Manual / Guide · c. 1977
TI-55 Owner's Manual
Texas Instruments' owner's manual for the TI-55 programmable scientific.
Manual / Guide · c. 1977
Texas Instruments' owner's manual for the TI-55 programmable scientific.
Texas Instruments advanced professional calculator TIS5 — — <a eRTRS M Ma a ——— ‘ OWNER'S MANUAL TABLE OF CONTENTS Section |. FEATURES AND FUNCTIONS il. BASIC OPERATIONS . Initial Operation... Standard Display Data Entry Keys ... Clearing Operations . Dual Function Keys ( [2nd] and [INV] ) Display Formats.... Scientific Notation. Engineering Notation Fix-Decimal Control . Flashing Display....... Ill. ARITHMETIC CALCULATIONS Basic Keys Combining Operations. . Hierarchy of Operations (AOS). Parentheses .......... IV. MATH FUNCTIONS. . ..... wea f Reciprocal and Factorial , es | Logarithms eee and Common) | Powers of 10 ande . eee vee Angle Calculations . . «2 Trigonometric Functions. 2 es Hyperbolic: Functions: .. 5.5 a siete. 23 Inverse Trigonometric and Hyperbolic Functions.................... 24 Square and Square Root . as Universal Roots and Powers - 26 Percent and Change Percent............... 27 V. MEMORY CAPABILITIES Storing and Recalling Data. Memory Organization ..... Direct Register Arithmetic . Memory/Display Exchange Copyright © 1977, Texas Instruments Incorporated TABLE OF CONTENTS (continued) Section Page Vi. SPECIAL CALCULATIONS -. . 33 Calculations with a Constan . 33 Unit Conversions .......... . 34 Polar to Rectangular Conversions . 36 Mean, Variance, Standard Deviation . 37 Linear Regression ......... . 39 Trend-Line Analysis . . . 44 Vil. SAMPLE MATH PROBLEMS - 45 Vector Addition . PP ces SOLE | 45 Rectangular/Spherical Coordinate Conversions . . .. 46 Area of Irregular Polygons .. nope vg Vill. PROGRAMMING KEYS AND EXAMPLES ....... 49 Programming Keys... - 52 Key Codes - 95 Using the Reset Key Inside a Program....... 57 Entering your Program .................+.- 57 Data EAtey 4 jan bare iniar 58 Typical Programming Examples . . 59 Special Tricks Programming Applications................. 72 Programming Notes... . bee &2) APPENDICES A. Maintenance and Service................+-..+- 76 B. Error Conditions............. C. Display Results versus Accuracy D. Instruction Codes............ E. Geometric Formulas . . F. Mathematical Expressions IMPORTANT Record the serial number from the bottom of the unit and purchase date in the space below. The serial num- ber is identified by the words “SERIAL NO." on the bottom case. Always reference this information in any correspondence. TI-55 Model No. Serial No. Purchase Date I. FEATURES AND FUNCTIONS The TI-55 you have just purchased is an advanced professional calculator designed specifically for those who demand a versatile and reliable business, scientific and mathematical tool. The availability of conversions, statistical analyses and a wide range of mathematical functions have been combined with the easy-to-use Algebraic Operating System to provide straightforward solutions to your most complex problems. + Algebraic Operating System (AOS) allows you to enter mathematical expressions in the same order that they are algebraically stated. Parentheses, an integral part of AOS, ensure proper and accurate interpretation of expressions. Up to 9 parenthesis levels with 4 pending operations are available. Consider the expression (x 4+8x1an 7) _ 0.017303 that can be entered directly as: (C13 [x] 4 5 0<)7 [tan] 0) ()9 7) 3 1. + Complete Set of Mathematical Functions including: Arithmetic Functions with algebraic hierarchy Trigonometric Functions (including inverse functions) Angles measured in degrees, radians or grads Hyperbolic Functions (including inverse functions) Logarithmic Functions (both natural and common) with 10* and e* Factorial, Reciprocal, Percent and Change of Percent Square and Square Root, y* and Vy Pi (7) accurate to 11 digits Constant feature for easy execution of repetitive calculations » Addressable Memory System with 10 separate memories for instant storage and recall of data. Complete memory arithmetic allows you to add, subtract, multiply or divide directly into any memory. Includes memory exchange with display. + Linear Regression routine provides both immediate statistical analysis of data and projection of new points. Trend-Line Analysis is also available. + Mean, Standard Deviation, Variance and Correlation capabilities to analyze one or two-dimensional statistical data. * Totally Portable when operating on its rechargeable battery system. It can also be operated while charging from an AC power source. * Conversions available from the keyboard provide easy transition between: inches and millimeters gallons (US) and liters pounds (av) and kilograms Fahrenheit and Celsius degrees and radians grads and radians polar and rectangular coordinates degrees, minutes, seconds and decimal degrees + Complete Display Versatility, featuring: Standard 8-digit display Scientific Notation entry from keyboard and