Manual / Guide · c. 1982
TI-30 SLR Owner's Manual
Texas Instruments' owner's manual for the TI-30 SLR.
Manual / Guide · c. 1982
Texas Instruments' owner's manual for the TI-30 SLR.
TEXAS INSTRUMENTS TI-30 SLR LIGHT POWERED CALCULATOR QUICK REFERENCE GUIDE KEY INDEX This indexed keyboard provides a quick page reference to the description of each key. 2 G2 2 & 6 @ 6 cS 35 CG 7 G32 G32 G32 &e)31 W224 G7 30 Me Wa W119 @37 @M5@5@5 @37 ©5@ 5 G38 CG) 5 @ 5 2 28 G4zo M505 IMPORTANT Record the serial number from the bottom of the calculator and the pur- chase date in the space below. The serial number is identified by the words “SERIAL NO.” on the bottom case. Always refer to this information in correspondence. TI-30 SLR Model No. — Serial No. Purchase Date Texas Instruments reserves the right to make changes in materials and specifications without notice. Copyright ©1982 Texas Instruments Incorporated TABLE OF CONTENTS DESCRIPTION Features and Functions. . . See . BASIG OPERATIONS. «0... ssc tscnene 3 Turning the Calculator On and Off 3 Display Indicators . . 4 DataEntry .. 5 Clearing . . 6 Inverse and Alternate Functions . is Scientific Notation . . ot Error Indication .... «td: Accuracy and Rounding. . . 12 ARITHMETIC FUNCTIONS .. 13D) Basle Keys’... 5.55.65. . - 13 Input Error Correction 14 Combining Operations. . . 18 Calculator Hierarchy .. . a) Parentheses........... - 19 Calculations with a Constant . - 24 . SPECIALFUNCTIONS....... - 26 Roots and Powers .. - 26 Reciprocal . . . 2 Factorial . - By Percent. . - 28 Natural Logarithm and Natural Antilogarithm ...........-..-.. 30. Common Logarithm and Common Antilogarithm . . . . 30 Trigonometric Functions . . AK Degree, Radian, Grad CONICS 6 555 = ccentisie nes 0.55 ate 36 MEMORY USAGE . . en Memory Clearing . Ft Memory Store. . HH Memory Recall . ear Sum to Memory .. . 38 Memory Exchange.......1...-..-..-.. 40 TABLE OF CONTENTS (continued) APPENDIX A Hyperbolic Functions Inverse Hyperbolic Functions . . APPENDIX B Conversion Factors . . . English to Metric . . Temperature Conversions . . APPENDIX C Service Information In Case of Difficulty . . If You Need Service Information Calculator Exchange Centers . WARRANTY INFORMATION |. DESCRIPTION We live in a world of mathematics. It is a part of our daily lives. Our science, technology, and business are absolutely dependent on it. It is more iMportant than ever that we understand how to make math work for us. But while math can be of great practical use, the often tedious and time consuming arithmetic has lead many people to believe that mathematics is beyond them. Adding, subtracting, multiplying, and dividing very cumbersome numbers can easily obscure the simplicity of the math itself. Your calculator is designed as a tool to remove most of the tedium and allow you to better understand the math behind the arithmetic. However, a calculator is “no more functional than the person who operates it”. As with any tool, whether it’s a pen, wrench, radio, or whatever, it's important to learn how to use it properly. This manual is designed to help you learn the capabilities of your calculator and how to use them. Here are a few of the calculator’s features. Features and Functions * Solar power cells located below the display operate your calculator wherever there is a source of light. Indoors or outdoors, direct or in- direct lighting. Any normal reading light level is adequate. * Never any batteries to replace. The solar power cells totally eliminate the need for batteries. * Easy to read Liquid Crystal Display (LCD). * AOST™ Algebraic Operating System provides a fixed set of rules for evaluating mathematical expressions. Even complicated problems may be entered simply and directly. * 50 Calculator Functions Arithmetic Data Entry Display Algebraic Clearing Data Grouping Memory Percent Trigonometric Angular Conversion Logarithmic Constant +, -,% + +/-,% Scientific notation x2, VX, 1x, yx, xVY, x! Clear, Clear Entry, All Clear AOS algebraic operating system. Open and close parentheses (up to 15), and full algebraic hier- archy (up to 4 pending operations). One memory with store, recall, sum, and exchange %, +%, —%,x%, =% Sin, Cos, Tan, Sin-1, Cos-1, Tan-1, and 3 angular modes. (Degrees, Radians, Grads) Degrees to Radians to Grads Inx, log, ex, 10x Operates with +, —, x, +, YX, and x/y © O25 o Blow © Accuracy—The internal calculating capacity is 11 digits even though only 8 can be displayed. The 8-digit displayed number is generally rounded to within +1 in the 8th digit for all functions except where noted. Il. BASIC OPERATIONS Your calculator is easy to operate because of its exclusive AOSTM Algebraic Operating System which allows a simple straightforward entry of most problems. Although many operations may be obvious, the following instructions and ex- amples will help you develop