Sharp EL-W516B - Scientific Calculator With WriteView Operation Manual Download

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Calculator Activity

INVERSE TRIGONOMETRIC FUNCTIONS

OBJECTIVE:

To perform operations with inverse trigonometric functions.

1. Find



in degrees when

tan





STEP 1: Set the angular units to degrees by pressing

STEP 2: Enter

)

(

tan



by pressing

STEP 3: Calculate the answer by pressing

2. Find



in degrees when

cos





STEP 1: Set the angular units to degrees by pressing

STEP 2: Enter

)

(

cos



by pressing

STEP 3: Calculate the answer by pressing

3. Find



in radians when

sin





STEP 1: Set the angular units to radians by pressing

STEP 2: Enter

)

(

sin



by pressing

STEP 3: Calculate the answer by pressing

Summary of Contents for EL-W516B - Scientific Calculator With WriteView

Page 1: ...EL W516B Calculator Teaching Activities For The Classroom Jeremy Ross ...

Page 2: ...s reserved This publication may not be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording or otherwise without written permission Sharp is a registered trademark of Sharp Corporation ...

Page 3: ...ractice Activity TRIGONOMETRIC FUNCTIONS Calculator Activity Practice Activity INVERSE TRIGONOMETRIC FUNCTIONS Calculator Activity Practice Activity COORDINATE CONVERSIONS Calculator Activity Practice Activity LOGARITHMS Calculator Activity Practice Activity INVERSE LOGARITHMS Calculator Activity Practice Activity BASE CONVERSIONS Calculator Activity Practice Activity CONSTANTS AND CONVERSIONS Cal...

Page 4: ... Practice Activity MATRIX CALCULATIONS Calculator Activity Practice Activity LIST CALCULATIONS Calculator Activity Practice Activity LINEAR QUADRATIC AND CUBIC EQUATIONS Calculator Activity Practice Activity SUMMATION Calculator Activity Practice Activity DERIVATIVES Calculator Activity Practice Activity INTEGRALS Calculator Activity Practice Activity ANSWERS 36 37 38 39 40 41 42 43 44 45 46 47 48...

Page 5: ...1 ...

Page 6: ...nd then choose your TAB or decimal setting To set the calculator for scientific notation press Now enter the number of significant figures To set the calculator for engineering notation press and then enter the desired TAB setting To set the floating point number system in scientific notation press either or to choose NORM1 or NORM2 To choose WriteView which displays formulas and equations just li...

Page 7: ...ated at Constant Press and then enter the corresponding value for the constant you want Conversion Enter the number you wish to convert Press and then enter the corresponding value for the conversion Then press Pi Press Imaginary Numbers When in CPLX mode press Summation Press Enter the lower bound Press and enter the upper bound Press and enter the expression Then press Degrees Minutes Seconds En...

Page 8: ...ess Cube roots Press Enter the radicand Then press Reciprocals Enter the number Press followed by Then press Antilogarithms Press Enter the exponent Then press Exponentials Press followed by Enter the exponent Then press Cubes Enter the number to be cubed Press Then press Scientific Notation Enter the number Press Enter the power Then press Euler s Number To enter e press followed by Fractions Ent...

Page 9: ...Press Press the location you wish to store your function Change You can change your answer from decimals to mixed numbers to fractions by pressing Also you can change your answer from decimals or fractions to answer containing the pi symbol or square root symbol by pressing Random You can generate random numbers dice coin flips or integers Press Press for random numbers between 0 and 1 Press for r...

Page 10: ...nter the number Then press Hexadecimal To convert from one of the supported base systems into hexadecimal enter the number Then press Octadecimal To convert from one of the supported base systems into octadecimal enter the number Then press Decimal To convert from one of the supported base systems into decimal enter the number Then press Pentadecimal To convert from one of the supported base syste...

Page 11: ...the keystrokes required to enter each problem From these simple examples more complicated expressions can be easily entered 9 2 1 3 1 4 3 2 3 2 17 4 3 2 3 2 1 33 153 e ln 10 log 4 log2 2 3 10 e 30 sin 0 cos 1 78 tanh 3 5 10C 1 6P 5 x x dx d dx x 2 1 2 7 ...

Page 12: ... and practice sheets found in this book have been designed to be used with the Sharp EL W516B calculator The activities have been written and developed for students in grades nine through twelve Some of the activities will be more appropriate for students in a particular grade while others could be used at any grade level Of course the classroom teacher can and should make the decision as the appr...