automatically from calculations Engineering Format displays scientific notation exponents as multiples of 3 Scientific or Engineering Notation removal Fix Decimal control to select desired number of decimal places in the displayed number All results are calculated with 11 digits and rounded to obtain the displayed values. * Automatic Clearing — when the [=] key is pressed, all calculations are completed, the answer is displayed and the calculator is ready for the start of anew problem. * Programmability — 4 programming keys and 32 program steps are available for running “‘straight- line" programs. Il. BASIC OPERATIONS The keys have been selectively positioned on the keyboard to provide for efficient calculator operation. Although many of the operations may be obvious, the following instructions and examples can help you develop skill and confidence in your problem solving routine. INITIAL OPERATION The fast-charge, nickel-cadmium battery pack furnished with your calculator was fully charged at the factory before shipping. However, due to shelf-life discharging, it may require charging before initial operation. If initially or during portable operation the display becomes dim or erratic, the battery pack needs to be charged. Under normal conditions, a fully charged battery pack provides typically 2-3 hours of continuous operation. With the battery pack properly installed, charging is accomplished by plugging the AC Adapter/Charger AC9132 into a convenient 115V/60 Hz outlet and connecting the attached cord to the calculator socket. About 4 hours of charging restores full charge with the power switch off or 10 hours if the calculator is in use. CAUTION: The battery pack will not charge if not properly installed in the calculator. Sliding the ON/OFF switch to the right applies power to the calculator and sliding it to the left removes power. The power-on condition is indicated by a lighted display. Your calculator is designed to be energy efficient. After about 1 to 3 minutes of non-use, the display will shut down to a single decimal point traveling in the display. To restore the display at any time, just proceed with a calculation, or press the key twice. STANDARD DISPLAY In addition to power-on indication, the display provides numerical information complete with negative sign and decimal point and flashes on and off for an overflow, underflow or error condition. An entry can contain as many as 8 digits. All digits entered after the eighth are ignored. decimal point 1 T T integer decimal floating minus sign Any negative number is displayed with a minus sign immediately to the left of the number. See Appendix C for the accuracy of the displayed result. DATA ENTRY KEYS [0] through [9 | Digit Keys — Enters the numbers 0 through 9. (+ ] Decimal Point Key — Enters Decimal Point. The decimal point can be entered wherever needed. If no decimal point is entered, it is assumed to be to the right of the number, and will appear when a function key is pressed. A zero will precede the decimal point for numbers less than 1. Trailing zeros on the decimal portion of anumber are not normally displayed. Only the first decimal point entered is accepted, all others are ignored. (2nd) J Pi Key —Enters the value of pi () to 11 significant digits (3.1415926536) for calculations; display indicates the rounded value to 8 digits. (EE) Enter Exponent Key — Instructs the calculator that the subsequent number entry is an exponent of 10. After the [EE] key is pressed, all further results are displayed in scientific notation format until or MGB is pressed or until the calculator is turned off. (INV) [EE] or [INV)\[2nd) {I can remove this format if the displayed number is in the range +9.9999999 x 10” <0 1(X-107".. Change Sign Key —Instructs the calculator to change the sign of the displayed number. When pressed after [EE], changes sign of the exponent. Example: Enter —12.6 Enter Press Display 12.6 ~12.6 CLEARING OPERATIONS [CE] Clear Entry Key — Clears entries made with the digit, decimal point and change-sign keys when pressed before a function key. This key does not clear calculated results, numbers recalled from memory or 7. [CE] also stops the flashing of the display when needed. Use of this key does not affect pending operations. (cik] Clear Key — Clears calculations in progress, the constant and the display. It resets scientific notation to standard format and will stop a flashing display. This key does not affect the contents of user memories, program memory, fixed-point (fix-decimal) location, angular mode or engineering format. (2nd) [EM Clear All Key — Clears the display, all memories including program memory, the constant and calculations in progress. Restores standard display mode and resets angular mode to degrees. Eliminates fixed-point (fix-decimal) format. The calculator effectively clears itself after most calculations. When the [=] key is pressed to complete acalculation, the answer is displayed and the calculator is ready for the start of anew problem without pressing any of the clear keys. The contents of the user memories are not automatically cleared. 