skill and confidence in problem solving. Turning the Calculator On and Off Notice the absence of an ON or an OFF key. To turn the calculator on, simply expose the solar power cells to any adequate light source. “DEG” and “0.” normally appear in the display. However, random segments and indicators may appear in the display. These do not affect normal operations of the calculator and are replaced with “DEG” and “0.” when the calculator is cleared. The calculator will remain on as long as the solar cells are exposed to light. The length of time before the display appears depends on the intensity of the light source, but under normal lighting conditions this time is within a few seconds. Under indirect or low-level lighting, covering even a portion of the solar cell panel may cause the display to disappear. Always be sure the entire panel is exposed to light. When the calculator is first “turned on,” be sure o completely clear the calculator by pressing To turn the calculator off, simply remove the solar cells from the light source. This is most easily done by closing the flap of the calculator’s carrying case. The calculator does not normally lose power until approximately 15 seconds after the light source is removed. If the solar cells are again exposed to light within 15 seconds, the previous display, any pending operations, and the memory are normally restored. Even though there are no batteries to run down, leaving the calculator on for very extended durations may reduce the operating life of the calculator.Therefore, it is suggested that the calculator be “turned off” when not in use. Never leave your calculator in direct sunlight for long periods or store it where high temperatures are possible. Display Indicators Error Indicator Floating Minus Sign rt Memory Indicator MAW 4e AA Eoooooooe. INV K DEG RAD GRAD () 1 1 Constant Open Indicator Parenthesis Inverse Angular !ndicator Indicator Mode Indicators NOTE: Eight digits may be entered into the display. Any digit keys pressed after the eighth are ignored. Memory Indicator— M—lIndicates a non-zero number is stored in the memory. Angular Mode Indicators— DEG—Indicates degree mode. RAD—Indicates radian mode. GRAD—Indicates grad mode. Inverse or Alternate Function Indicator— INV—Indicates inverse is in effect. Open Parenthesis Indicator— ()—Indicates an unpaired open parenthesis. Constant Indicator— K—Indicates constant is in effect. Error Indicator— E—Indicates an error condition. Floating Minus Sign— Any negative number is displayed with a minus sign immediately to the left of the number just as negative numbers are normally written. Data Entry For maximum versatility, your calculator operates with a floating decimal point. When entering numbers, the decimal is assumed to the right of the mantissa until CJ is pressed. Then the fractional part of the number is entered and the decimal point floats with the entered number. A maximum of 7 digits may be entered to the right of the decimal. ©) through (2) Digit Keys—Enter numbers 0 through 9. ©) Decimal Point Key—Enters a decimal point. A decimal point is automatically displayed to the right of an integer. Change Sign Key—When pressed after a number entry or a calculation, changes the sign of the displayed number. The sign of the exponent is changed when this key is pressed after the CE) key. C= Pl Key—Enters the value of pi correct to 11 digits. This value is rounded to 8 digits (3.1415927) for display. Numbers up to 8 digits in length can be entered into the calculator directly from the keyboard. The calculator can hold and work with 11 digits. Numbers of this length can be entered as the sum of two numbers. Example: Enter 123456.78943 Enter Press Display 123456 123456. 78943 S 123456.79 Notice the rounding of the eighth digit in the display. Clearing Clear Entry/Clear Key— Removes an incorrect entry from the display when pressed before any function or operation key is pressed. When pressed after an operation or function key (including )), this key clears the display, the constant, and all pending operations. Pressing always clears the display, the constant, and pending operations. The memory is not affected by this key. Ge) All Clear Key—Clears the display, the constant, and pending operations as does & However, GE) also clears the memory and sets the angular mode of the calculator to degrees. NOTICE: It is a good practice to clear the calculator with €) or whenever possible. (4¢) should be used only to clear the calculator when it is first “turned on” and before beginning any calculation which requires a clear memory. During a memory calculation, this practice will prevent you from inadvertently clearing the memory. Inverse and Alternate Functions (@) Inverse Key—Selects the inverse or the alternate function of the next key pressed. The display shows “INV” while inverse is in effect. Inverse has no effect and is cancelled if the next key pressed has no inverse or alternate function, or if 4) is pressed again. Keys affected by inverse are those on the second and third rows (except) and e). Factorial and angular conversions are alternate functions of and, (as), Scientific Notation Scientific notation allows you to enter very large or very small numbers, where the number is entered as a mantissa multiplied by 10 raised to some power (exponent), such as — 3.6089 x 10-32. Mantissa Exponent ! : raed =a [st 2 a eer So | ‘ ! 