Page 13: ... was designed with you and your students in mind The following activities have been written to provide the practice students need to succeed in mathematics as they become familiar with the wonderful features of this exciting and powerful mathematical tool 9 ...

Page 14: ...y pressing STEP 2 Add by pressing STEP 3 Enter 54 by pressing STEP 4 Find the first sum by pressing STEP 5 Add 13 again by pressing 2 Subtract 9 from 32 once STEP 1 Enter 32 by pressing STEP 2 Subtract by pressing STEP 3 Enter 9 by pressing STEP 4 Find the difference by pressing 3 Multiply 2 by 5 three times STEP 1 Enter 2 by pressing followed by STEP 2 Multiply by pressing STEP 3 Enter 5 by press...

Page 15: ...is by adding 3 6 ___ ___ ___ ___ 4 Find the first three numbers of the sequence starting with 144 where each additional term is found by dividing by 2 144 ___ ___ 5 Find the first six terms of the sequence starting with 729 where each additional term is found by dividing by 3 729 ___ ___ ___ ___ ___ 6 Find the first three terms of the sequence starting with 1 where each additional term is found by...

Page 16: ... 1 Then convert to a decimal STEP 1 Enter 2 1 by pressing STEP 2 Subtract by pressing STEP 3 Enter 13 5 by pressing STEP 4 Find the difference by pressing STEP 5 Convert to a decimal by pressing 3 Simplify 3 2 6 4 3 1 Then convert to an improper fraction STEP 1 Enter 4 3 1 by pressing STEP 2 Multiply by pressing STEP 3 Enter 3 2 6 by pressing STEP 4 Find the product by pressing STEP 5 Convert to a...

Page 17: ...etic mean of the following fractions 16 1 4 1 2 1 2 Find the arithmetic mean of the following fractions and convert to a decimal 12 5 11 4 10 3 9 2 8 1 3 Simplify 5 1 9 7 6 20 1 1 4 Simplify 8 7 6 5 4 3 2 1 5 Simplify 3 1 2 1 1 3 1 2 1 1 6 Simplify 11 6 2 1 11 6 2 1 8 5 3 3 4 and convert to an improper fraction 7 Simplify 6 1 6 2 3 5 8 8 Simplify 2 2 2 4 5 4 5 2 13 ...

Page 18: ... Calculate the answer by pressing 2 Calculate 6 5 3 STEP 1 Enter 5 3 by pressing STEP 2 Raise the expression to the 6th power by pressing STEP 3 Calculate the answer by pressing 3 Calculate 3 1 5 STEP 1 Enter 3 by pressing STEP 2 Enter 1 5 by pressing STEP 3 Calculate the answer by pressing 4 Evaluate 4 2 STEP 1 Enter 4 2 by pressing STEP 2 Calculate the answer by pressing 14 ...

Page 19: ... 1 Simplify 2 2 2 2 2 5 4 3 2 1 ____________________________ 2 Simplify 5 4 3 2 1 ____________________________ 3 Is 7 3 7 3 2 2 2 Explain your answer ____________________________ ____________________________ ____________________________ 4 Simplify 3 3 2 ____________________________ 5 Simplify 3 33 2 ____________________________ 6 Simplify 2 2 2 4 5 5 2 2 2 4 5 5 2 2 ____________________________ 15...

Page 20: ...ise 2 to the third power by pressing and then STEP 5 Calculate the answer by pressing 2 Edit the previous equation and solve the volume of the sphere given the radius is 1 Then convert the answer to a decimal STEP 1 Recall the previous equation by pressing or STEP 2 Move the cursor so it is to the immediate right of the third power STEP 3 Delete the power the parenthesis the 2 and the square root ...

Page 21: ...the sphere whose radius is 6 ____________________________ 2 Find the volume of the sphere whose radius is 5 ____________________________ 3 Find the volume of the sphere whose radius is 9 ____________________________ 4 Find the volume of the sphere whose radius is 10 ____________________________ 5 Find the volume of the sphere whose diameter is 10 ____________________________ 6 Find the volume of a...

Page 22: ... conversion press and then choose the appropriate angular units 1 Convert 45 to radians and grads STEP 1 Set the angular units to degrees by pressing STEP 2 Enter 45 by pressing STEP 3 Convert to radians by pressing STEP 4 Convert to grads by pressing 2 Convert 58 23 11 to decimal degrees STEP 1 Enter 58 23 11 by pressing STEP 2 Calculate decimal degrees by pressing STEP 3 Convert to a decimal by ...

