering a Calculation The TI-81 display can show up to eight lines of 16 characters per line. This lets you see each expression in its entirety as It is entered. The result Is displayed on the following line. . Using trial and error, determine when $1000 invested at 6% annual compounded interest will double in value. For the first guess, compute the amount available at the end of 10 years. Enter the expression just as you would write it down. Key in 1000 [Xx] 1.06 [A] 10. The entire expression is shown in the first line of the display. . Press to evaluate the expression. The result of the expression is shown on the right side of the second line on the display. The cursor is positioned on the left side of the third line, ready for you to enter the next expression. . The next guess should be greater than 10 years. Make the next guess 12 years. To calculate the amount after 12 years, key in 1000 [x] 1.06 A] 12, followed by [ENTER]. Getting Started Continuing a Caiculation To save keystrokes, you can use the Last Entry feature to recall the last expression entered and then edit It fora new calculation. In addition, the next expression can be continued from the previous result. 1. The next guess should be less than, but close to, 12 years. Compute the amount available at the end of 11.9 years, using the Last Entry feature. Press [2nd], followed by [ENTRY] (the second function of [ENTER)). The last calculated expression is shown on the next line of the display. The cursor is positioned at the end of this expression. . You can edit the expression. Press [] to move the cursor over the 2. Then type in 1.9 to change 12 to 11.9. Press to evaluate the expression. Note: This process can be continued to obtain a solution with the desired accuracy. . You can continue a calculation using the result of the last calculation. For example, if the final amount determined above is to be divided among seven people, how much would each person get? To divide the last calculated amount by seven, press [=] 7, followed by [ENTER]. Assoonas you press [7], Ans/is displayed at the beginning of the new expression. Ans is a variable that contains the last calculated result. In this case, Ans contained 2000.505716. Ge 1600*1 Ph: 2660,.565716 Ans’? a 285, 7865389 Getting Started 5 Graphing Features The keys on the Ti-81 that are related most closely to graphing are located immediately under the display. In the rest of the Getting Started section, you will use all of these keys to graph and explore the behavior of a pair of functions. Graphing Keys rc ~ Texas INSTRUMENTS TI-81 bd nang] wal | <aasael p \ ¢ Key When you press [Y=], an edit screen is displayed where you enter and select the functions that you want to graph. Key When you press [RANGE], an edit screen is displayed where you define the viewing rectangle for the graph. Key When you press [ZOOM], you access a menu of instructions that allow you to change the viewing rectangle. [TRACE] Key When you press , you can move the cursor along a graphed function and display the X and Y coordinate values of the cursor location on the function. Key When you press [GRAPH], a graph of the currently selected functions is displayed in the chosen viewing rectangle. 6 Getting Started Defining Functions to Graph Solve the equation X?—2X=2cosX graphically using the TI-8t. Stated another way, solve the system of two equations and two unknowns: Y=X3 — 2X and Y=2cosX. 1. The Y= edit screen allows you to define functions to be graphed. Press [Y=] to access this edit screen. <<c-t-d rw Hin wal | The display shows labels for four functions. The cursor is positioned at the beginning of the first function. 2. To define the function Y1 in terms of X, enter the first expression, X/3—2X, by pressing Als E)2 [xi]. Press to move the cursor to the next function. oan ee <<< rwn Wu The {xit] key lets you enter the X variable quickly without pressing [ALPHA]. The = signis highlighted to show that Y1 is “selected” to be graphed. 8. To define the function Y2 in terms of X, enter the expression 2cosX by pressing? [GOS] Ia. B2cos * runs il <<< GettingStarted 7 Checking the Viewing Rectangle The viewing rectangle defines the portion of the coordinate plane that appears in the display. The values of the RANGE variables determine the size of the viewing rectangle. You can view and change the values of the RANGE variables. 1. Press to display the RANGE variables edit screen. You view and 8 edit the values of the RANGE variables on this screen. The values shown on the RANGE edit screen are the standard default values. . The standard default RANGE variables define the viewing rectangle as shown. Getting Started Xmin + = Ysot Xsel ‘Ymin xmax Displaying the Graph Now that you have created and selected the functions that you want to graph and determined that you want the standard viewing rectangle, you can display the graph. 