1 pa a mi = t U 7 O x ou: Lr ce hr ~ Le St ved a= T Exponent Sign Floating Mantissa Sign CE) Exponent Entry Key—When pressed after a keyboard entry or calculation, prepares the calculator to accept the next digits entered as the exponent. 1 GDS Scientific Notation Key Se- quence—Converts a number in standard display format to scientific display format. IMPORTANT: Pressing without press- ing GO 1 may result in the calculator using only the eight displayed digits for subsequent calculations and discarding the internally car- ried guard digits. GOED Scientific Notation Removal Key Se- quence—When pressed after a function key, removes the displayed number from scientific notation if it is between +1x 10-7 and + 9.9999999 x 107, and displays it in standard display format. If the displayed number is out- side the range listed above, the scientific nota- tion removal key sequence will be ignored and the number will remain in scientific notation format until the number is within the standard display range. The entry procedure is to key in the mantissa (including its sign), press (££), and enter the power of ten. Any number smaller than +1x10-7 or larger than + 99999999 must be entered in scientific notation. The number 320,000,000,000 can be written as 3.2 x 1011 and can be entered into the calculator as Enter Press Display ee 0. 3.2 ic3) 3.2 00 11 3.211 The last two digits on the right side of the display are used to indicate the exponent of 10. Additional digits can be entered after pressing (£8), but only the last two numbers pressed are retained as the exponent. In scientific notation, a positive exponent in- dicates how many places the decimal point of the mantissa should be shifted to the right. If the exponent is negative, the decimal should be shifted to the left. Regardless of how a mantissa is entered in 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. Enter Press Display ea 0. 6025 @ 6025. 00 20 6025. 20 S 6.025 23 The decimal point of the entered mantissa must not be beyond the 5th digit from the left because the mantissa for scientific notation is limited to 5 digits in the display. Eight digits can be entered, but only 5 are displayed when (£5) is pressed. However, the entire eight digit mantissa is used for calculations. The display does not go into scientific notation format if more than 5 numbers are entered to the left of the decimal point. The change sign key can be used to attach a negative sign to the mantissa and to the power-of-ten exponent. Example: Enter — 4.818 x 10-10 Enter Press Display 33) 0. 4.818 Beep — 4.818 00 10 wD — 4.818-10 Any displayed value can be easily converted from standard display format to scientific nota- tion by pressing GO 1 GE). Example: 89 x 987 = 87843 = 8.7843 x 104 Enter Press Display ee 0. 89 ea) 89. 987 @oo 87843. 1 cr3 ea) 8.7843 04 Data in scientific notation form may be entered intermixed with data in standard form. The calculator converts the entered data for proper calculation. Example: 3.2 x 103 + 12575.321 = 15775.321 Enter Display 3.2 3.2 00 3 3.2 03 12575.321 1.5775 04 15775.321 Notice that the complete answer to the problem is 15775.321 and this is the number used for further calculations. Actually, the calculator internally carries all intermediate calculations and final results to 11 places. These numbers are rounded to a maximum of 5 digits for a scientific notation mantissa or to 8 digits for standard display. Error Indication The display shows “E” and “0.” whenever overflow or underflow occurs or when an im- proper mathematical operation is requested. When this occurs, no entry from the keyboard is accepted until or Gs) is pressed. Press- ing clears the error condition and all pend- ding operations. Pressing G=) clears the error condition, all pending operations, and the memory. You must now return to the beginning of your problem and start again. 