Page 23: ...n radians _____________________ 2 A pentagon has four angles which are 30 30 60 and 100 Find the missing angle and express your answer in grads _____________________ 3 A triangle has two angles which are 100 grads and 20 grads Find the missing angle and express your answer in radians _____________________ 4 A hexagon has five angles which are 5 1 radians 3 radians 4 radians 5 radians and radians F...

Page 24: ...ab b a c 1 Using the law of sines find the length of side a given 4 53 37 b STEP 1 Set the angular units to degrees by pressing STEP 2 Multiply 4 by 37 sin by pressing STEP 3 Divide by 53 sin by pressing 2 Using the law of cosines fine the length of c given radians b a 2 12 5 STEP 1 Set the angular units to radians by pressing STEP 2 Add 2 5 and 2 12 by pressing STEP 3 Subtract 2 cos 12 5 2 by pre...

Page 25: ... c b a The law of cosines is cos 2 2 2 2 ab b a c 1 Given 11 63 30 a determine the length of side c ___________________ 2 Given 16 grads 69 grads 123 b find the length of side a ___________________ 3 Given 5 1 40 30 b a radians find the length of side c ___________________ 4 Given 45 30 15 c a find the length of side b ___________________ 5 Given 100 23 13 c b grads find the length of side a using...

Page 26: ...ressing STEP 2 Enter 1 tan 1 by pressing STEP 3 Calculate the answer by pressing 2 Find in degrees when 0 cos STEP 1 Set the angular units to degrees by pressing STEP 2 Enter 1 cos 1 by pressing STEP 3 Calculate the answer by pressing 3 Find in radians when 2 2 sin STEP 1 Set the angular units to radians by pressing STEP 2 Enter 2 2 sin 1 by pressing STEP 3 Calculate the answer by pressing 22 ...

Page 27: ...ng angle The law of sines is sin sin sin c b a The law of cosines is cos 2 2 2 2 ab b a c 1 Given 23 7 2 b a find in grads ___________________ 2 Given 94 21 34 c a grads find in radians ___________________ 3 Given 5 4 3 c b a find in degrees ___________________ 4 Given 17 24 40 c b a find in radians ___________________ 5 Given 13 12 5 c b a find in degrees ___________________ 23 ...

Page 28: ...ounterclockwise from the positive x axis 1 While in degrees convert the rectangular coordinates 1 1 to polar coordinates STEP 1 Set the angular units to degrees by pressing STEP 2 Enter 1 1 by pressing STEP 3 Convert to polar coordinates by pressing 2 While in radians convert the polar coordinates of 60 2 2 to rectangular coordinates STEP 1 Set the angular units to radians by pressing STEP 2 Enter...

Page 29: ...While in degrees convert the rectangular coordinates 2 2 to polar coordinates r ______ __________ r ______ __________ 2 While in radians convert the rectangular coordinates 3 3 2 to polar coordinates r ______ __________ r ______ __________ 3 While in degrees convert the polar coordinates 5 3 4 to rectangular coordinates y x ______ __________ x ______ __________ y 4 While in degrees convert the pol...

Page 30: ...essing 2 Find 10 log STEP 1 Enter log by pressing STEP 2 Enter 10 by pressing STEP 3 Calculate the answer by pressing 3 Find e ln STEP 1 Enter ln by pressing STEP 2 Enter e by pressing STEP 3 Calculate the answer by pressing 4 Find 2 lne STEP 1 Enter ln by pressing STEP 2 Enter 2 e by pressing STEP 3 Calculate the answer by pressing 5 Find 4 log2 STEP 1 To enter 2 log press STEP 2 Enter 4 by press...

Page 31: ... the unknown 1 Solve for x 123 log 2 5 x _____________________ 2 Solve for y 3 ln 1 5 21 y _____________________ 3 Solve for z 2 36 log 54 6 z _____________________ 4 Solve for x 2 1 ln 100 log e x _____________________ 5 Solve for y 2 21 ln 100 log y _____________________ 6 Solve for z 200 ln 25 log 32 log2 z _____________________ 27 ...

