-., " " Rockwell International ..where science gets down to business 2520·Q-62-R2-407 Litho in U.S.A. Welcome to the world of Rockwell reliability! If your problems involve trigonometric and logarithmic functions, now you have The Answer-the Rockwell 61 R Advanced Slide Rule. 1. Degrees/Radians selection switch 2. Display/Register and Display/ Memory exchange key 3. Clear/Entry Correction and Clear Function key 4. Equal/Memory Display key 5. Change Sign/Store Display key 6. Add/Add to Memory key 7. Subtract/Subtract from Memory key 8. Function/Data Recovery key 9. On/Off switch 10. Overflow indicator 11. Negativ:e number indicator Copyright 1974, Rockwell International Your Rockwell 61 R has been designed not only to perform the four basic functions of arithmetic but also to compute natural and common logs and anti-logs, trigonometric and inverse trigonometric functions, square roots, roots and powers for any real numbers, and reciprocals. The constant pi may be recalled for use at any time, and there is an addressable memory for storing data or accumulating results. Your Rockwell 61 R uses one of the most sophisticated electronic devices on the market: a single microelectronic silicon chip. This device is no bigger than a fleck of confetti, yet it is programmed to provide the capabilities for solving many types of complex problems. Rockwell International has had more experience with these remarkable devices than anyone else in the industry. 1 .' This instruction manual will assist you in understanding the various key functions and the operation of your calculator. CONTENTS General Information _ _ _ _ Before Operating Your Calculator . Operating Power __ Battery Charger. . . . . . . . Special Care and Precautions Getti ng Started . . . . . . . .. Display. _ _ Explanation of Switches and Indicators - . . . . . .. Operation .. - 5 5 5 5 6 7 8 9 10 Basic Operations .. _ 13 Repeat Operations. _ __ Constant Operations _ Clear Operations Overflow Conditions . Wrap-Around Decimal .... Computations With Very Large or Very Small Numbers . . . . . . . . . Change Sign Operation __ .. Register Exchange Operation Key Secondary Functions .. Memory Operation _ .. Constant 1T Key 17 18 23 27 28 30 31 32 33 33 37 Trigonometric Functions (SIN), (COS). (TAN). _ . _ 41 I nverse Trigonometric Func- tions (ARC) (SIN), (ARC) (COS). (ARC) (TAN) ... 46 2 3 J -------~~----..... Square Root (vx>. . . . . .. Reciprocals (l/x) Common Logarithms Function (log X) . . . . .. Natural Logarithms Function (In X) - - - . - _. Antilogarithms Function (exl. (lOX) . __ Exponential Function (XY) . Recovery Techniques ..... Sample Problems. . . . . . . . Mathematics _. _. _ Statistics . . . . . . . . . .. The Pythagorean Theorem 50 52 54 54 55 56 60 63 63 63 68 Rectangular to Polar Coor- dinates Conversion. .. Law of Sines. . . . . . . .. Law of Cosines . . . . . .. Hyperbolic Functions __ . Inverse Hyperbolic Functions. . . . . . . .. Engineering _ Parallel Resistors . . . . . . RC Network. . . . . . . .. Simply Supported Beam . Shaft Stress Sound Pressure . . . . . .. Range of Accuracy ... . . . . . Consumer Warranty 69 71 73 75 78 82 82 83 85 87 90 92 96 GENERAL INFORMATION BEFORE OPERATING YOUR CALCULATOR Your Rockwell 61 R Advanced Slide Rule calculator is supplied with rechargeable internal batteries and a battery charger. Part No. 328R07·001. DO NOT OPERATE YOUR CALCULATOR WITHOUT THE CHARGER UNTIL YOU HAVE CHARGED THE BATTERIES FOR FIVE HOURS. Failure to do so can damage the batteries. OPERATING POWER Your calculator operates from nickel cadmium rechargeable batteries. You may use the calculator while the nickel cadmium batteries are being charged; however, your battery charger is not an AC adapter and should not be left plugged in indefi nitely. BATTERY CHARGER To charge the nickel cadmium bat· teries, simply plug the charger into the jack provided in your calculator and a standard 120-volt wall outlet. With ihe calculator turned off, allow 4 5 -----~_.- approximately five (5) hours for the batteries to be fully charged. Your calculator CAN be used while the batteries are being charged, but the time required for the batteries to become fully charged will increase. The nickel cadmium batteries will provide a minimum of three (3) hours operating time when fully charged. The nickel cadmium battery life will be prolonged by recharging the batteries after approximately three (3) hours operating time. The need for recharging is indicated by the display becoming 2. Do not charge the batteries continuously as battery degradation could occur after approximately 72 hours. 3. Avoid exposing your calculator to extreme cold or heat. Keep it out of direct, intense sunlight and away from heating devices. 4. Keep your calculator away from moisture and liquids. 5. Do not drop or subject your calculator to heavy shock or vibration. 6. When not in use, turn the calculator off and place it in its carrying case for maximum protection. dimmer. Do not continue to use your calculator on battery power once the display becomes dim. The nickel cadmium batteries may be permanently damaged by overuse without charging. 7. Never use a dry or wet cleaner of any kind on the case. Simply wipe the case with a clean dust cloth. 