10 “E” appears for the following reasons. we en 10. Number entry or calculation result (in- cluding memory sum) outside the range of the calculator, + 1.0 x 10-99 to + 9.9999 x 1099. Dividing a number by zero. Calculating Gs), =), or C2) of zero. Calculating the Oth root of any number or the Oth power of zero. Calculating (3), (=), a power, or a root of a negative number. Inverse of sine or cosine (arcsine, arc- cosine) when the absolute value is greater than 1. Tangent of 90°, 270°, 7/2 radians, 3 7/2 ra- dians, 100 grads, 300 grads, or their rota- tion multiples like 450°. Having more than 15 open levels of paren- theses with each pending operation or more than four pending operations. Factorial of any number except a non- negative integer < 69. Multiplying numbers with negative ex- ponents when the sum of those exponents (as displayed in normalized scientific nota- tion format) exceeds — 99. Example: 4x 10-45x5x10=9=20 10-100 =2x 10-99 This example produces an error because of the — 100 exponent in the intermediate result, even though the final result is within the range of the calculator. = Accuracy and Rounding Each calculation produces an 11-digit result. These 11 digits are more than can be displayed. The result is, therefore, rounded to an 8-digit standard display or to a 5-digit mantissa and 2-digit exponent for scientific notation. The 5/4 rounding technique built into this calculator adds 1 to the least significant digit of the display if the next, non-displayed digit is five or more. If this digit is less than five, no rounding is applied. In the absence of these extra digits, inaccurate results would frequently be displayed, such as 1+3x3=0.9999999 However, because of rounding, the internal 11-digit string of nines in your calculator is rounded to 1 in the display. The higher order mathematical functions use iterative calculations. The cumulative error from these calculations in most cases is maintained beyond the eight-digit display so that no inaccuracy is displayed. Most calculations are accurate to + 1 in the last displayed digit. There are a few instances in the solution of high-order functions where display accuracy begins to deteriorate as the function approaches a discontinuous or undefined point. These particular instances are noted where appropriate. 12 lll. ARITHMETIC FUNCTIONS This calculator uses the AOSTM Algebraic Operating System. This advanced system allows key sequences to be interpreted correct- ly by storing certain quantities and operations until they can be completed following standard algebraic rules. A more complete discussion of this system occurs later in this section. Basic Keys @ Add Key—Completes any previously entered +, —, X, +, y%, or */y function when not separated by an open parenthesis and in- structs the calculator to add the next entered quantity to the displayed number. © Subtract key—Completes any previously entered +, —, x, +, y%, or %\/y function when not separated by an open parenthesis and in- structs the calculator to subtract the next entered quantity from the displayed number. C® Multiply Key—Completes any previously entered x, +, yx or xy function when not separated by an open parenthesis and in- structs the calculator to multiply the displayed number by the next entered quantity. Divide Key—Completes any previously entered x, +, yx or %\/y function when not separated by an open parenthesis and in- structs the calculator to divide the displayed number by the next entered quantity. © Equals Key—Combines all previously entered numbers and operations. This key is used to obtain both intermediate and final results. 13 Example: 23.79 + 0.54 — 6 = 18.33 Enter Press Display [e73) 0. 23.79 23.79 54 S 24.33 6 S 18.33 Notice the straightforward manner in which the numbers and functions are entered. In the following examples, notice that @ need not be pressed if the preceding problem has been completed with an @). Example: -—3.7 —(—7.09)+.014=3.404 Enter Press Display 3.7 ee) -3.7 7.09 GAG 3.39 014 So 3.404 Example: -4x7.3+2= Enter Press Display 4 G2aGo 4. 7.3 = 29.2 2 -146 Input Error Correction At any point in a calculation, @® can be press- ed twice to clear all calculations, including any errors, and start over. 'f an incorrect number entry is made, pressing the key before any non-number key clears the incorrect number without affecting any calculation in progress. Press Ge) only if you wish to clear all calcula- tions, including any errors, and the memory. 14 When there are no stored operations, as when the first operation is keyed in, and an un- wanted operation key is entered, simply press the correct operation and continue. This ap- plies to @), ©), GO, G), @, and IG. If an incorrect operation is entered while there al nding calculations, it is safest to press and restart the problem. Combining Operations After a result is obtained in one calculation, it may be directly used as the first number in a second 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 184 @ 1.84 323 LW 2.23 1.844+0.39 2.23 365 0.0061096 | 2.23 + 365 Calculator Hierarchy In order to efficiently combine operations, the AOS™ Algebraic Operating System provides the calculator with a fixed set of standard algebraic rules. These rules assign priorities to the various mathematical operations. Without a fixed set of rules, expressions such as 5x4+3%x 2 could have several meanings: 5x(4+3)x2=70 or (5x 4)+ (3x 2)=26 or (5 x 4)+3)x 6 or 5x (4+ (3x 2))=50 15 Algebraic 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 ex- pressions is 1. Single-variable functions 2. Exponentiation (yx), Roots (x/y) 3. Multiplication, Division 4. Addition, Subtraction 5. Equals 1. Single-variable functions (trigonometric, logarithmic, square, square root, factorial, percent and reciprocal) immediately replace the displayed value with their respective functions. 