Page 32: ... the answer by pressing 2 Find 3 6 10 in scientific notation with three significant figures STEP 1 Set the calculator to scientific notation with three significant figures by pressing STEP 2 Press STEP 3 Enter 6x3 by pressing STEP 4 Calculate the answer by pressing 3 Find 3 4 7 e STEP 1 Enter e by pressing STEP 2 Enter 3 4 7 by pressing STEP 3 Calculate the answer by pressing 28 ...

Page 33: ...uations for the given unknown 1 Solve for x 2 6 5 10 2 x _____________________ 2 Solve for y 2 5 e y _____________________ 3 Solve for z 3 2 10 3 1 z _____________________ 4 Solve for x 4 5 2 5 10 e x _____________________ 5 Solve for y 1 3 10 2 2 e y _____________________ 6 Solve for z 1 3 2 6 3 2 10 10 e z _____________________ 29 ...

Page 34: ...ary by pressing STEP 2 Enter 10011001 by pressing STEP 3 Convert to decimal by pressing 2 Convert the hexadecimal number 16841601 to octadecimal STEP 1 Set the calculator to hexadecimal by pressing STEP 2 Enter 16841601 by pressing STEP 3 Convert to octadecimal by pressing 3 Convert the decimal number 144169 to pentadecimal STEP 1 Set the calculator to decimal by pressing STEP 2 Enter the number 1...

Page 35: ...cimal ____________________________ 2 Convert the hexadecimal number 123 to binary ____________________________ 3 Perform the indicated operations in hexadecimal and then convert your answer to octadecimal 12 3 2 2 8 ____________________________ 4 Perform the indicated operations in decimal and then convert your answer to binary 24 36 6 1 3 15 ____________________________ 5 Convert the binary numbe...

Page 36: ... 3 Square c by pressing STEP 4 Solve for E by pressing 2 What is the energy of an object given the mass of that object is 123 kilograms STEP 1 Enter 123 by pressing STEP 2 To multiply by the constant c press STEP 3 Square c by pressing STEP 4 Solve for E by pressing 3 What is F 95 equal to in Celsius STEP 1 Enter 95 by pressing STEP 2 To select to convert to Celsius press STEP 3 To convert press 4...

Page 37: ...nergy does a particle whose mass is 10 kilograms have ____________________ 2 How much energy does a particle whose mass is 5 kilograms have ____________________ 3 How many feet are in 3 meters ____________________ 4 How many yards in are 5 meters ____________________ 5 How much energy does a particle whose weight is 200 pounds have ____________________ 6 How much energy does an object whose weight...

Page 38: ...ress STEP 2 To generate random dice throws press STEP 3 Generate the first random dice throw by pressing STEP 4 Generate the second random dice throw by pressing STEP 5 Generate the third random dice throw by pressing 3 Generate 3 random coin tosses STEP 1 Press STEP 2 To generate random coin flips press STEP 3 Generate the first random coin flip by pressing STEP 4 Generate the second random coin ...

Page 39: ...___ ___ ___ ___ ___ 3 Generate a sequence of 10 random coin flips ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 4 Generate a sequence of 3 random integers ___ ___ ___ 5 Generate a sequence of 12 dice throws and based on that sequence what is the probability of rolling a 6 ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ _______________ 6 Generate a sequence of 10 random coin flips and based on that seque...

Page 40: ... many different ways can you choose 1 from a group of 6 STEP 1 Enter the larger number 6 by pressing STEP 2 Enter the combination symbol by pressing STEP 3 Enter the smaller number 1 by pressing STEP 4 Calculate the answer by pressing 3 Find the number of permutations of 4 things taken 2 at a time STEP 1 Enter the larger number 4 by pressing STEP 2 Enter the permutation symbol by pressing STEP 3 E...

Page 41: ...ss of 10 where order does matter ____________________________ 3 How many sets of 3 officers can be formed from a group of 15 where order does not mater ____________________________ 4 How many sets of 3 officers can be formed from a group of 15 where order does matter ____________________________ 5 Evaluate 5 ____________________________ 6 What is 0 What is 1 Explain why the answer is so __________...

Page 42: ...y pressing STEP 3 Enter 25 by pressing STEP 4 Enter 35 two times by pressing STEP 5 Enter 50 by pressing STEP 6 To determine the mean of the sample press STEP 7 To determine the sample mean standard deviation press STEP 8 To determine the population standard deviation press STEP 9 To determine the number of samples press STEP 10 To determine the sum of the samples press STEP 11 To determine the su...