8_ Do not attempt to repair the calculator yourself. The parts SPECIAL CARE AND PRECAUTIONS are replaceable, but not repairable. Observance of the following will prevent damage to and assure GETTING STARTED trouble-free service from your Your machine has a feature that automatically clears all registers when power is turned on. Place the power switch in the ON position, and a zero appears in the right hand digit position. The calculator is now calculator and the charger and nickel cadmium batteries supplied with it. 1. Use only the charger furnished with vour calculator. 6. J 7 1 ready to accept key entries and per· form calcu lations. EXPLANATION OF SWITCHES AND INDICATORS DISPLAY ON/OFF SWITCH Numbers with an absolute value of 0.0000001 to 99999999 can be dis· played. Negative entries and results are indicated by a minus symbol at the far left of the display. Results The ON position applies power to your calculator and clears it of all previously entered data. in excess of eight digits are indicated by the overflow indicator, a large dot in the far left of the display. The eight most significant digits are displayed with the decimal adjusted eight places to the left of the correct position (see Wrap-Around Decimal). For fractional numbers less than one, a zero is displayed to the left of the decimal point. No leading zeros are displayed for numbers greater than one. The results of the calculations are displayed DEG/RAD SWITCH Refer to page 41 . OVERFLOW INDICATOR \e187.65432\ elights if the answer exceeds 8 digits to the left of the decimal point. The e indicator also lights if memory accumulation exceeds eight whole digits (no fraction). (See Overflow conditions, page 27 and Wrap-Around Decimal, page 28 for detailed information on calculator overflow_) instantaneously for most calculations. NEGATIVE NUMBER INDICATOR NOTE: Computations using very large or very small numbers may be performed on your I 1.2451 - lights when negative numbers are displayed. slide rule calculator by utilizing appropriate scal ing (see page 30). 9 OPERATION The Rockwell 61 R Advanced Slide Rule has 20 keys, including a unique "second function" key that allows each key to have two separate uses. The first (primary) use is identified on the face of the key; the second (secondary) use is identified above the key. In this manual, the first use is represented (except for digits) by enclosing the identification in a box, 0; the second use, by enclosing the identification in parentheses, ( ). The following explanation will help you understand the operation and TIPLY, G DIVIDE: Depressing any of these four keys selects the next operation to be performed by the calculator and causes the previously selected operation to be executed. During calculations, intermediate results are automatically displayed after these keys are depressed. ANSWER KEY 0: Depressing the 0 key causes your answer to appear in the dis- play, then terminates the calculation. The answer can be retained as the first number for your next calcu- uses of each key. lation (see page 16). DIGIT ENTRY KEYS CLEAR KEY [Q] THROUGH ffil: Depressing any digit key enters that digit and causes it to appear in the displaY.,. To enter the number 24, depress W first, then @1 ~: Depressing the ~ key clears DECIMAL POINT ENTRY KEY 0: Depressing the 0 key places the display of erroneous entries, cancels overflow conditions, or clears the calculator of stored numbers and functions. (See Clear Operations, page 23, for detailed instructions on use of the ~ key.) the decimal point in your entries. CHANGE SIGN KEY ARITHMETIC FUNCTION KEYS 1+/-1: Depressing the 1+/-1 key changes the sign of a displayed number. [±] ADD, EJ SUBTRACT, Ii] MUL10 11 ~ .. REGISTER EXCHANGE KEY >- 8: Depressing the 8 key inter- '"Q. changes the contents of the display and the working register. o ~ FUNCTION KEY [£]: Depressing the [£] key conditions the calculator to interpret the next key depressed in accordance with the function identified above the key. NOTES: The secondary functions of the keys are described under Key Secondary F unctions, page 33. Techniques for recovery of data following unintentional depression of the wrong arithmetic function key or the [£] key are given under Recovery Techniques, page 60. Recovery of data with the (DR) key is also de- r-Ii <0" scribed under Recovery ~ <: + w Techniques. M .. C Eo ~.-+:: - ." to 0 ...0: .0'- >- 01) " ~ :>.. -0 0.« 12 - 13 r--- t.n N Problem: Multiplication 3 x 5 = 15 Keyboard Entry 3 ~ Display 3. 05 ... Problem: Division 36 -;. 4 = 9 Display 36. 36 84 5. o Keyboard Entry 4. o 15. 9. Mixed Calculations The following example shows how the calculator is used to solve complex mathematical problems with a minimum of key depressions. The examples also illustrate how the arithmetic function keys execute preceding operations and cause intermediate results to be displayed. _.. --_. Problem: (4 + 61 8- 7 8 Keyboard Entry 4 86 0 ~ <I1 8 G 7 8 8 0 = 9.125 Display 4. 6. 10. 8. 80. 7. 73. 8. 