2. Exponentiation (yx) and roots (xVy) are per- formed as soon as the single-variable func- tions are completed. 3. Multiplicaton and division are performed as soon as the special functions, exponentia- tion, root extraction and other multiplication and division are completed. 4. Addition and subtraction are performed only after all operations through multiplication and division as well as other addition and subtraction are completed. 5. Equals completes all operations. 16 To illustrate, consider the interpretative order of the following example: Example: 4+52x7+3 x .5cos 60° — 3.241321 Enter Press Display Comments G& 0. Clears calculator and sets angular mode to degrees 4. (4 +) is stored 5 G@ 25. (52) single- variable func- tion G evaluated immediately cw 0.16 (4+52) evaluated because x is same priority as + 1.12 x higher prior- ity than +, so (4+52x7) evaluated, + stored aw 3. (3 x) stored ) [ea3) 0.5 (.5 yx) stored. 60 Ges) 0.5 cos 60° evaluated immediately S 3.2413203 Completes all operations: (.5cos 60°) evaluated, then (3 x .5cos 60°) next, then this is added to 1.12. 17 The important thing to remember here is that operations are performed 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 execu- tion 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. NOTE: The keys on the right side of your calculator are positioned in such a way as to help you remember the AOSTM hierarchy. Exponentiation and roots Division and Multiplication Subtraction and Addition “Equals” which completes all operations. All single-variable functions when pressed are performed on the displayed number immediately. HHO8H8 18 Parentheses (OG) Parentheses Keys—'solates particular numerical expressions for separate math- ematical interpretation. When CZ is pressed after a pending operation, “()” appears in the display until all parenthesis pairs are completed. 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+3)=? To evaluate this expression using only the calculator hierarchy, many independent steps would be required. Also, intermediate results would have to be stored and the sequence cer- tainly would be more difficult to enter. Parentheses should be used here and whenever a mathematical sequence cannot be directly entered using the previously mentioned algebraic rules or when there is doubt in your mind as to how the calculator is going to reduce an expression. NOTICE: You may see equations or expres- sions with parenthesis indicating implied multiplication: (2+ 1) (3+ 2)=15. Your calculator will not perform implied multiplica- tions. An operation must be entered between parentheses: (2+ 1) x (3+2)=15. 19 To illustrate the benefit of parentheses, try the following experiment: press 0) 5 9C), and you will see the value 14 displayed. The calculator has evaluated 5+ 9 and replaced it with 14 even though the (=) key was not pressed. Because of this function of parentheses, the algebraic rules now apply their hierarchy of operations within each set of parentheses. Use of parentheses insures that your problem can be keyed in simply and directly. The calculator remembers each operation and evaluates each part of the expression as soon as all necessary information is available. When a closed paren- thesis is encountered, all operations included within the parenthesis pair are completed. Open parentheses have the additional capabili- ty of supplying a missing operand, as shown by the following example: Example: 4-(4+2)= -2 Enter Pre: Display 4 om 2 jas) Nip > If no value is entered after a CO, the calculator uses the value in the display register. In this example, 4 was automatically inserted before the +. Example: 4 x (5 + 9) + (7 — 4X\2+3) = 0.2304527 Key in this expression and follow the path to completion. Enter Press 4 coc 5 9 jan) [= 3) 7 {=a 4 i=") Gc 2 @ 3 wo eS Display 4. 