1. Press to graph the selected functions in the viewing rectangle. The graph of the functions ra Y = X43 -— 2Xand Y = 2cosX for we -10 s X s 10 isshown in the display. The display shows that there are two areas that may contain solutions (points where the two functions appear to intersect). 2. Press [>] once to display the graphics cursor just to the right of Zod, the center of the screen. The bottom line in the display shows the X and Y ra a] coordinate values for the positionof =|” yf the graphics cursor. 3. Using the cursor-movement keys (C4, 1, (4), and Ly), move the cursor until it is positioned at the apparent intersection of the two ran Ps ca functions on the right side of the CA “4 <r display. As you move the cursor, the X and Y coordinate values are updated continually with the cursor position. GettingStarted 9 Zooming In on the Graph You can magnify the viewing rectangle around a specific location by selecting the <Zoom [n> instruction from the ZOOM menu. 1. Press to access the menu of built-in ZOOM functions. This menu is typical of all the menus of built-in operations on the TI-81. To select an item from amenu, either press the number to the left of the instruction you want, or press [¥] to position the cursor on that instruction and then press [ENTER]. 2. To zoom in, press [2] to select the <Zoom In) instruction from the menu. The graph is displayed again. The cursor has changed to indicate that you are using a ZOOM instruction. 8. With the cursor positioned at the apparent point of intersection on the right side of the display, press [ENTER]. The current position of the cursor becomes the center of the new viewing rectangle. The new viewing rectangle has been adjusted in both the X direction and the Y direction by factors of 4, which are the default values for the zoom factors. 10 = Getting Started 2oom In oom _ Ou Set Factors Square Standard Trig Mi o x oO fa OF Cl — an as ee wa i NN Moving between the Graph and Range Screens When the TI-81 executes a ZOOM Instruction, It updates the RANGE variables to reflect the new viewing rectangle. You can check the RANGE values to see the size of the new viewing rectangle and then return to the graph without having to replot the graph. 1. When you zoom in on the graph, a ARIGE new viewingrectangleisdefined, EAmin= —. 92105263 updated automatically. gnaxs i 8r894°565 Ymin=-2.34126934 Press [RANGE] to view the updated = values of the RANGE variables. ynaxse »698738159 Notice the modified valuesresulting SP ES= 1 from the <Zoom In) instruction. Depending on the exact cursor position when you executed the <Zoom In> instruction, the RANGE variables on your display may be different. 2. Press [GRAPH] to see the graph again. uo GettingStarted 11 Moving the Cursor along a Function The TRACE feature allows you to move the cursor along a function, showing the X and Y coordinate values of the cursor location on the function. 1. Press [TRACE]. The cursor appears near the middle of the screen on the cal Y= X3— 2X function. The coordinate values of the cursor location are displayed at the bottom of the screen. The Y value shown is 4 the calculated value of the function — a for the displayed value of X. = = 2. Press [¥]. The cursor moves to the other function at the same X value cal where it was located on the first function. [Zand [¥] allow you to move between functions. 4 B=1. B0S2632 Y=-. N6agz 3. Press [>] several times to move the cursor to the right. [>] and [] allow you to move along afunction. 12 Getting Started 4. Press [<] several times until the cursor is positioned on the point of intersection between the two can a functions in the first quadrant. You see from the graph that the two functions do intersect; therefore, you have found one solution to the equation X3 —2X =2cosX. This B21. 4473684 Y=. 2462295 solution is X=1.4473684, within an accuracy of one display dot width (0.0526316). The width of a display dot is (Xmax—Xmin) 95 Getting Started 13 Using Zoom Box You have estimated one solution to the equation. Now determine if the other apparent intersection also is a solution. The Zoom <Box> Instruction lets you adjust the viewing tectangle by drawing a box on the display to define the new viewing rectangle. 1. To adjust the viewing rectangle to the standard default range, press to access the ZOOM menu. 2. Press [6] to select <Standard>. This automatically adjusts the viewing rectangle to the standard default range. This display shows the same graph that you saw earlier. 3. Press to display the ZOOM menu again. Press [1] to select <Box>. This lets you specify two diagonal corners of a new viewing rectangle. The cursor is in the middle of the screen. Its new appearance indicates that you have selected a ZOOM instruction. 