9.125 Comments (4 + 6) executed (4 + 6)8 executed (4 + 618 - 7 executed Final result If you want to use an answer in further calculations, there is no need to re·enter the number. Just depress the desired arithmetic function key for the next oper· ation and enter another number. - (j) Problem: Answer Re-entry: 17.4 + 3.7 ~ 21.1 21.1 + 32.4 ~ 53.5 Keyboard Entry 17.4 [±] 3.7 0 [±] 32.4 0 Display 17.4 3.7 21.1 21.1 Comments Not necessary to re·enter 21.1 32.4 53.5 REPEAT OPERATIONS The repeat operation capability of your Rockwell 61 R is a time-saving feature that enables you to add, subtract, multiply or divide a series of identical numbers without re·entering the numbers each time. Problem: ((((6 x 61 - 6) -;- 6),. 6) :::j ~ 11 Keyboard Entry Display 6 6 6. IZI B EJ [±] o 36. 30. 5. 11 . Comments Not necessary to re-enter 6 ~ 00 CONSTANT OPERATIONS The automatic constant is another time·saving feature of your Rockwell 61 R. This feature enables you to add, subtract, multiply, or divide by the same num· ber repeatedly without re·entering the number for each new calculation. The number entered after the last arithmetic function key depressed is always saved as the constant laddend, subtrahend, multiplier or divisor). The constant function is the last function key depressed before depressing the 0 key. To perform mul· tiple operations with this constant, si.r!Ply enter a new augend, minuend, Inulti· plicand or dividend, and depress the l=J key for an answer. Problem: Constant Addend: 6 + 3 = 9 8+3='1 Display Keyboard Entry 6. 6+3= 9 6 3. III 3 ~ '" 8+3=1' 13 9. 8 8. 13 11. Problem: Constant Subtrahend: 9- 5=4 Keyboard Entry 9-5=4 9 EJ5 "o §] 11 -5=6 11 §] Problem: Constant Multiplier: 12 x 4 = 48 Keyboard Entry 12x4=48 1 " ~ 3x4=12 11-5=6 Display 9. 5. 4. 11 . 6. 3 x 4 = 12 Display §] 12. 4. 48. 3 §] 12. 12 04 3. Problem: Constant Divisor: 10.;. 5 ~ 2 Keyboard Entry 10';'5~2 12';'5~2.4 Display 10 10. 5. 85 §] '"'" 12 .;. 5 ~ 2.4 2. 12. 2.4 12 §] Mixed Operations with Constants Problem: (5 + 3? - 2 ~ 11 Keyboard Entry '"w Display 5. 5 [£)3 3. EJ 24. o 8. 2 2. §] 22. 11 . 8 Comments Undetermined Constant = 3 Constant ~ 3 Constant ~ 3 Constant ~ 2 Constant ~ 2 Constant ~ 2 CLEAR OPERATIONS 1. One depression of the [£] key when there is no overflow condition clears the displayed number but does not affect the stored constants or the operation: Problem: Entry Correction: 12 + 5.5 = 17.5 Keyboard Entry Display 12 12. 5.6 5.6 [g o. 5.5 5.5 m iii "" a § Comments Error; wrong number Cleared 17.5 2. A double depression of the © key clears any operation in progress and ciears the calculator except the memory. Problem: Clear Calculator (Except Memory) Keyboard Entry Display 2 m "" tn Comments 2. 2. [g' O. Entry cleared [g O. Calculator cleared 3. Depressing the © key during an overflow (see Overflow Conditions) cancels the overflow condition. The number in the display is correct if multiplied by 108 and may be used in further calculations. Chain and constant operations are not affected by overflowing. Problem: Clear Error (Overflow): 12345678 x 9 = 111111102 Keyboard Entry Display 12345678 09 EJ 12345678. 9. _ 1.1111110 [£) 1.1111110 N O"l Comments Overflow Indicator lights; calculator accepts only clear entry key Answer must be multi· plied by 10 8 (see page 281 4. Depressing the (CF) key after pressing the [fJ key clears the secondary function operation and restores the previous conditions (see page 60). 5. Depressing the [£), [E] and (X .) M) keys clears the memory (see page 33). OVERFLOW CONDITIONS The following operations result in an overflow condition which causes the Overflow I ndicator._, to light and all keys except [£) to become inoperative: ..., N 1. Any answer or subtotal exceeding 8 digits to the left of the decimal point, re9ardless of its arithmetic sign (absolute value greater than 99,999l99.), The 8 most significant digits are displayed as follows:I_XXXXX.X X [. Calculations can be continued, if desired (see Wrap·Around Decimal). 2. Memory accumulation exceeding 8 whole digits to the left of the decimal point, regardless of the arithmetic sign. The number used in the last memory operation remains in the display: IXXX. [, Calculations can be continued, if desired (see Wrap·Around Decimall. 3. Division by zero. A 0 is displayed:! [] 4, Exceeding capacity or range of scientific functions (see pages 92 through 961. WRAP-AROUND DECIMAL The wrap·around decimal feature of your calculator lets you proceed when the answer obtained in the display or memory exceeds the capacity of the calculator (10 8 or greater), except when the overflow condition is the result of computing a scientific function. The calculator automatically retains the 8 most significant digits, places the decimal point 8 positions to the left of its true position, and ~ lights the Overflow Indicator. You may proceed with the problem solution after depressing the [Q] key once to clear the overflow condition, but you must multiply the final problem answer by 108 (100,000,000) or move the decimal point 8 places to the right. Any numbers subsequently added or subtr8cted must be divided by 10 8 before entering. If two overfiows occur in the S8me problem, the final answer must be multiplied by 10 8 X 10 8; 10 16 and so on. This same feature applies to the numbers in memory. Problem: '"CD 98,000.000 x 2.000 0.04 _ 20 000,000 ' Keyboard Entry Display 98000000 02000 [±] [Q] 98000000. 