0.2304527 21 Comments (4 x) stored pending evaluation of parentheses. (5 +) stored. (6+9) evaluated. Hierarchy evaluates (4x 14). (56 +) stored pending evalua- tion of paren- theses. (7 —) stored. (7-4) evaluated. Prepares for exponent. (2+3) evaluated. (7-4)(2+3) evaluated; then divided into 4x (5+9). There are limits on how many operations and associated numbers can be stored. Actually, as many as fifteen parentheses can be open at any one time and four operations can be pend- ing, but only in the most complex situations would these limits be approached. If you do at- tempt to open more than 15 parentheses or if the calculator tries to store more than four operations, “E” appears in the display. The following example, requiring the storage of 4 pending operations, shows the order of inter- pretation provided by the calculator’s operating system. Example: 5 + (8 = (9 — (2 + 3) =5.96 Enter Press Display Comments ) ew 5. (5 +) stored 8 ew 8. (8 +) stored 9 Geen 9. (9 —) stored 2 2. (2 +) Stored 3 jan) 0.6666667. (2+ 3) evaluated wo 8.3333333 (9—(2+3)) evaluated @ 0.96 (8+(9-(2+3)) S 596 5+(8+(9- (2+ 3) Because the ©) key completes all operations whenever it is used, it could have been used here instead of the three (1) keys. Try working this problem again and pressing &) instead of the first G0. 22 Each time a closed parenthesis is en- countered, 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. Example: 3 x (4(2~ AV) = 4.9053384 Enter Press Display Comments [373] 0. 3 eo 3. 4 @o 4. 2 wo bs 1 We 5. 4 [aa 1.4953488 (V3) (e723) -1.4963488 = — (4/3) oO 0.3546951 2-(4V5) ao 1.6351128 4.354... S 4,9053384 3.x 4.354... Note that in all these examples the expressions are entered in a simple and direct sequence. 23 Calculations With a Constant CG Constant Key—Stores a number and its associated operation for repetitive calcula- tions. Enter the number, then the operation, then press G2). “K” appears in the display un- til the constant is cleared. Repetitive calculations have been simplified through the use of the constant feature of the calculator. Entry of a recurring sequence such as +3, x(— 17.3) or y7 can be stored and used by the calculator to operate on any displayed number. To use the constant feature, enter the repetitive number, m, then enter the desired operation, then press G2). m@oo adds m to each subsequent entry m@G9 subtracts m from each subsequent entry m GoGo multiplies each subsequent entry by m m@G9 divides each subsequent entry by m raises each subsequent en- try to the mth power m @)G5G9 takes the mth root of each subsequent entry After storing the constant, each calculation is completed by entering the new number and pressing ©). The constant is cleared by press- ing @)@8, G), or any of the above arithmetic keys. 24 Using G2 in any other sequence than describ- ed above may affect entered numbers. Example: 31+ 1.8026 = 32.8026 745.797 + 1.8026 = 747.5996 — 8.002 + 1.8026 — 6.1994 3.2x 10-24 1.8026 = 1.8346 Enter Press Display ED 0. 1.8026 1.8026 co] S 32.8026 745.797 S 747.5996 8.002 ee) 6.1994 3.2 ic3) 3.2 00 2 1.8346 00 Example: Evaluate (3.75) - 3.2, (.1066) - 3.2, (0692) - 3.2 Enter Display 0. 3.2 = 3.2. 3.75 0.0145579 -1066 1291.7455 0692 5148.2603 IV. SPECIAL FUNCTIONS The special function keys described in this section are single-variable functions except for y* and *\/y which are two-variable functions. The single-variable functions operate only on the displayed value without interfering with calculations in progress. The two-variable func- tions may be isolated within a calculation by parentheses or used with the calculator hierar- chy. NOTE: The display is blank during the short time the calculator is computing a result. Be sure the calculator has completed an operation before presssing the next key. Roots and Powers G2 Square Key—Calculates the square of the number x in the display. Example: (4.235)2 = 17.935225 Enter Press Display 4.235 Ge. 17.935225 Square Root Key—Calculates the square root of the number x in the display. The x value can- not be negative. Example: V6.25=2.5 Enter Press Display 6.25 (ca) 25 Example: (Vv 3.1452 —7 + (3.2)2)1/2 = 2.2390782 Enter Press Display 3.1452 1.7734712 7 — §.2265288 3.2 10.24 5.0134712 2.2390782 CG y to the xth Power Key—Raises the displayed value y to the xth power. Order of entry is y @) x. The y value cannot be negative, but both x and y can be fractional. GG (= x\/y) xth Root of y Key Sequence— Takes the xth root of the displayed value y. Order of entry is y GG) x. The y value cannot be negative but both x and y can be fractional. These two universal roots and powers functions are the only special functions that do not act on the displayed value immediately. They require a second value before the function can be realized. Use of these two keys is identical. Enter y, press G®) or G@)G®), enter x, and press ©) or an arithmetic function key to yield the answer. A closed parenthesis also completes these func- tions as well as other stored operations back to the nearest open parenthesis. Example: 2.86 ~-42 = 0.6431707 Enter Press Display 2.86 ee 2.86 42 wD —0.42 SoS 0.6431707 Example: 9'2V'7460 = 10.332744 Enter Press Display 1460 [73] 623) 1460. 