14 ~~ Getting Started FEES. =Z0o0m In 3! Z00m_Out 4:Set Factors 5: Soauare 6: Standard rtTrig a ra Ls C7 a 4. Move the cursor from the middle of the graph to where you want one corner of the new viewing rectangle tobe. Press [ENTER]. Notice that the cursor has changed toasmall box. 5. Move the cursor to the diagonal corner of the desired viewing rectangle. The outline of the new viewing rectangle is drawn as you move the cursor. 6. Press [ENTER] to accept the cursor location as the second corner of the box. The graph is replotted immediately using the box outline as the new viewing rectangle. Repeat steps 3 through 6 until you see that the two functions do not intersect. Thus, there is only one solution to the equation X3-2X=2cosX. a 8. To leave the graph display, press [QUIT] to return to the Home screen. Getting Started 15 Other Features This Getting Started section Introduced you to basic calculator operation and the function graphing features, including ZOOM and TRACE capabllities. The remainder of this manual describes these features in more detail and also covers the other capabilities of the TI-81. Other In addition to the features demonstrated in the Getting Capabilities of Started section, other features of the TI-81 are described the TI-81 below. © Parametric graphing allows you to save, graph, and analyze up to three parametric equations using all of the ZOOM and TRACE features. (See Chapter 4.) ¢ Drawing and shading features allow you to add emphasis or perform additional analysis on a graph. (See Chapter 5.) © You can enter and save up to three matrices with maximum dimensions of 6x6. These matrices can be manipulated with standard matrix operations, including elementary row operations. (See Chapter 6.) ¢ The TI-81 performs one- and two- variable statistical analyses. You can enter and save up to 150 data points. Four regression models are available: linear, logarithmic, exponential, and power models. You can analyze data graphically with histograms, scatter plots, and line drawings and combine them with other graphing capabilities to plot regression equation graphs. (See Chapter 7.) e@ Programming capabilities include extensive control and I/O instructions. You can save up to 37 programsin atotal of 2400 bytes. (See Chapter 8.) 16 = Getting Started Chapter 1: Operating the TI-81 This chapter describes the TI-81 and provides general Information about Its operation. Chapter Contents The Keyboard ............ 00s see ee eeeeeenee The Second and Alpha Keys ........-..22-seeee Turning the TI-81 On and Off. ...........000005 Setting the Display Contrast . The Display ........--.cee00: The Equation Operating System .........---++- Entering Expressions for Evaluation............ Editing Expressions ............seeeeeeeeeees Setting Modes ......... 6... cee e cece nee eeees Entering Numbers in Scientific Notation ........ SelectingfromaMenu ........-.seeereeeeeeee Storing and Recalling Variable Values ........... Last AMSWEF 2.0... cece cece cere eee nee Last Entry... 2... cece eee cece teen tees Clearing Expressions and Entries ............-- Leaving a Menu or Edit Screen...........----+- Error Conditions.........-- ResettingtheTI-81............ss.s.sssseeeee Operating the TI-81 1-1 The Keyboard The keys on the Ti-81 keyboard are divided into four zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys. The Zones of the Keyboard Texas INsTRUMENTS TI-81 bd sf i Graphing—{_ Jaecmcege” Editing —~+ A-LOCK Advanced | yest A STAY B DRAW C Y-vaRs QUIT Functions CF) EE) ee) (AE) C4 to) ese E cose e Taurs fey Scientific _| | foe) OCI CoA Calculator a a a = x (Aly {B}_ 2 {[cl__@ RESETU CLIC ILI) OFF fh ty ANS? ENTRY L eo / \ Graphing Keys These keys are most frequently used to access the interactive graphing features of the TI-81. Editing Keys These keys are most frequently used for editing expressions and values. Advanced These keys are used to access the advanced functions of Function Keys the TI-81. Scientific These keys are used to access the capabilities of a Calculator Keys standard scientific calculator. 