6 DUAL FUNCTION KEYS ( (2nd) and (inv) ) Most of your calculator's keys have dual functions. The first function is printed on the key and the second function is written above it. To execute a function shown on a key, simply press the desired key. To use the second function of a key, press the key, then press the key immediately below the desired second function. For example, to find the natural logarithm of a number, press [Inx]. To find the common logarithm of a number, press {Inz]. In order to make sequences of this type clear, in this manual it will be shown as (2nd) (EH. First function operations, therefore, are indicated by [__]. Second functions are indicated by (2nd) MM. When is pressed twice in succession the calculator returns to first function operation. The inverse key [iNV) provides additional computing capabilities without increasing the number of keys on the keyboard just like the key does. When [INV] precedes another key, the purpose of that key is reversed. The inverse can be used with the following keys to obtain the indicated function. 1stfunction keys 2nd function keys sin— sin” sinh— sinh cos— cos” cosh— cosh" tan— tan“ tanh — tanh" SUM-— subtract Prod-— divide EE— removes EE Eng— removes Eng or EE Fix— removes Fix conversions — reverses conversions Mean — Mean of x data Var— Variance of x data S.Dev — Standard Deviation of x data This key can also be used to obtain the mean, standard deviation and variance of the independent variable, x, in the linear regression routine. An inverse instruction may be cancelled by pressing [INV] a second time, if no other keys have been pressed, or by pressing a key without an inverse function. When used in conjunction with the second function key, the inverse key can be pressed before or after the second function key is pressed, i.e., [INV] [2nd] J or [2nd] [INV] JJ. When programming, the [INv] key must always precede the key. For examples of [INV] uses with a specific key, see the section relating to each key. DISPLAY FORMATS Even though a maximum of 8 digits can be entered or displayed, the internal display register always retains results to 11 digits. The results are then rounded for display only. In addition to the versatile 8-digit standard display, there are several other display capabilities that increase the operating range and flexibility of your calculator. Scientific Notation Any number can be entered as the product of a value (mantissa) and 10 raised to some power (exponent). mantissa exponent 1 ar ee decimal point decimal exponent sign floating minus sign This capability allows you to work with numbers as small as +1 10~* or as large as +9.9999999 x 10°. Numbers smaller than+1 x 107’ or larger than +9.9999999 x 10’ must be entered in scientific notation. When calculations exceed these limits, the 8 calculator automatically shifts into scientific notation. The entry procedure is to key in the mantissa (including its sign), then press (EE) and enter the exponent of 10 and its sign. For example, the number 320,000,000,000 can be written as 3.2 x 10" and can be entered into the calculator as: Enter Press Display (cir) 0 3.2 3.2 (ee) 3.2 00 11 3.2641 More than 2 digits can be entered after pressing (EE), but only the last two entered are retained as the exponent. In scientific notation, a positive exponent indicates how many places the decimal point of the mantissa should be shifted to the right. If the exponentis negative, the decimal should be moved to the left. Regardless of how a mantissa is entered for scientific notation, the calculator normalizes the number, displaying a single digit to the left of the decimal point, when any function or operation key is pressed. Example: Enter 6025 = 10” Enter Press Display [CLR| 0 6025 6025 (EE) 6025 00 20 6025 20 a] 6.025 23 A mantissa resulting from a calculation is displayed to 8 digits, but internally is carried to 11 digits. This 11-digit value is the one used for all ensuing calculations. See Appendix C. The change sign key can be used to attach a negative sign to the mantissa and to the power-of-ten exponent. Simply press after entry of the mantissa to change its sign or after the exponent to change its sign. To change the sign of the mantissa or to enter numbers in its decimal portion after the [EE] key has been pressed, press [= ], then enter the mantissa’s sign change or additional numbers to the decimal portion. Data in scientific notation form can be intermixed with data in standard form. The calculator converts the entered data for proper calculation. After the [EE] key has been pressed, the calculator displays all results in scientific notation format until (CLR), [2nd) MEW, (INV) (EE) or [INV] Gl is pressed, or until the calculator is turned off. Example: 1.816 x 10° — 58 1.43219 = 1.2345678 x 10° = 1234.5678 Enter Press Display (cr) to) 1.816 (EE) 1.816 00 3 | 1.816 03 581.43219 3] 1.2345678 03 (NY) [EE]: 1234.5678 When [Inv] [EE] is pressed to remove scientific notation and the number is outside of the range +9.9999999 x 10’ to+ 1 10°7, the calculator will return to standard format only when or if a calculated result is in the displayable range. 