3.12 Sa 10.332744 There is a restriction on these functions—the variable y must be non-negative. When y is negative, “E” appears in the display after x and an operation key are pressed. The value y eannot be negative because logarithms are used to per- form these functions. The Oth root of a number is not a natural mathematical operation and conse- quently results in an error conditiion. Any non- negative number taken to the zero power is 1. 27 For roots and powers, the calculator only carries its calculations to nine significant digits. Accuracy for these roots and powers is within + 1 in the 8th significant digit over all ranges except for values of y very near 1 and very large, exponents or very small roots. For example, 1 05719 is accurate for all displayed digits where 1.0000005 — 1,600,000 ig, accurate to only six digits. The error increases as y approaches 1 and the exponent becomes extremely large or when roots become extremely small. Reciprocal C@) Reciprocal Key—Divides the displayed value x into 1. x # 0. Example: | = 0.3125 3.2 Enter Press Display 3.2 0.3125 Factorial 3 Factorial Key—Calculates the factorial (x) (x — 1)(x — 2) ... (2)(1) of the value x in the display for integers 0 < x < 69. 0! =1 by definition. Example: 36! = 3.7199 x 1041 Enter Press Display 36 ica) =: 3.7199 41 Percent C@ Percent Key—Converts the displayed number from a percentage to a decimal. Example: 43.9% = .439 Enter Press Display 43.9 [e73) 0.439 28 When C2) is pressed after an arithmetic opera- tion, add-on, discount, and percentage can be computed as follows: n GE) adds n% to the number Example: What is the total cost of a $15 item when there is a 5% sales tax? Enter Press Display 15 15. 5 we 15.75 Gn GHG) subtracts n% from the number displayed. Example: How much is paid for a $5 item that has been discounted 2%? Enter Press Display 5 a, 5. 2 we 49 © n GE multiplies the number in the display by n%. Example: What is 2.5% of 15? Enter Press Display 15 w 15. 25 we 0.375 n C&)E) divides the number displayed by n%. Example: 25 is 15% of what number? Enter Press Display 25 25. 15 ee 166.66667 Natural Logarithm and Natural Antilogarithm (=) Natural Logarithm Key—Caiculates the natural logarithm (base e) of the number x in the display. x>0. Example: \n 1.2 =0.1823216 Enter Press Display 1.2 ic) 0.1823216 (@™)(=) Natural Antilogarithm (e to the xth power) Key Sequence—Calculates the natural antilogarithm of the number in the display. This sequence raises the constant e to the displayed power. Example: e3.81 = 45.150439 Enter Press Display 3.81 es) 45.150439 Example: e(7.5 + in 1.4) = 2531.2594 Enter Press Display Comments Sea 0. 755 GC 75 Enter 7.5 14 (cx3) 0.3364722. In 1.4 @ 7.8364722 = (7.5 + In 1.4) Ges) 2531.2594 Answer Note that the ©) key is not needed since the special function produces the final result. Common Logarithm and Common Antilogarithm (s) Common Logarithm Key—Calculates the common logarithm (base 10) of the number x in the display. x >0. Example: log 32.01 = 1.5052857 Enter Press Display 32.01 & 1.5052857 GOs) Common Antilogarithm (10 to the xth power) Key Sequence—Caiculates the com- mon antilogarithm of the displayed value. This sequence raises 10 to the displayed power. Example: 10-7.12=7.5858 x 10-8 Enter Press Display parr Bee 7.5858-08 Example: log (303 + 101.36) = 2.5130959 Enter Press Display Comments 303 303. Enter 303 1.36 CGw)es) 22.908677 101.36 a 325.90868 303 + 101.36 Gs) 2.5130959 = Answer The results from logarithms (natural and com- mon), when displayed in normal form rather than in scientific notation, are accurate within +1 in the last displayed digit, allowing for round off. Trigonometric Functions (85) Degree, Radian, Grad Key—Selects the units for angular measurement. When the calculator is first “turned on,” it is in the degree mode. Pressing the ©85) key once places the calculator in the radian mode. Press this key again and your angles are measured in grads (right angle = 100 grads). The mode changes in a rotary fashion each time the key is pushed. Another key push, for instance, returns the calculator to the degree mode. The display indicates the current angular mode of the calculator. “DEG” is displayed for degree mode. “RAD” is displayed for radian mode. “GRAD” is displayed for grad mode. 31 The angular mode has absolutely no effect on calculations unless the trigonometric functions are being used. Selecting the angular mode is an easy step to perform—and to forget! Neglecting this step is responsible for a large portion of errors in operating any calculating machine that offers a choice of angular units. Memory registers and calculations in progress are not affected by changing angular modes. When the trig functions (sine, cosine, and tangent) are activated, they compute their respective functions of the angle in the display. The inverse trig functions find the smallest angle whose function value is in the display. G®) Sine Key—instructs the calculator to find the sine of the displayed value. GG) Arcsin (sin- 1) Key Sequence— Calculates the smailest angle whose sine is in the display (first or fourth quadrant). =» Cosine Key—Instructs the calculator to find the cosine of the displayed value. (G@0G) Arccosine (cos - 1) Key Sequence— Calculates the smallest angle whose cosine is in the display (first or second quadrant). (=) Tangent Key—Instructs the calculator to find the tangent of the displayed value. (G@)(=) Arctangent (tan - 1) Key Sequence— Calculates the smallest angle whose tangent is in the display (first or fourth quadrant). 