2000. • 1960.0000 1960.0000 .04 .2 0.04 49000. 0.2 §J 48999.8 EJ = 4,899,980,000,000 Comments Overflow Indicator lights Displayed number times 10 8 equals true number Number entered (20000000';' 108 ) ; .2 This answer times 108 equals true answer COMPUTATIONS WITH VERY LARGE OR VERY SMALL NUMBERS Computations which may exceed the a·digit capacity of the calculator can be scaled, entered as if they were expressed in scientific notation, and the appro· priate power of 10 determined as a second step, Problem: 2 x 10- 6 X 5 X 10- 5 = 10 X 10- 11 ~ Keyboard Entry Display 2 2. 05 5. EJ 10. Comments Times 10- 6 Times 10- 5 Times 10- 11 CHANGE SIGN OPERATION Depressing the Gl=1 key changes the sign of the nllmber in the display. The Rock· well 61 R Advanced Slide Rule allows sign change at any point in a calculation, 2 4 (-31 Problem: =-a 6 Keyboard Entry 4 w ~ o o 3 m;:J G:J 6 EJ Comments Display 4, 4. 16, 3. 3, 48, 6, 8. Negative Number Ind icator Iigh ts REGISTER EXCHANGE OPERATION Another useful feature of your Rockwell 61 R Advanced Slide Rule calculator is the register exchange capability. Depressing the B key exchanges the data (number! in the display with the number in the working register (the previously dis· played number or the constant). w '" 3 ~56 Problem: ~ 1.6666666 Keyboard Entry Display 3 3. 3. m 6 6. 15 9. 15. 9. 8 B El 1.6666666 Working Register Constant Undetermined 3 3 6 9 15 9 KEY SECONDARY FUNCTIONS Depressing the [f] key conditions the 61 R Advanced Slide Rule to perform the second function of the next key depressed. The secondary function is cancelled after execution of all second function operations except (ARC) (see page461 or (DR) (see page61). Operation and uses of the keys in performing their second function are described in subsequent paragraphs. w w NOTES: The display is blank during many operations using the scientific function keys. No keyboard entries should be attempted before the display turns on again. Range of accuracy of the Rockwell61R calculator is given on pages 92 through 94. MEMORY OPERATION Your Rockwell 61 R Advanced Slide Rule calculator has a completely independent memory which is unaffected by arithmetic or scientific operations. Through the use of this memory, you can perform chain operations involving complex mathematical problems with a minimum of key depressions. All of the memory operation keys are activated by depressing the [£] key. The functions of the memory operation keys are as follows: Key ~ Function (M+I (M-) (X <- MI (X .... MI Add to memory. Subtract from memory. Display number in memory. Store displayed number in memory. Any number previously in memory is destroyed. (X - M) Exchange number being displayed with number in memory. (M + X2) Add square of contents of displayed number in memory; display is not altered. The following example illustrates use of the memory operation keys and the memory clearing procedure. Keyboard Entry Display Memory ~ O. [£] (X -> M) O. o 4 [£] (M+ J 4. 4. 4. [£) (M + X2) 4. 20. w '" o Comments Memory cleared: displayed number copied into memory; display not altered. Displayed number added to memory; display not altered. Square of displayed number added to memo ory; display not altered. Keyboard Entry Display Memory 1Kl 4. 20. 3 (M-I 3. 3. 20. 17. [±] 12. 17. 1Il (X+-M) 17. 17. EJ 29. 17. 1Il w OJ Comments Multiply operation established Displayed number sub· tracted from memory; display not altered 3 x 4 executed and addi· tion operation established Contents of memory reo called to display; original number moved to work· ing register 12 + 17 executed • [I] (X ++M) 17. 29. Contents of memory exchanged with dis· played number CONSTANT" KEY The value of" may be entered into the display at any time by depressing the ...,w lIland (,,) keys. The display will be 3.1415926. Problem: Area of Circle: Find area (A) of a circle 6 feet in diameter (D) Formula: A = 11 ~2 Keyboard Entry ~ A = 28.274332 Display Comments 6 6. [I]~ 6. 36. 3.1415926 113.09733 o o Diameter 02 rr 02 4. 4 El 28.274332 Area Problem: Degrees to Radians: Convert 200 degrees (d) to radians Ir) Formula: r = 1:a Keyboard Entry 200 w CD 00 (~ 180 §] r = 3.4906584 RAD Display Comments 200. 3.1415926 628.31852 180. 3.4906584 Degrees (dl Radians (r) Problem: Radians to Degrees: Convert 10 radians Ir) to degrees Id) Formula: d ... a = 180 r 11 d = 572.9578' Keyboard Entry Display Comments 10 0180 10. 180. 1800. 3.1415926 572.9578 Radians (r) B [£]~ Degrees Id) TRIGONOMETRIC FUNCTIONS (SIN), (COS), (TAN) Depressing the [£] key and then the ISIN), ICOS) or (TANI key causes the calculator to compute and display the trigonometric function for the value of the angle that was displayed. ... ~ DEG/RAD SWITCH: The position of the DEG/RAD switch selects whether the trigonometric functions are to be computed with angles expressed in degrees or radians . Problem: sin 30' = 0.5 Keyboard Entry Display 30 30. [£] lSI N) 0.5 Comments DEG/RAD switch in DEG position 'l· ,\ , Problem: cos 300· = 0.5 Display Keyboard Entry i!3 300 300. [£] (COSI 0.5 2 2. [£] (TAN) 2.185042 Koyboard Entry .. DEG/RAD switch in DEG position Problem: tan 2 radians = -2.185042 Problem: sin ; w Comments radians = 0.5 Display [£] (11) 3.1415926 86 § 6. 