10 Example: (7 x 10’ + 5 x 10") + 25+ 25 = 80112000 Enter Press Display 7 [EE] 7 00 rd 7. 07 5 (ee) 5 00 10 (=) Ginv) [ee] 5.007 10 5.007 10 25 2.0028 09 25 80112000. Pressing [EE} while a result is displayed will cause the non-displayed digits to be discarded and only the rounded display value will be carried to the next calculation. Example: 3.1415927 — 3.1415926536 = 4.64 x 107°. Press Display Comments [2nd] 3.1415927 11 digits internally (EE) 3.1415927 00 Discards non-displayed digits [=] Bad) HM 3.1415927 00 11 digits internally 3) 4.64-08 Difference This feature can be used in conjunction with Fix- Decimal Control to limit the number of decimal places used by the calculator at any point in a calculation. Remember that [EE] will only affect the displayed number and has to be repeated each time you want the non-displayed digits discarded. Engineering Notation This modified form of scientific notation is accessed by pressing (B. The displayed value in this mode consists of a mantissa and an exponent that have been adjusted so that the exponent is a multiple of three (10%, 10-*, etc.) and the mantissa has 1, 2 or 3 digits to the left of the decimal point. This allows the calculator to display results in units that are readily usable such as 10-" for picofarads, 10~° for millimeters, 10° for megohms or 10-° for nanoseconds. ” Example: What is the diameter of a cable in microns (1 micron = 10~* meter) whose circumference is 3 x 10-* meters? C=ad d=C/r Enter Press Display (CuR} (2ng) 0. 00 3 [EE] 3 00 3 =) 3.-03 (2nd) KE [=] 954.92966-06 Pressing [INV] (2nd) [GM or (2nd) (E will remove this display mode, [cir] Or [INV] [EE] does not affect it. Fix-Decimal Control In standard display format, scientific notation or engineering notation, you can selectively choose the number of digits to display following the decimal point. Pressing [2nd] [ff . then entering the desired number of decimal places (0 to 7), instructs the calculator to round all results to the selected number of decimal places. Pressing (2nd) MEM , (2nd) HIM 8, (2nd) HEM 9, or [INV] [2nd] HB returns the calculator to the standard display. Data entries can still be made with 8 digits with all subsequent calculations using the 11-digit unrounded results. Only the display is altered to the requested number of decimal places. 12 Example: 2/3 = 0.6666667 Enter Press Display 0 2 Ce) 2 3 (=) 0.6666667 (2nd) EM S 0.66667 (2nd) TM 2 0.67 (2nd) MT 1. Remember that the display value is rounded to the desired format. Example: 1 x 10° = 2 = .0005 Enter Press Display (2nd) te) 1 [ee] 1 00 GA) [=] 1-03 2 (=) 5.-04 (2nd) MM 2 5.00-04 {inv} [EE] 0.00 (2nd) EM 3 0.001 (2nd) TE 4 0.0005 (2nd) TE 5S 0.00050 Flashing Display The display flashes off and on whenever the limits of the calculator are violated or when an improper mathematical operation is requested. Press [CE] to stop the flashing without disturbing any calculations in progress. Calculations can continue from this point if the number in the display is still usable. See Appendix B for a list of error and overflow/ underflow conditions. 13 Ill. ARITHMETIC CALCULATIONS The Algebraic Operating System's method of entering numbers and operations is straightforward allowing entry of most problems just as they are mathematically stated. The accuracy of results is discussed in Appendix C. BASIC KEYS (+), (=) Add and Subtract Keys —Correspondingly alters the present display value by the next entered quantity. These keys also complete any previously entered arithmetic (+, —, x, +), y*, Wy orA% functions. (<), =) Multiply and Divide Keys — Correspondingly alters the present display value by the next entered quantity. These keys also complete any previously entered multiply, divide, y*, /y or A% functions. (=) Equals Key — Computes results by completing all previously entered numbers with associated operations, preparing the calculator for a new problem. (:¥] x Exchange y Key — Exchanges factors in multiplication and exchanges divisor and dividend in division. Interchanges x and y in A%, y* and Vy calculations. Also used for data entry and fast display for polar to rectangular conversions and linear regression problems. Pressing at the beginning of a new sequence clears any calculations in progress and always ensures that no pending operations from prior calculations remain. This is not required if the previous problem used [=] to obtain the result. Following [=] witha numeric entry accomplishes the same as pressing {cir} , except that [=] does not remove scientific notation or stop a flashing display or clear the constant. Pressing any two of the operation keys (+, —, x, +, y%, Wy, and A%) in succession causes a flashing display. Also, following any of these with = or), or preceding with (, causes the same result. 