1-2 = Operating the TI-81 The Second and Alpha Keys Some of the keys provide access to more than one function. These additional functions are printed above the keys and are accessed by first pressing the [2nd] or key. Key Labels Second Functions Alphabetical Characters Alpha-Lock Vv. I —— Alpha function 2 | —— Primary function Second function The operation printed to the left above a key is accessed by first pressing and releasing the key and then pressing the appropriate key. When you press the key, the cursor changes to a blinking up-arrow to indicate that the next keystroke isa second function. You can cancel second by pressing again. In this manual, second functions are shown in brackets and preceded by the key symbol; for example, Iv. The letter or symbol printed to the right above a key is accessed by first pressing and releasing the key and then pressing the appropriate key. When you press the key, the cursor changes toa blinking A to indicate that the next keystroke is an alphabetical character. You can cancel alpha by pressing again. Inthis manual, alphabetical characters are shown in brackets and preceded by the key symbol; for example, oi. You can press [A-LOCK] to set alpha-lock, which makes each subsequent key press an alpha character. This is useful when entering display text in programs, for example, so that you will not need to press [ALPHA] before every letter. Cancel alpha-lock by pressing the [ALPHA] key. Operating the TI-81 1-3 Turning the TI-81 On and Off To turn the TI--81 on, press the [ON] key. To turn the TI-81 off, press [OFF]. After about five minutes without any activity, the APD™ Automatic Power Down feature turns the Ti-81 off automatically. Turning the Press [ON] to turn the TI-81 on. TI-81 On © Ifyou turned the TI-81 off by pressing [OFF], the display shows the Home screen with the cursor in the top left corner (see page 1-6). ¢ Ifthe APD™ feature turned the calculator off, the TI-81, including the display, cursor, and any error conditions, will be exactly as you left it. Turning the Before turning the TI-81 off, be certain that you have Ti-81 Off saved any expressions or values that you want to recall later. To turn the TI-81 off, press [OFF]. © The display is cleared. e Any error condition is cleared. e Stored variables, programs, MODE settings, RANGE variables, contrast setting, Last Answer, Last Entry, and the most recent graph are retained in memory by the Constant Memory™ feature. The APD™ To prolong the life of the batteries, the APD feature turns Automatic the TI-81 off automatically after about five minutes Power Down without any activity. When you press [ON], the TI-81 will Feature be exactly as you left it. ¢ The display, cursor, and any error conditions are exactly as you left them. © Stored variables, contrast setting, Last Answer, Last Entry, programs, MODE settings, RANGE variables, and the most recent graph are retained in memory. 1-4 Operating the TI-81 Setting the Display Contrast The brightness and contrast of the display depend on room lighting, battery freshness, viewing angle, and adjustment of the display contrast. The contrast setting Is retained in memory when the TI-81 is turned off. Adjusting the Display Contrast When to Replace Batteries You can adjust the display contrast to suit your viewing angle and lighting conditions at any time. As you change the contrast setting, the display contrast changes, and a numberin the upper right corner between 0 (lightest) and 9 (darkest) indicates the current contrast setting. Note that there are 32 different contrast levels, so each number 0 through 9 represents more than one setting. To adjust the contrast: 1. Press and release the key. 2. Use one of two keys: ¢ Toincrease the contrast to the setting that you want, press and hold [4]. © Todecrease the contrast to the setting that you want, press and hold [¥]. Caution: If you adjust the contrast setting to zero, the display may become completely blank. If this happens, press and release and then press and hold [4] until the display reappears. When the batteries are low, 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 toa setting of 8 or 9, you should replace the batteries soon. OperatingtheTI-81 1-5 The Display The TI-81 displays both text and graphs. When textis displayed, the screen can display up to eight lines of 16 characters per line. When alt eight lines of the screen are filled, text “scrolls” off the top of the screen. The Home Screen Display Cursors Busy Indicator Returming to the Home Screen When you turn the TI-81 on, the Home screen is displayed. The Home screen is the primary screen of the TI-81. On it you enter expressions and instructions and see the results. Tr*stin 3 —— 92,.69861229 ——__ Expression Result The TI-81 has several special cursors. In most cases, the appearance of the cursor indicates what will happen when you press the next key. The cursors that you see on the Home screen are described here. Other special cursors are described in the appropriate chapters. Cursor Appearance Meaning Entrycursor _ Solid blinking The next keystroke rectangle is entered at the cursor, overwriting any character Insertcursor _ Blinking The next keystroke underline is inserted at the cursor 2nd cursor Blinking t The next keystroke isasecond function ALPHA cursor BlinkingA The next keystroke is an alpha character When the TI-81 is calculating or graphing, a box inthe upper right of the screen is highlighted. You can return to the Home screen from any other screen by pressing [Quit]. 