0.5235987 0.5 I:II (SIN) DEG/RAD switch in RAD position Negative Number Indicator lights Comments DEG/RAD switch in RAD position Problem: (2 x 3) + 3 (tan 15°) ~ 6,803848 Keyboard Entry Display 2 2, 03 "" ElIIJ(X .... M) 3. 6. "" 15 [£](TAN) 0.267949 Comments DEG/RAD switch in DEG position 15. 03 III 3. 0.803847 • Keyboard Entry [£] (X +- M) EI • Display Comments 6. 6.803847 Some chain operations using scientific and arithmetic functions can be accom· plished without the use of memory by rearranging the problem. Problem: (2 x 3) + 3 (tan 15°) ~ (2 + tan 15°) 3 ~ 6.803848 "" (J'l 15 [£] (TAN) 1lJ2 III 3 13 15, 0,267949 2. 2.267949 3, 6.803847 DEG/RAD switch in DEG position INVERSE TRIGOI\IOMETRIC FUNCTIONS (ARC) (SIN), (ARC) (COS), (ARC) (TAN) +> Ol Depressing the [£]and (ARC) keys and then the (SIN), (COS) or ITAN) key causes the number in the display to be interpreted as the value of a trigono· metric function and the inverse trigonometric function (the angle) to be cal· culated and displayed. Problem: sin -, 10.5) ~ 30° Keyboard Entry I£J (ARC) Display .5 0.5 (SI N) 30. DEG/RAD switch in DEG position .. . • Problem: cos -, (0.5) ~ 60° Display Keyboard Entry 0.5 .5 [£] IARC) ICOS) Comments Comments DEG/RAD switch in DEG position 59.99999 Problem: tan -, 111 ~ 45° ~ 1 1, [£] (ARC) (TAN) 44.99999 (Continued on page 50) DEG/RAD switch in DEG positon Model lOR 8-digit Electronic Calculator* Basic Answer features: 8 digits • 4 function (+ - x';-) • Algebraic logic • Floating decimal • Repeat function Model20R Electronic Calculator with Memory and Percent* • All Basic Answer features PLUS • Fully addressable memory • Automatic constants • % key • Automatic fully addressable memories. 2-place or floating decimal· Automatic constants • Fraction calculations. 224 fixed conversions plus programmable conversion • AC charger and case ~Model61R Advanced Slide Rule j Electronic Calculator • All Basic Answer features PLUS • Fully addressable memory. Automatic constants. Register exchange • Sign change. Reciprocals. Sum of squares. Square roots. Log functions mark-on and discount Model30R Slide Rule Memory Electronic Calculator* • All Basic Answer features PLUS • Fully addressable memory. Automatic constants· % key. Automatic • Trig functions in degrees or radians • Powers· AC charger and case Model80R lO-digit Printer Electronic Calculator • 4 functions • Commercial logic mark-on and discount • Register exchange • Sign change • Reciprocals • Squares • Square roots Model51R Universal Converter Electronic Calculator • 10 digits plus 2 columns of symbols • Thermal printer • Floating decimal or dollar decimal with override • Auto~ matic constant and repeat • Subtotals, \ group totals and grand totals • All Basic Answer features PLUS *Moael 01 R Accessory Kit (AC Adapter and Carrying Case) Available at Extra Cost. Problem: ; + tan -, (1) = 2.3561945 radians Keyboard Entry Display 1 gJ [I] (ARC) (TAN) [IJIX-+M} I£] (rr) 02 [±] [I] (X<- M) EJ Comments 1. 0.785398 0.785398 3.1415926 DEG/RAD switch in RAD position 2. 1.5707963 0.785398 2.3561943 Radians SQUARE ROOT (-IX) Depressing the [I] and (-IX) keys causes the square root of the number being displayed to be computed and displayed. ProQlem: .J:]8f = 3 Keyboard Entry 81 [I](~I WI.,[X} Display 81. 9. 3. The.,[X function can also be used in chain operations, ~ Problem: V4 + V9 4 W I-./X} [±] 9 WI";><I EJ = 5 4. 2. 9: 3, 5, RECIPROCALS (l/x) Depressing the 1£J and (l/x) keys causes the reciprocal of the number being displayed to be computed and displayed. Problem: '" IV io = 0.05 Keyboard Entry Display 20 1£J(1/x) 20. 0.05 The l/x function can also be used in chain operations. Probl,em: iJ + -fcJ Keyboard Entry '" w 20 m(l/x) [±] 10 m(1/x) G = 0.15 Display 20. 0.05 10. 0.1 0.15 COMMON LOGARITHMS FUNCTION Ilog X) Depressing the [£] and (log Xl keys causes the common logarithm of the displayed number to be computed and displayed. Problem: log,o 100 ~ 2 (J1 ~ Keyboard Entry Display 100 [£] (log XI 100. 2. NATURAL LOGARITHMS FUNCTION lin X) Depressing the [£] and lin X) keys causes the natural logarithm of the displayed number to be computed and displayed. Problem: In 132 3 ) ~ 3 In 32 ~ 10.397211 Keyboard Entry 32 [£] (In XI 03 EI 31 Display 32. 3.465737 3. 10.397211 ANTI LOGARITHMS FUNCTIONS lexl, (10 X ) Depressing the [£] and lex) or [£] 'and (1 OX) keys as desired causes the antilogarithms of the displayed number for the bases e (e ~ 2.718281) or 10 to be computed and displayed. Problem: 10 2 ~ 100 Keyboard Entry Display Comments 2. 2 X 1IJ(10 I 100. Problem: e- 3 = 0.049787 ~ 3 3. 1m 3, [E) (eX) 0.049787 Negative Number I ndicator lights EXPONENTIAL FUNCTION (XY) The exponential function raises X (first number entered) to the power y (second number entered I for any real vaiues of y. Depressing the [E) and (XY) keys causes the displayed number to be taken as the value of X and the natural log of X to be com£!!ted and displayed. The function is completed by entering y and pressing the L::J key, Problem: 33 <11 -..J ~ 27 Keyboard Entry Display 3 Y [l] (X ) 3 3. 1.098613 3. 