14 Example: 23.79 + .54 — 6 = 18.33 Enter Press Display 0 23.79 4) 23.79 54 J 24.33 6 & 18.33 Again note that the numbers and functions are entered in the same order as they are mathematically stated. Example: —4 x 7.3+2=-14.6 Enter Press Display 4 og —4. 7.3 es] ~29.2 2 Ee -14.6 COMBINING OPERATIONS After a result is obtained in one calculation it may be directly used as the first number in asecond calculation. There is no need to reenter the number from the keyboard. Example: 1.84 + 0.39 = 2.23 then (1.84 + 0.39)/365 = 0.0061096 Enter Press Display Comments 1.84 1.84 39 & 2.23 1.84 + 0.39 2.23 365 ee) 0.0061096 2.23 + 365 HIERARCHY OF OPERATIONS Algebraic hierarchy is an essential feature of the Algebraic Operating System. To efficiently combine operations, the standard rules of algebraic hierarchy have been specifically programmed into the calculator. 15 These algebraic rules assign priorities to the various mathematical operations. Without a fixed set of rules, expressions such as 5 x 4+ 3 x 2 could have several meanings: § x (4+ 3)x 2=70 or 5x4+3x2=26 or (6x 4+3)x 2=46 or 5x (4+3x 2)=50 Algebraic hierarchy rules state that multiplication is to be performed before addition. So algebraically, the correct answer is (5 x 4) + (3 x 2) = 26. The complete list of priorities for interpreting expressions is: 1) Special Functions 2) Percent Change (A%) 3) Exponentiation (y*), Roots (W’y) 4) Multiplication, Division 5) Addition, Subtraction 6) Equals 1) Special functions (trigonometric and hyperbolic, logarithmic, square, square root, factorial, e*, 10*, percent, reciprocal and conversions) immediately replace the displayed value with its functional value. 2) Percent change has only the ability to complete other percent change operations. 3) Exponentiation (y*) and roots (¥/y) are performed as soon as the special functions and percent change are completed. 4) Multiplication and division are performed after completing special functions, percent change exponentiation, root extraction and other multiplication and division. 5) Addition and subtraction are performed only after completing all operations through multiplication and division as well as other addition and subtraction. 6) Equals completes all operations. 16 Operations of the same priority are performed left to right. To illustrate, consider the interpretative order of the following example: Example: 4+ 5* x 7+ 3 x 0.5°* © = 3.2413203 Enter Press Display Comments 4 4. (4+) is stored 5 (2) 25. (5°) special function [z2] evaluated immediately ba] 0.16 (4+5?) + evaluated because x is same priority as +. 7 1.12 x higher priority than + so (4+ 5? x7) evaluated, + stored 3 5-4] 3. (3x) stored 5 we) 0.5 .S entered, y* stored 60 (cos) 0.5 Cos 60° evaluated immediately 3) 3.2413203 Completes all operations -5°°s © evaluated, then 3 x .5°°* ©" next, then this is added to 1.12. Thus, by entering the expression just as it is written, the calculator correctly interprets it as {[(4 + 5?) x 7] + (3 x 0.5995 8} The important things to remember here are that operations are enacted strictly according to their relative priority as stated in the rules. The calculator remembers all stored operations and recalls each and its associated number for execution at exactly the correct time and place. Once familiar with the order of these operations, you will find most problems are extremely easy to solve because of the straightforward manner in which they can be entered into the calculator. Additional control over the order of interpretation is provided through the use of parentheses. 17 PARENTHESES There are sequences of operations for which you must instruct the calculator exactly how to evaluate the problem and produce the correct answer. For example: 4x (5+ 9) + (7 -4)2*9 = 2 To evaluate this expression as written using only the calculator hierarchy, many independent steps would be required. Also, intermediate results would have to be stored and the sequence certainly could not be input in the same order in which it is written. Parentheses should be used here and whenever a mathematical sequence cannot be directly entered using the previously mentioned algebraic rules or to simplify entry of a problem without reference to the hierarchy rules. To illustrate the benefit of parentheses, try the following experiment: Press (5 x 7), and you will see the value 35 displayed. The calculator has evaluated 5 x 7 and replaced it with 35 even though the [=] was not pressed. Because of this function of parentheses, the algebraic rules now apply their hierarchy of operations to each set of parentheses. Use of Parentheses ensures that your problem can be keyed in just as you have written it down. The calculator remembers each operation and evaluates each part of the expression as soon as all necessary information is available. When a closed parenthesis is encountered, all operations back to the corresponding open parenthesis are completed. 