Page 43: ...____________ x ______________ 2 x ______________ 2 Analyze the set 25 25 20 15 10 x ______________ sx ______________ x ______________ n ______________ x ______________ 2 x ______________ 3 Analyze the set 8 5 3 2 1 1 x ______________ sx ______________ x ______________ n ______________ x ______________ 2 x ______________ 4 Analyze the set 32 16 8 4 2 1 x ______________ sx ______________ x _________...

Page 44: ... for x press STEP 8 To determine the population standard deviation for x press STEP 9 To determine the number of samples for x press STEP 10 To determine the sum of the samples for x press STEP 11 To determine the sum of squares of samples for x press STEP 12 To determine the mean of the samples for y press STEP 13 To determine the sample mean standard deviation for y press STEP 14 To determine th...

Page 45: ..._____________ x ______________ n ______________ x ______________ 2 x ______________ y ______________ sy ______________ y ______________ y ______________ 2 y ______________ a ______________ b ______________ 2 Analyze the set and run a linear regression X 1 2 3 4 5 6 Y 2 7 1 8 2 8 x ______________ sx ______________ x ______________ n ______________ x ______________ 2 x ______________ y _____________...

Page 46: ...n CPLX mode by pressing 1 What is the modulus of i 2 STEP 1 To start the absolute value press STEP 2 To enter 2 press STEP 3 To enter i press and then press STEP 4 To determine the modulus press 2 What is the complex conjugate of i 2 1 STEP 1 Press STEP 2 To enter i 2 1 press STEP3 Press to get the complex conjugate 3 Simplify i i 6 3 2 1 STEP 1 To enter 3 2 1 i press STEP 2 To subtract press STEP...

Page 47: ...mplify complex expressions 1 What is the modulus of i ____________________ 2 What is the modulus of 2 3 i ____________________ 3 What is the complex conjugate of i ____________________ 4 Simplify i i 1 1 ____________________ 5 Simplify 2 2 i i ____________________ 6 What is 3 2 1 0 i i i i ____________________ 7 Simplify sin cos i ____________________ 43 ...

Page 48: ...8 7 6 5 B To enter matrix A press Then press Then press To enter matrix B press Then press Then press Now matrix A and B are stored 1 Evaluate AxB STEP 1 To enter A x Press STEP 2 To enter B press STEP 3 To solve press 2 What is the inverse of A STEP 1 To enter A press STEP 2 To take the inverse press STEP 3 To solve press 3 Augment A with B STEP 1 To augment press STEP 2 To enter A press STEP 3 T...

Page 49: ...r the following problems use 8 6 4 2 A 7 5 3 1 B 34 21 13 8 5 3 2 1 1 C 1 0 0 0 1 0 0 0 1 D 1 Calculate 1 D ____________________ 2 Evaluate CD ____________________ 3 Evaluate DC ____________________ 4 Augment matrix A with matrix B ____________________ 5 What is the determinant of matrix A The determinant is done by entering ____________________ 45 ...

Page 50: ...ss After this press Now L1 and L2 are stored 1 Evaluate L1 L2 STEP 1 Press to enter L1 STEP 2 To add L2 press STEP 3 To calculate the sum of the lists press 2 Sort L2 descending STEP 1 To bring up sort press STEP 2 To enter L2 press STEP 3 To sort press NOTE To sort ascending can be done in a similar manner 3 Calculate the min L1 STEP 1 For min press STEP 2 To enter L1 press STEP 3 To calculate th...

Page 51: ..._______________ Median ____________________ Sum ____________________ Product ____________________ Standard Deviation ____________________ Variance ____________________ 2 Put 3 1 4 1 5 9 in L1 and 2 7 1 8 2 8 in L2 Add L1 and L2 and put this new list into L3 Then determine the min max mean median sum product standard deviation and variance of L3 Min ____________________ Max ____________________ Mea...

Page 52: ...ion by pressing STEP 3 Enter the coefficients for the second equation by pressing NOTE 3 simultaneous equations can be done by choosing 3 VLE and entered in a simlar fashion as 2 VLE 2 Solve the following quadratic equation 0 6 2 x x STEP 1 Chose QUAD by pressing STEP 2 Enter the coefficients by pressing 3 Solve the following cubic equation and express the answer in factored form 0 6 11 6 2 3 x x ...