32 Trigonometric values can be calculated for angles greater than one revolution. However, in the radian mode, the rounded value of m may limit accuracy at very large rotational multiples of n and n/2. Sine and cosine functions are accurate throughout all displayed digits, except where noted above for the radian mode. The tangent of + 90°, + n/2 radians, or + 100 grads results in an error condition because the function is undefined at these points. Example: sin 30° =0.5=sin 390° Enter Press Display (select degree mode “DEG”’) 30 e 05 390 e& 0.5 Example: (sin (.301277)) — tan (16.2°) = 1.0626654 Enter Press Display Comments (select radian mode “RAD"’) 0. 3012 GO 0.3012 @e 3.1415927 a 0.9462477 (301277) & 0.8112271 sin (.301277) [e23) 0.8112271 16.2 (@nc)ora)(=) 0.2905269 tan (16.2°) Rme| 1.0626654 Answer The largest angle resulting from an arc func- tion is 180 degrees (7radians or 200 grads). Because certain angles have identical function values within one revolution, i.e. arcsin =.5 for 30° and 150°, the angle returned by each func- tion is restricted as follows: Arc Function Quadrant of for x 20. Resultant Angle arcsin x (sin-1 x) First (0 to 90°, 77/2, or 100 G) arcsin —x(sin-1 —x) Fourth (0 to —90°, — 7/2, or — 100 G) arccos x (cos—1 x) First (0 to 90°, 7/2, or 100 G) arccos —x(cos-1 —x) Second (90° to 180°, 7/2 to 77, or 100 to 200 G) arctan x (tan-1 x) First (0 to 90°, 77/2, or 100 G) arctan —x(tan-1 -—x) Fourth (0 to -90°, — 7/2, or — 100 G) Arcsin .5, for example, always returns 30° as the angle even though sin 150°=.5 and sin 390°=.5 as well. Example: sin-1 .712= 45.397875 degrees = 0.7923424 radians = 50.442083 grads Enter Press Display (select degree mode “DEG") 712 Mme) 45.397875 (select radian mode “RAD") 712 ME) 0.7923424 (select grad mode “GRAD”) ure GG) 50.442083 le: V 72° a = SiBORT?S degrees ost” BOE Enter Press Display Comments (select degree mode “DEG”) 9.72 Ges) 84126038 arctan 9.72 9.1720248 = V arctan 9.72 808 GG) 53.900984 = arcsin .808 ® 0.0185525 1/ arcsin .808 So 9.1905773 Answer Degree, Radian, Grad Conversions GES Conversion Key Sequence—Instructs the calculator to change angular mode and convert the displayed value to its equivalent angular value in the new mode. The key se- quences to make this conversion are simple, involving the @) and keys. The memory and calculations in progress are not affected by changing angular values. Be sure that the calculator is in the correct angular mode for entry of the angle to be converted. Conversion Key Seruerice Degrees to Radians Degrees to Grads Grads to Degrees Grads to Radians Radians to Degrees feca | onc [ea] onc] Radians to Grads wes 35 Each calculation should be completed before pressing the next key. Example: Express 50 degrees in radians, then grads, then back to degrees. Enter Press Display Comments (select degree mode “DEG”) 50 GOGS 0.8726646 Radians Ges 55.555556 Grads mes 50. Degrees Example: Convert 100 grads to degrees and radians. Enter Press Display Comments (select grad mode “GRAD") 100 we 90. Degrees @OES 15707963 Radians V. MEMORY USAGE Your calculator has one memory that is able to store data as long as the calculator’s solar cells are exposed to light. This feature allows you to store often used numbers in memory or to keep a running total of figures over a long period of time without having to write them down and re-enter them each time they are needed. Use of the memory does not affect any calculations in progress, so memory opera- tions can be used whenever needed. Memory Clearing Be very careful when clearing your calculator while working with data in memory. Use Ge) only before beginning any calculation which re- quires a clear memory. Use at all other times. Memory Store (9) Memory Store Key—Stores the displayed quantity in the memory without removing it from the display. Any previous value stored in the memory is replaced by the new entry. “M” appears in the display when a non-zero value is stored in memory. Memory Recall (@&) Memory Recall Key—Recalls the contents of the memory into the display without affec- ting the content of the memory. Example: Store and recall 45.68 Enter Press Display 45.68 M 45.68 ™ 0. M 45.68 37 Use of these keys a