18 Example: 4 x (5 + 9) + (7 — 4)?** =0.2304527 Key in this expression and follow the path to completion. Enter Press Display Comments 4 Go 4. (4x) stored pending evaluation of parentheses 5 5. (5+) stored 9 14. (5 + 9) evaluated 56. Hierarchy evaluates 4x14 56. 56 + stored pending evaluation of parentheses (7-) stored (7 — 4) evaluated Prepares for exponent ARON ) 3 (2+ 3) evaluated 0.2304527 (7 — 4)'** evaluated then it is divided into 4x (5+9) There are limits on how many operations and associated numbers can be stored. Actually, as many as nine parentheses can be open at any one time and four operations can be pending, but only in the most complex situations would this limit be approached. If you do attempt to open more than 9 parentheses or if the calculator tries to store more than four operations, the display flashes. WHERE B WEE 19 Example: 5 + {8/[9 — (2/3)]} = 5.96 Enter Press Display Comments 5 5. 8 8. 9 9. 2 2: 3 0.6666667 (2/3) evaluated 8.3333333 [9 — (2/3)} evaluated 0.96 {8/[9—(2/3)]}} 5.96 5+ {8/[9— (2/3)]} Because the [=] key has the capability to complete all pending operations whenever it is used, it could have been used here instead of the [_) | keys. Try working this problem again and pressing [=] instead of the first DO]. ‘oh Example: 3 x (42°) = 4.700434 Enter Press Display Comments {eur} LC} 0. 3 GICO 3. 4 pe ted all 4. 2 IO 2. ? ikea 7 4 oO 1.6265766 VF ~1.6265766 ~(V7) O04 0.3238558 2% jax) 1.56668 11 4-923... OI 4.7000434 axa Each time a closed parenthesis is encountered, the contents are evaluated back to the nearest open parenthesis and are replaced with a single value. Knowing this you can structure the order of interpretation for whatever purpose you may want. Specifically, you can check intermediate results. 20 IV. MATH FUNCTIONS The simplest operations to describe and understand are the single-variable functions. These functions operate on the displayed value immediately, replacing the displayed value with its corresponding function value. These functions do not interfere with any calculations in progress and can therefore be used at any point in a calculation. Be sure that each calculation has been completed before the next key is pressed. Key entries are not recognized while a calculation is being performed. RECIPROCAL AND FACTORIAL (%] Reciprocal Key — Calculates the reciprocal of the value, x, in the display register by dividing x into 1. x#0. (2nd) 3M Factorial Key — Calculates the factorial (1x2x3x4x..x x) of the value, x, in the display for integersO = x= 69. O!= 1 by definition. Example: 1/3.2 = 0.3125 Enter Press Display 3.2 Vx 0.3125 Example: 1/(—12 + 5!) = 0.0092593 Enter Press Display 12 + =12. 5 (2n¢) Ea 120. =) 108. () 0.0092593 Note that as soon as one of the math function keys is pressed, the displayed value is immediately replaced with its corresponding function value. LOGARITHMS {Inx] Natural Logarithm Key — Calculates the natural logarithm (base e) of the value, x, in the display register. x > 0. 21 (2nd) EE Common Logarithm Key — Calculates the common logarithm (base 10) of the value, x, in the display register. x > 0. Example: log(1 + In 1.7) = 0.1848697 Enter Press Display xa) 1 1. 17 {inz) 0.5306283 Oo 15306283 (2nd) 0.1848697 POWERS OF 10 ANDe (2*] e to the x Power Key — Calculates the natural antilogarithm of the value, x, in the display register. —227.95592 = x = 230.25850. Ei 10 to the x Power Key — Calculates the common antilogarithm of the value, x, in the display register. -99 =< x < 100 Example: e® + 1°” = 147.71169 Enter Press Display 3 3. 3 1.9952623 OI 4.9952623 | id) 147.71169 ANGLE CALCULATIONS Your calculator provides maximum flexibility when performing calculations involving angles. Angular Modes Angles can be measured in degrees, radians or grads (right angle = 90° = 7/2 radians = 100 grads). You select the mode desired by pressing either Gg. (2nd) EE or I. The calculator powers-up in the degree mode and stays in that mode until altered by one of the other choices. Once in a certain angular mode, all entered and calculated angles are measured 22 in the units of that mode until another mode is selected, (2nd) is pressed or until the calculator is turned off [2nd) IM restores the degree mode. [CE] and [ctr] do not affect the angular mode. The angular mode has absolutely no effect on calculations unless the trigonometric functions or polar to rectangular conversions are being performed. Selecting angular mode is easy —and easy to forget. Neglecting this step is responsible for a large number of errors in operating any calculation device that offers a choice of angular units. TRIGONOMETRIC FUNCTIONS (sin) , , [tan] Trigonometric Keys — Calculates the sine, cosine or tangent of the value in the display register. Example: sin 30° + tan 315° = -0.5 Enter Press Display Lich 0 30 (sin) (#] 05 315 {tan} “1 & -0.5 Trigonometric values can be calculated for angles greater than one revolution. See page 85 for additional information. HYPERBOLIC FUNCTIONS EES , (2n¢] SY , (2nd) FEY Hyperbolic Function Keys Calculates the hyperbolic sine, cosine or tangent of the value x in the display register. |x| = 227.95592 for sinh and cosh. Example: tanh (100 = 3.3 x 10?) = 2.940833 x 107' Enter Press Display 100 & 100. 