27.00005 EI Comments In 3 The (X Y) key may be chained with the (l/x), (11) or (v'X) key. Problem: 5y'32 = 32 1 / 5 = 2 Keyboard Entry Display 32 mil/xl 32. 3.465737 5. 0,2 §] 2. m(X y ) 5 g] sin Y 38 to In 32 (x) can be computed easily. Problem: sin 1/3 (38°) = 0,850708 Keyboard Entry Display (]1 Comments [£] (51 N) [£](X Y ) 3 [£](l/X) §] 38. - 0.615661 0.485058 3. 0.3333333 0,850709 Comments DEG/RAD switch in DEG position Negative Number Indicator lights RECOVERY TECHNIQUES Occasionally you may unintentionally depress one of the function keys. The following techniques allow easy correction without loss of the displayed number. ~ Unintentional 0 or W: Depress 1, then G. If constant multiplication or division is being performed, the constant is replaced by 1. Unintentional [±] or B: Depress 0, then G. If constant addition of subtraction is being performed, the constant is replaced by 0. Clear Function (CF) Depressing the (CF) key immediately after an unintentional [£J key clears the calculator of secondary function operation, Problem: 4 x 3 = 12 Keyboard Entry (J) ~ Display 4 03 4, 3, [£J 3, (CF) 3. 13 12. Comments Error!! Did not want to press [£J Data Recovery (DR) Depressing the III and (DR) keys immediately after a digit entry recalls the last number displ2Yed. The selected function remains set. If only one digit has been entered, the l.EJ (DR) key sequence recalls the previous result to the display, If more than one digit has been entered, the III (DR) key sequence eliminates the last digit, If more digits are to be entered or primary functions are to be executed, the (CF) key must be depressed to clear the function. Keyboard Entry O'l '" Display 45 45. (SIN) 451. ill (DR) (SINI 45. 0.707107 12346 IIJ(DR) (CF) 5 12346. 1234. 1234. 12345. Comments DEG/RAD switch in D EG position Error!! Forgot to press IIJ Error!! Did not want 6 SAMPLE PROBLEMS Your Rockwell 61 R Advanced Slide Rule calculator is a versatile problem solving tool. Several practical examples were chosen from different fields of interest to familiarize you with your calculator. We recommended that you gain familiarity with your Rockwell61R by working the sample problems. O'l W MATHEMATICS Many problems can be arranged so that two parallel calculations are performed with one entry of data: one in the display, the other in memory. Some examples of this procedure are shown on following pages. Problem: Statistics: Find the mean (M), variance (V), standard deviation (SD), and standard error (SE) of the mean olthe following values of X (10, 11, -3, 14, 181 I Note: n = 51 'ii, a. Formulas: i LX 2 LX, n M~ b. V ~ M ~ 10. \ I c. SO ~ SD Keyboard Entry ~ LX I (LX )2 I - 11 n 7.9056941 Display d. SE ~ ~ SE ~ 3.535534 Memory Comments o. o 10m(M+X 2 ) 10. 100. Display and memory cleared X~ added to memory 10. 11. 21. 3. 100. 221. 221. 221. ill 3. 18. 230. 230. X~ added to memory Xl + X displayed 2 Negative Number Indicator lights X~ added to memory Xl + X + X 3 displayed 14 [£] 1M + X2 1 14. 426. X~ added to memory ill 32. 426. 18[£](M+X 2 ) 18. 750. X+X+X+X I 2 3 4 displayed X~, added to memory 2 ) 31m [fJ (M + X2 1 '" --' n n- 1 [£]m IX-+ M) m 11 [fJ (M + X m (LX.)2 V ~ 62.5 2 ~ ,- - (J1 (Continued on page 66) 2 Keyboard Entry Display Memory 13 50, 5, 10, 5, 50, 750, 750. 750, 750. 750. 13 500, 750, III 5 W EJ tI '" '" [I) (M-I 500. 250, [I) (X .... MI 250, 250, III 4 o [I)(..fl(1 III 5 [I){v'X1 o '"...., 4. 62,5 7.9056941 5. 2.2360679 3.535534 250. 250. 250. 250. 250. 250. Comments :EXi displayed n Mean (M) displayed M. n = :EX., displayed (:EX,I M2 • n = - - n displayed , (:EX 12 :EX n subtracted from memory , 2 (n - 1) Variance (VI Standard deviation (SDI n ..;n Standard error (SEI of the mean B Problem: :;11 Given right triangle ABC with sides 3 and 4, find the hypotenuse c. i Ol co c 3 4 A Formula: C=----Cc=' c'= ;/3 2 + 42 c= 5 Keyboard Entry Memory Display [£] [£]{X--+ M) 3 I£J 1M + X2) 41£] 1M + X 2 1 O. O. o 3. 4. 9. 25. I£J(X+-M) 25. 25. I£J (y'X) 5. 25. Comments Memory cleared 3 2 added to memory 4 2 added to memory Sum of squares recalled from memory Hypotenuse (c) Problem: Converting From Rectangular to Polar Coordinates: Convert the point' (24,701 into polar coordinates. Ol <0 C Formulas: Magnitude of Vector V = y"'X"2'+"-y2" angle tan (J= -1 ~~ ) Where x = 24 and y = 70 (J = 71.07536" V= 74. Keyboard Entry G -...I a Display Memory C [I] (X---> M) O. 0 70 [I] (M + X2) 24 [I] (M + X~ IIJ (X <- M) 70. 24. 2.9166666 71.07536 5476. 4900. 5476. 5476. 5476. 5476. II] (v'X) 74. 5476. II] (ARC) (TAN) Comments Display and memory cleared y2 added to memory X2 added to memory Y/X Angle a (degrees) y2 + X2recalled from memory Magnitude of vector (V) Problem: Law of Sines: A b Given the above triangle. find angle B. -...I ~ Formula: !!.- sin A ~ b c sillB sin C or sin B = b sin A a Where A ~ 30" a ~ b ~ 105 B ~ sin 75 (bSinA -1 B ~ 44.42701° a ~ Keyboard Entry Display 30 I 30. [EJdJS1N ) X 105 ;\ I 75 N DEG/RAD switch in DEG position sin A Length of side b b sin A Length of side a sin B Angle B in degrees 0.5 105. 52.5 75. 