Page 53: ... EQUATION mode by pressing 1 Solve the two linear equations for x and y 0 5 3 10 2 y x y x ____________________ 2 Solve the three linear equations for x y and z 0 6 5 z y z y x y x ____________________ 3 Solve the following quadratic equation 0 1 2 x x ____________________ 4 Solve the following cubic equation and express the answer in factored form 0 1 2 3 x x x ____________________ ______________...

Page 54: ...luate 20 1 1 x STEP 1 Bring up the summation symbol by pressing STEP 2 Enter the lower bound 1 by pressing STEP 3 Enter the upper bound of 20 by pressing STEP 4 Enter x 1 by pressing STEP 5 To determine the sum of the series press 3 Evaluate 10 0 2 1 1 x x STEP 1 Bring up the summation symbol by pressing STEP 2 Enter the lower bound 0 by pressing STEP 3 Enter the upper bound of 10 by pressing STEP...

Page 55: ...16B to calculate the sum of the series 1 Evaluate 5 1 2x ____________________ 2 Evaluate 10 3 3 1 2 x ____________________ 3 Evaluate 4 0 2x e ____________________ 4 Evaluate 9 1 ln x x x ____________________ 5 Evaluate 20 10 x x ____________________ 6 Evaluate 100 1 1 x ____________________ 51 ...

Page 56: ...sing STEP 3 Enter 5 by pressing STEP 4 To solve press 2 Evaluate x dx d sin where x radians STEP 1 Set the calculator to radians by pressing STEP 2 Press STEP 3 Enter x sin by pressing STEP 4 Enter by pressing STEP 5 To solve press 3 Evaluate x dx d ln when 2 x STEP 1 Press STEP 2 Enter x ln by pressing STEP 3 Enter 2 by pressing STEP 4 To solve press 52 ...

Page 57: ...vative 1 Evaluate x dx d when 2 x ___________________ 2 Evaluate x x dx d when 5 x ___________________ 3 Evaluate x x dx d 2 3 when 1 3 x ___________________ 4 Evaluate x e dx d when 4 x ___________________ 5 Evaluate x e dx d x ln when 5 x ___________________ 6 Evaluate x dx d 1 sin when 0 x grads ___________________ 53 ...

Page 58: ...by pressing 2 Find the area under the curve of 2 x given the lower bound is 1 and the upper bound is 2 STEP 1 Press STEP 2 Enter the lower bound of 1 by pressing STEP 3 Enter the upper bound of 2 by pressing STEP 4 Enter 2 x by pressing STEP 5 Evaluate the integral by pressing 3 Find the area under the curve of 3 x given the lower bound is 1 and the upper bound is 2 STEP 1 Press STEP 2 Enter the l...

Page 59: ...he lower bound is 1 and the upper bound is 1 ____________________ 3 Find the area under the curve of 3 x given the lower bound is 1 and the upper bound is 1 ____________________ 4 Find the area of 2 x x given the lower bound is 1 and the upper bound is 1 ____________________ 5 Find the area under the curve of 100 y given the lower bound is 1 and the upper bound is 1 ____________________ 6 Find the...

Page 60: ...382 3 No 4 512 5 2048 6 2 1 Logarithms p 26 1 3 2 1 3 1 4 2 5 2 p 27 1 180 9 2 507 10 3 55 4 2 2 2 5 777 0 6 950 18 Parentheses and Editing p 16 1 11 848 2 4 189 p 17 1 288 2 3 2 166 3 972 4 3 1 1333 5 3 2 166 6 288 Inverse Logarithms p 28 1 1000000 2 18 10 00 1 3 2 718 p 29 1 17 10 1 2 677 0 3 925 12 4 230 0 5 405 8 6 052 98 Angle Conversions p 18 1 4 50 2 11 399 3 8 4 43 2 p 19 1 12 5 2 9 5 355 ...

Page 61: ...33 2 494 6 20 104 4 10 5 11 862 10 828 6 63 1365 Summation p 50 1 154 2 0 3 55 p 51 1 62 2 0 103 3 3447 374 4 34 057 5 26 10 069 1 6 5 187 2 Variable Statistics p 40 1 3 4 3 782 3 382 5 17 115 5 3 464 3 382 25 173 2 147 0 839 p 41 1 2 5 1 291 1 118 4 10 30 3 75 3 096 2 681 15 85 2 2 3 2 3 5 1 871 1 708 6 21 91 4 667 3 327 3 037 28 186 2 467 0 629 Derivatives p 52 1 75 2 1 3 0 5 p 53 1 1 2 8154 493...

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