332 & 3.030303-01 (2nd) EE 2.940833-01 23 INVERSE TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS {INV} Inverse Key —Preceding another key, reverses the intention of that key. When used with the trig or hyperbolic functions, the inverse of those functions is obtained. For example, arcsine (sin~') is obtained by pressing [INV] [Sin] , hyperbolic arctangent (tanh™') results from [INV] (2nd] (EY - The inverse trig functions calculate the angle whose functional value is in the display. The largest angle resulting from an arc function is 180 degrees (7 radians or 200 grads). Because these functions have many angle equivalents, i.e., arcsin .5 = 30°, 150°, 390°, etc., the angle returned by each function is restricted as follows: Arc Function Range of Resultant Angle arcsin x (sin~* x) 0 to 90°, 7/2 radians, or 100G arcsin—x(sin“'—x) 0to—90°, — 7/2 radians, or —100G arccos x (cos™' x) 0 to 90°, 7/2 radians, 100G arccos — x (cos*'~ x) 90° to 180°, 7/2 to z radians, or 100 to 200G arctan x (tan™’ x) 0 to 90°, 7/2 radians, or 100G arctan—x(tan"'—x) Oto —90°, —7/2 radians, or —100G For arcsin x and arccosin x, -1 = x = 1. Example: 7/4 + tan~ (.27) = 1.3463803 Enter Display 0 3.1415927 4 0.7853982 2 0.6283185 0.5609821 1.3463803 24 The selection of the radian mode could have been made at any point before [INV] [tan] . Note the following restrictions. arcsinh x (sinh * x) —10% < x < 10° arccosh x (cosh’' x) 1=x< 10° arctanh x (tanh ' x) td a ed, Example: .25 + tanh ' (.866) = 15668563 Enter Press Display 25 ) 0.25 866 — [inv] [2nd] MY 1.3 168563 =) 1.5668563 SQUARE AND SQUARE ROOT (#2) Square Key — Calculates the square of the number in the display register. 10°*9 = |x| < 10° (= ] Square Root Key — Calculates the square root of the number in the display register. x > 0. Example: [\ 3.1452 — 7 + (3.2)?]'? = 2,2390782 Enter Press Display 3.1452 COG) 1.7734712 7 —5.2265288 3.2 (=) 10.24 fa 5.0134712 2.2390782 25 UNIVERSAL ROOTS AND POWERS Universal Power Key — Raises the display register value, y, to the x power. The entry sequence is y [¥*] x followed by an operation key or equal. y = 0 [=| Universal Root Key — Takes the x root of the value, y, in the display register. The entry sequence is y #4 x followed by an operation key or equals. y = 0,x = 0 ‘¥) x Exchange y Key — interchanges the x andy es after they have been keyed in. Can also be used with arithmetic operations and special calculations. These math functions do not act on the display register immediately. They require entry of asecond value followed by an operation before the function can be realized. Example: \ 2.36” = .9362893 Enter Press Display Comments 2.36 [Ea 2.36 Enter y for y* 23 os -0.23 Enter x for y* irra 0.8207866 Produces y for Vy 3 3) 0.9362893 Enter x for Vy and produce answer Note that logarithms are used in computing universal powers and roots. Therefore, a few entries involving negative numbers, zero and one are invalid and will produce a flashing display. Forexample, any negative y value will cause a flashing display. 26 PERCENT AND CHANGE PERCENT Percent Key — Converts the displayed number from a percentage to a decimal. (2nd) EZ Percent Change Key — Calculates the percentage change — two values. Press x, (2nd) EWA x, [=] and ~—*2 == x 100 is calculated. Example: 43.6% = ey Enter Press Display 43.6 C" 0.436 Example: What is the percentage increase (markup) of a $766.48 refrigerator that wholesales for $515.22? Enter Press Display 766.48 (2nd) 766.48 515.22 Ee 48.767517 The refrigerator has been marked up almost 49%, When is pressed after an arithmetic operation, add-on, discount and percentage can be computed. (=) adds n% to the displayed value | Example: What is the total! cost of a $45 pair of boots when there is a 5% sales tax? Enter Press Display 45 45. 5 2.25 3) 47.25 Note that the percent (tax) is shown for recording, if necessary, then the total is displayed. 27 (=) subtracts n% from the value Example: How much do you have to pay for a$110 sleeping bag that has been discounted 15% with 6% sales tax? Enter Press Display Comments 110 oa 110. Enter amount 15 [%]} 16.5 15% of 110 GI 93.5 110-15% 6 5.61 6% of 93.50 &) 99.11 Total Cost {XJn (=) multiplies the displayed value byn% Example: If you have hiked 35% of a 62-mile trail, how far have you traveled? In other words, what is 35% of 62? Enter Press Display 62 Ca 62. 35 0.35 t=] 21.7 You have traveled 21.7 miles. jn (=) divides the displayed value by n% Example: If you have eaten 9 meals and find that 30% of your food supply is gone, how many meals will your initial food supply provide? 