0.7 44.42701 G " Comments B [EJ (ARC) (SIN) B Problem: Law of Cosines: c=5 a=3 Given three sides of the above triangle, find angle A. C A b=4 Formula: "w a2 = c2 + b 2 - 2cb cosA 2 2~~ - A = cos -1(C + Keyboard Entry Display Memory [£][EJ(X-> M) O. 0 3[R] 3. (Continued on Page 74) 2 a A = 36.8699° ) Comments Display and memory cleared a Keyboard Entry Display Gill (M-) 9, - 9, 4 4, 4, 5, 5, 20, 2, 40, 32, - 9, 7, 7, 32, 32, 32, 32, 32, 40, 0,8 36,8699 32, 32, 32, [I] (M + X2) [K)5 ill(M ..., + X2) [K) 2 .l> G illIX<-M) EJ o::J G (ARC) (COS) Problem: Hyperbolic Functions: Formula: sinh a = Keyboard Entry ..., (J1 2,1 ill (eX) EJ ill 11/Gj ill G ea Memory Comments a 2 subtracted from memory b b 2 added to memory c c 2 added to memory cb 2 cb c 2 + b 2 - a 2 recalled from memory 2 cb cos A Angle A (degrees I sinh 2,1 = 4,021856 _ e- a 2 Display 2,1 8,166168 8,166168 0,1224564 8,0437116 2, 4,0218558 Comments a ea e- a ea _ e-a sinh a Problem: Hyperbolic Functions: Formula: I a ,. " 1.3 m(eX) m m(l/x) ill 2 B Problem: Hyperbolic Functions: "" = 1.970914 cosh a =e . 2e Keyboard Entry CJ) cosh 1.3 -a Display 1.3 3.669295 3.669295 0.2725319 3.9418269 2. 1.9709134 = 0.655794 a e" - eFormula: tanh a = e" + e- a Memory Display Kp.yboard Entry 3.1415926 I£J (11) 4. 84 0.7853981 B [f] (eX) 2.193279 2.193279 2.193279 l.E.]( X -> M) 2.193279 2,193279 B 2.193279 0.4559383 I£J (l/x) 2.6492173 0.4559383 {M+I (Continued on page 78) m Comments a e· e-· e" + e- a cosh a tanh: Comments a e· e-· Keyboard Entry G iIJIX+-MI EJ " ex> Display Memory 1.7373407 2.6492173 0.6557939 2.6492173 2.6492173 2.6492173 Problem: Inverse Hyperbolic Functions: Formula: sinh- 1 1.3356469=1.1 sinh- 1 a= In la + V a2 + 1 Keyboard Entry m IlJ IX ,- M) IlJ h.!X~ IlJ lin XI 1. 1. 2.7839526 2.7839526 2.7839526 2.7839526 2.7839526 2.7839526 2.7839526 1.668518 3.0041649 1.1 Problem: Inverse Hyperbolic Functions: Formula: Comments Memory Display 11. IlJ IX-+MI 1. 1.3356469 1.3356469 [£] 1M + X2) 1.3356469 1.3356469 "<0 Comments ea _ e- a e a + a-a tanh a a a2 + 1 ~.-:.1_ a + va 2 + 1· sinh- 1 a cosh- 1 1.3374385 = 0,8 cosh- 1 a = In (a + va 2 -1 I£J IlJ IX"" M) mllJ 1M-I 1.3374385 O. 1. 1.3374385 (Continued on page 80) o - 1. - 1. a Keyboard Entry Display W(M + X~ 1.3374385 1.3374385 0.7887417 0.8881113 2.2255498 0.800003 [fJ(X+-M) [fJ (yx) G 00 a [fJ (In Xl Problem: Inverse Hyperbolic Functions: Formula: tanh- 1 a = % In l' 00 --> Keyboard Entry 19WIX-M) 1 [fJ (X --> M) W .7615942 [fJ (M-) W [fJ (X +- M) G [fJ (In Xl W2 EJ Memory 0.7887417 0.7887417 0.7887417 0.7887417 0.7887417 0.7887417 Comments a2 - 1 ya 2 - 1 a+..(a2-1 cosh- 1 a tanh- 1 0.7615942 = 1. + : 1. 1. 1. 0.7615942 0.7615942 1.7615942 0.2384058 7.3890576 2. Memory 0 0 1. 1. 1. 0.2384058 0.2384058 0.2384058 0.2384058 0.2384058 2. 1. 0.2384058 0.2384058 Display O. Comments a 1+a 1- a (1+a)/(1-a) In 1 + a 1- a tanh- 1 a ENGINEERING Problem: Parallel Resistors: Three resistors of 5 ohms, 20 ohms and 10 ohms are can· nected in parallel. What is the equivalent resistance? Formula: Re 1 Re = 2.8571428 ohms q 1 1 1 q -+--+-R! R2 Ra 00 '" Keyboard Entry 5 o (1 Ix) m 20 o (1 Ix) m 10 o (l/x) G o (l/x) 0 isplay 5. 0.2 0.2 Comments R, l/R, 20. 0.05 R2 0.25 10. l/R, + l/R 2 0.1 0.35 2.8571428 1/R 2 R3 1/R 3 l/R, + l/R 2 + 1/R 3 Equivalent Resistance (Reo I 00 w Problem: RC Network: A step voltage (V,) of 25 volts is applied across series RC network with R = 50,000 ohms and C = 0.1 microfarads. What is the voltage (V I across the capacitor after 15 milliseconds? C Vc = VI (1 _ e-t/RCI Formula: Keyboard Entry Comments 0.015 1II.0000001 0.0000001 G 50000 150000. 50000. ttQ 3. EI 3. I£JkX ) 0.049787 El1 t (15 + 1000) = 0.015 seconds C(0.1+10 6 1= 0.0000001 farads tiC R tlRC - tlRC a-t/R C 1. El 0.049787 0.950213 25. 23.755325 o25 EI U1 =23.755325 volts Display .015 ~ '" Vc (1 _ e- t/RC ) VI Voltage across capacitor (V cl Problem: Simply Supported Beam: A beam simply supported at the ends carries a uniformly distributed load (wi of 10 pounds per inch across its full length. Find the maximum deflection (Y cl. ~ Formula: Y = c ~n":: ~4. E = .3 X lOB psi 1=1.2in'· I = 200 in. Keyboard Entry 200 co m 0 0 0 0 © [[] 0 10 G 384 G .3 G 1.2 co ...., o • Display Comments 200. 200. 40000. 8000000. 16.000000 Length (I) I 16.000000 5. 80. 10. 800. 384 2.0833333 0.3 6.9444443 1.2 5.7870369 2 13 1 4 1 ; overflow; answer to be times 108 14 -; 10 8 5 X 14 -;. 10 8 Load (w) 5 x (w) 14 -;. 108 (5 (wi 14 -;. 108 ) 384 Entry scaled by 108 (5 (w) 14 ) -;. 1384 E) Moment of inertia (I) Deflection (Ye) in inches Problem: Shaft Stress: A shaft 3 inches in diameter (d) has a 1000 inch-pounds bending moment and a 2000 inch-pounds torque (T). What is the maximum stress? IMI 16 Formula: (J max Keyboard Entry E9[£J(X->M) 1000 [£JIM + X 2 1 (Xl (Xl [±] 2000 [£J(M+X2) [£J~X<-M) [£] (v'X) IE] 16 Display rJ max = 610.41323 psi Memory o o 0, 1000, 1000, 1000, 2000. 2000. 1000000. 1000000. 1000000. 5000000. 5000000. 2236.0679 3236.0679 16. 5000000. 5000000. 5000000. 5000000. 5000000. 5000000. 5000000. 3 3. 5000000. G ill 5493.7193 5000000. 1831.2397 5000000. 