1-6 Operating the TI-81 Menu Screens Graph Screens Editing Screens You can access functions and operations that are not on the keyboard through menus, Menu screens temporarily replace the screen where you are working. After you select an item from a menu, the screen where you are working is displayed again. Using menus is described on pages 1-18 and 1-19. The graph screen displays a graph of selected functions and the cursor coordinate values. os im “ wa HE S1S7894? Y= (Ebr S06 There are several editing screens that are used to enter or edit expressions or values. Statistical data Matrix values Functions in the Y= list for graphing RANGE variables for the viewing rectangle Zoom factors for exploring graphs Programs OperatingtheTI-81 1-7 The Equation Operating System The Equation Operating System (EOS) allows numbers and operations to be entered into the TI-81 In a simple, straightforward sequence. EOS evaluates expressions according to the standard priorities of mathematical operations and uses parentheses for grouping. Order of Evaluation EOS evaluates operations in an expression in the following order: © Polar/rectangular conversions, numerical derivative, round, and row operations. Math operations and functions that are entered after the argument, such as x2, x-!, x3, x!, 9", and transpose. Universal powers, suchas 4. ¢@ Implied multiplication where the second argument is anumber, a variable, or a matrix, such as 21, 4B, 3[¢], orsin(A+B)4. ¢ Math and trig functions that are entered before the argument, such as negation, sine, cosine, tangent, and their inverses, log and antilog, natural log and antilog, absolute value, square root, greatest integer, integer part, fractional part, cube root, determinant, and hyperbolic functions. ¢ Implied multiplication other than above, such as 8log4 or sin 4(A+B). @ Permutations and combinations (nPr and nCr). © Multiplication and division. ¢ Addition and subtraction. © Relational operators, such as>or<. Within a priority group, EOS evaluates operations from left to right. If an expression contains two or more single- argument functions that precede the same argument, EOS evaluates them from right to left. Calculations inside a pair of parentheses are evaluated first. When you press [ENTER], regardless of the cursor location, the expression is completed; the cursor does not need to be at the end of the expression. 1-8 OperatingtheTI-81 Implied Multiplication Using Parentheses Enteringa Negative Number Negation When a number precedes a variable, matrix, math or trig function, left parenthesis, or 7, it is not necessary to enter the multiplication sign. The TI-81 understands 27, 4sin 45, 5(1+2), (2*5)(7—4), or AB, for example, as implied multiplication. See the previous page for how the TI-81 evaluates implied multiplication. All calculations inside a pair of parentheses are done first. Then the result of that calculation is used to continue the evaluation. For example, in the expression (1+2)4, the TI-81 first evaluates the portion of the expression inside the parentheses, 1+2, and then multiplies the result, 3, by 4. You may omit any right (close) parenthesis at the end of an expression. All “open” parenthetical elements are closed automatically at the end of the expression when you press [ENTER]. For clarity, however, all close parentheses are shown in this manual. To enter a negative number, use the negation function. Press [(=)], and then enter the number. For example, press [(—)] 1.7 to enter -1.7. Note: The [=] key is used for subtraction. The TI-81 displays the error message ERROR 06 SYNTAX for either of the following cases: ¢ Ifyou press [-] fora negative number, asin 9 [x] E]7 {ENTER]. ¢ Ifyou press {(—)] following a number to indicate subtraction, asin 9 (=) 7 [ENTER]. On the TI-81, negation is a function in the fifth group in the EOS heirarchy. Its place in the order of evaluation in an expression occurs according to EOS. Therefore, functions such as squaring are evaluated before negation. The result of -x2 is a negative number; the result of -9? is -81. Use parentheses when you want to square a negative number entry, (-9)?. Operating the TI-81 1-9 Entering Expressions for Evaluation Anexpression is a complete sequence of numbers, operations, variables, functions, and their arguments that can be evaluated to a single result. On the TI-81, an expressionis entered in the same order that it normally is written. Entering an Expression Example of Entering an Expression You enter numbers, variable names (see page 1-20), symbols, functions, and operations from the keyboard and from menus to create an expression. An expression is completed when you press [ENTER], regardless of the cursor location. The entire expression is evaluated according to EOS, and the result is di