9 is 30% of what number? Enter Press Display 9 9. 30 0.3 Ee 30. Your initial food supply will provide for 30 meals. 28 V. MEMORY CAPABILITIES Your calculator has ten user-accessible memories to greatly increase the flexibility of calculations. Because there are ten memories, you must specify which memory you are addressing by entering its number, n=O thru 9 immediately after pressing any memory related key. Failure to enter one of these numbers after a memory key results in a flashing of the current display value. These memory registers can store or accumulate data for later use, in a variety of ways. STORING AND RECALLING DATA n Store Key—Stores the display value into memory register n.n= 0 thru 9. Any previously stored data in nis cleared. {RCt] n Recall Key — Recalls and displays the value stored in memory register n and retains the value in memory. A recalled number can be used as a number entry in any mathematical expression..n= 0 thru 9. Example: Store and recall 3.012 in memory 2. Enter Press Display 3.012 [Sto] 2 3.012 {cur} 0 2 3.012 Use of these keys can save you keystrokes by storing long numbers that are to be used several times. Example: Evaluate 3x? — x — 7.1 for x= 2.9467281 Enter Press Display {cir} 0 3 4] 3. 2.9467281 [sto] 1 2.9467281 (=) 8.6832065 f=9 26.049619 ¢ 2.9467281 f=) 23.102891 7A = 16.002891 n © The long value of x only had to be entered once. The storage and recall did not interfere with calculator operations. The memories can also be used to hold intermediate results as well as repetitive numbers. Example: Evaluate {sin(3x/2) — cos(3x/2)] x SEE) for x = 20.682177 degrees Enter Press Display Comments (2nd) 0. 3 6-4) 3. 20.682177 [sTo) 1[+] 62.046531 Store x 2 (1) [sto] 2 31.023266 Store 3x/2 [sin] [=) 0.5153861 {Rel} 2 31.023266 Recall 3x/2 0.8569581 Cos(3x/2) -0.341572 20.682177 ~— Recall x ~—0.0165153 = Answer MEMORY ORGANIZATION Because of the complexity of some of the statistical calculations, the calculator preempts certain memories to store data and results for these advanced computations. Also, memories 8 and 9 are used for storing program steps 17 through 31 (steps 17-24 in memory 9, steps 25-31 in memory 8). The chart below shows the arrangement and use of the calculator’s 10 memories. Memory Number o | 1 * eens. | 4 iter] 6 fevelese| 0 STATISTICAL CALCULATIONS PROGRAMMING Cleared By [2nd] [J ———_——_>| 30 DIRECT REGISTER ARITHMETIC You can store a displayed number at any time during a calculation without affecting the calculation in any way. Additionally, you can add, subtract, multiply and divide the displayed value for calculations in progress. Pressing [El clears the memories as well as the entire calculator. n Sum Key—Adds the displayed value to the content of memory register n and stores the result in n. n= Othru9 (inv) n Subtract Sequence — Subtracts the displayed value from the content of memory register n and stores the result inn.n=0thru9 n Product Key —Multiplies the content of memory register n by the displayed value and stores this product inn.n=0thru9 inv) GM n Divide Key — Divides the content of memory register n by the displayed value and stores the resultinn.n=Othru9 These capabilities eliminate the lengthy recall, perform operation, store-again sequences. Example: Evaluate x? + 9 for x = —1, 2,3 and total the results. Enter Press Display Memory 3 1 ees) 1. 0 9 (=) S19) 3 10. 10 2 ZG) 4. 10 9 (=) sum 3 13. 23 3 9. 23 9 18. 41 3 41. 41 Notice that the first evaluation was placed in memory 3 using the [ST] key. The clears any previous content of that register before storing the new value. 31 Example: The percentage of students completing each year at a particular college is 76.8% first year, 81.3% second year, 92.2% third year and 95.9% last year. What percentage of the students graduate and what percentage complete their third and fourth years? Enter Press Display 76.8 Go 0.768 81.3 Gd 0.624384 92.2 (sto) 11) 0.575682 95.9 (2nd) G1 (=) 0.5520791 (Re 1 0.884198 About 55% of the students that enter the school graduate. Over 88% of those entering their junior year graduate. MEMORY/DISPLAY EXCHANGE (2nd) EB} n Exchange Key — Exchange the content of memory register n with the display. The display value is stored and the previously stored value is displayed. The exchange key has several uses. You can use it to examine two results without losing either. Also, numbers can be temporarily stored and used as needed. Example: Evaluate A? + 2AB + B* for A= 0.258963 and B= 1.255632 Enter Press Display Comments -258963 — (STO) 1 [x#) 0.0670618 Store A 1.255632 [X] 1.255632 Enter B (2nd) EH 4 0.258963 Store B, RecallA 0.3251622 AxB 0.7173863 A’ + 2AB 1.255632 Recall B 1.5766117 B? 2.293998 Answer 32 VI. SPECIAL CALCULATIONS There are several often-used mathematical sequences that have been programmed into your calculator. These operations have been specially designed to provide optimum calculator efficiency by minimizing th