0 610.41323 5000000. [I] (lTl G <0 1M + VT2 + M2 51777.086 3.1415926 16481.158 G (Xl :: rrd3 Comments Memory cleared Bending moment (M) M2 added to memory Torque (T) T2 added to memory T2+ M2 + M2 M + y'':T::=2'''+-M=2 02 161M + 0 2-+ M2 ) 16 ViM + y'T2+ T2 + M2 ) Diameter Idl 1E.. 1M + VT2 + M2 ) (lTd) ~ (M + .Jf2+ M2 ) (lTd 1 Maximum stress in shaft ( rJ ma) ~ o Problem: Sound Pressure: What is the sound pressure (PI of a jet airplane taking off that was measured to have sound pressure level of 133 decibels (db), where reference pressure (Pol is 2 x 10- 4 fl bar? Formula: P ~ anti-log (~g + log Po) P ~ 893.367 fl bars '0 Keyboard Entry .0002 Display 0.0002 IIJ (log XI 3.69897 [£] (X"'" MI 133 3.69897 133. 820 20. 6.65 3.69897 EI 2.95103 - 3.69897 ill (1 OX) 893.367 - 3.69897 [£] (X +- MI ~ - 3.69897 - 3.69897 - 3.69897 - 3.69897 - 3.69897 [±] ~ Memory - Comments Reference pressure ( J.l bar) log Po; Negative Number Indicator lights db db 20 Negative Number Indicator lights db (20 + log Po) Sound pressure ( fl bar) RANGE OF ACCURACY Your Rockwell 61 R Advanced Slide Rule is capable of performing the following scientific functions with great accuracy. All calculations take less than three seconds; in general, functions rarely take more than 1.5 seconds. The six leftmost digits displayed will be correct to within ±1 in the sixth digit displayed. including any suppressed zeros necessary to achieve six digits (except for the few instances noted in the following paragraphs). TRIGONOMETRIC FUNCTIONS Sin X, Cos X, and Tan X may be calculated with X in degrees or radians according to the position of the DEG/RAD switch. The result will have the correct algebraic sign. The range of magnitude for sin and cos functions is -360° LX L+360° (211" radians). For values of X outside of this range, the accuracy may be less than six digits and the computation time greater than 3 seconds. Tan X accuracy may be less than six digits for 89.5° L lIXI-1800n) L 90.5° (corresponding radians) where n = 0, 1, 2, 3, _.. If X is 92 large enough to cause an overflow in an intermediate result, the overflow condition occurs and computation is terminated. INVERSE TRIGONOMETRIC FUNCTIONS For Arc Sin X and Arc Cos X. the result is displayed in degrees or radians (according to the position of the DEG/RAD switch) with the correct algebraic sign and the following principal angles: _90° (-11"/2 radians) L arc sin X L 90° (11"/2 radians). 0° (0 radians) L arc cos X L 180° (11" radians). The acceptable range of magnitude of X is IXI L 1. For values of IXI> 1, the calculator will overflow. Arc Tan X: The result will be displayed in degrees or radians (according to the position of the DEG/ RAD switch) with the correct algebraic sign and with the following principal angles: _90° (-11"/2 radians) Larc tan X L90° (11"/2 radians). The acceptable range of magnitude of X is 0.0000001 L Ixi L99999999 and X~O. 93 LOGARITHMETIC FUNCTIONS NOTES lin X and log Xl Both natural and common logarithms may be calculated. The acceptable range of the argument is 0.0000001 L X L99999999_ For values of X La, the calculator will overflow_ ANTILOGARITHMETIC FUNCTIONS (eX and 10 X) The range of the argument for ex is 0.000001 LX Lin 99999999 (approximately); the range of the argument for 10' is -6 LX < 8_ It the value of X is outside of these ranges, the calculator will overflow or underf low. SQUARE ROOT FUNCTION (y'Xl The range of the argument is a L X L99999999. If X is negative, the calculator will overflow. EXPONENTIAL FUNCTION (xY ) The range of X is 0.0000001 LX £.99999999; the range of y is In 0.000001 L L In 99999999 _ In X -y - In X The calculation is in two parts according to the formula XY = ey1n x. 94 95 Consumer Warranty Rockwell International Corporation Electronic Calculator This electronic calculator from ROCKWELL is warranted to be free from defects in materials and workmanship under normal use and service for one year from the date of retail purchase. Rockwell will, free of charge, repair or replace (at its option) any part(s) which are found to have become defective through normal use, provided that the calculator and charger are returned prepaid within one year to one of the Rockwell Customer Service Centers. (The original packaging is ideal for this purpose.) To assure proper handling.and servicing of your calculator under the one-year warranty, you must send with your calculator a copy of the sales receipt (or other proof of purchase date). Calculators returned without proof of purchase date will be serviced out-of-warranty at our prevailing service rates. 96 This Warranty does not extend to any article which has been subject to misuse, neglect or accident, or if the Serial Number has been altered or defaced, or if the calculator has been serviced by anyone other than a Rockwell Consumer Service Center. This Warranty contains the entire obligation of Rockwell and no other warranties express or implied or statutory are given. In no event shall Rockwell be liable for consequential damages. For service under this Warranty, send your Rockwell electronic calculator prepaid, with copy of sales receipt or other proof of purchase date, to your nearest Rockwell Consumer Service Center. Out-af-Warranty Service If the calculator fails to operate satisfactorily beyond the one'year warranty period, Rockwell International Service Centers will repair and return the calculator to you for a nominal sum.

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