Explanation Formula used: The graphs of the form y = a sin ( b x + c ) or y = a cos ( b x + c ) has the displacement − c b . Calculation: The given function is, y = 0.5 sec ( 0.2 x + π 25 ) . Since the period for sec x is 2 π , the period of sec 0.2 x will be 2 π 0.2 = 10 π . That is, the period of y = 0.5 sec ( 0.2 x + π 25 ) is 10 π . Thus, one-fourth of the period will be, 1 4 ( 10 π ) = 5 π 2 . Since sec x = ( cos x ) − 1 , the curve y = 0.5 sec ( 0.2 x + π 25 ) will have the same displacement as that of y = 0.5 cos ( 0.2 x + π 25 ) . By the above mentioned formula, the displacement of y = 0.5 cos ( 0.2 x + π 25 ) is − ( π 25 ) 0.2 = − π 5 . That is, the displacement of y = 0.5 sec ( 0.2 x + π 25 ) is − π 5 . Thus, the curve starts at − π 5 and starts repeating 10 π units to the right of − π 5 . Since the period is 10 π , the one complete cycle ends at − π 5 + 10 π = 49 π 5 . Thus, the two complete cycles ends at − π 5 + 2 ( 10 π ) = 99 π 5 . That is, two cycles occur between x = − π 5 and x = 99 π 5 . The important values for the first cycle are at − π 5 , − π 5 + 5 π 2 , − π 5 + 2 ( 5 π 2 ) , − π 5 + 3 ( 5 π 2 ) and − π 5 + 4 ( 5 π 2 ) . That is, at − π 5 , 23 π 10 , 24 π 5 , 73 π 10 and 49 π 5 . Substitute x = − π 5 in the equation y = 0.5 sec ( 0.2 x + π 25 ) . y = 0.5 sec ( 0.2 x + π 25 ) = 0

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 10.4, Problem 24E

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To sketch: At least two cycles of graph of the function y=0.5sec(0.2x+π25) on a calculator.

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Chapter 10.4, Problem 23E

Chapter 10.4, Problem 25E

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10 5 Obtain by multiplying matrices the composite coordinate transformation of two transformations, first x' = (x + y√√2+2)/2 y' = z' (x√√2-2√2)/2 z = (-x+y√√2-2)/2 followed by x" = (x'√√2+z'√√2)/2 y" = (-x'y'√√2+2')/2 z" = (x'y'√√2-2')/2.

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Chapter 10 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 10.1 - For the graph of y = −6 sin x, set up a table of...Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - In Exercises 3–6, complete the following table for...Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - In Exercises 7–22, give the amplitude and sketch...Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E

Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - In Exercises 7–22, give the amplitude and sketch...Ch. 10.1 - In Exercises 7–22, give the amplitude and sketch...Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - In Exercises 27–32, solve the given problems. 32....Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.2 - Prob. 1PE Ch. 10.2 - Prob. 2PE Ch. 10.2 - Prob. 3PE Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - In Exercises 3–22, find the amplitude and period...Ch. 10.2 - Prob. 5E Ch. 10.2 - In Exercises 3–22, find the amplitude and period...Ch. 10.2 - 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Prob. 43E Ch. 10.2 - Prob. 44E Ch. 10.2 - Prob. 45E Ch. 10.2 - Prob. 46E Ch. 10.3 - Prob. 1PE Ch. 10.3 - Prob. 2PE Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Prob. 10E Ch. 10.3 - Prob. 11E Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - Prob. 19E Ch. 10.3 - In Exercises 3–26, determine the amplitude,...Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Prob. 23E Ch. 10.3 - Prob. 24E Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Prob. 31E Ch. 10.3 - Prob. 32E Ch. 10.3 - 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At least two cycles of graph of the function y = 0.5 sec ( 0.2 x + π 25 ) on a calculator.

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To sketch: At least two cycles of graph of the function y=0.5sec(0.2x+π25) on a calculator.

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Chapter 10 Solutions