Explanation Result used: The functions y = a sin ( b x + c ) or y = a cos ( b x + c ) each has an amplitude of | a | , period of 2 π b and displacement is − c b . Calculation: The given function is y = 360 cos ( 6 π x − 3 ) . Compare the equations y = a cos ( b x + c ) and y = 360 cos ( 6 π x − 3 ) . Thus, a = 360 , b = 6 π and c = − 3 . By the above mentioned result, the amplitude of y = 360 cos ( 6 π x − 3 ) will be, | a | = | 360 | ( ∵ a = 360 ) = 360 That is, the maximum value will be 360 and the minimum value will be –360. The period is obtained as follows: 2 π b = 2 π 6 π ( ∵ b = 6 π ) = 1 3 The displacement is obtained as follows: − c b = − ( − 3 ) 6 π ( ∵ b = 6 π and c = − 3 ) = 1 2 π Therefore, the amplitude, period and displacement for the function y = 360 cos ( 6 π x − 3 ) is 360 , 1 3 and 1 2 π _ , respectively. It is known that an important distance in sketching a sine or cosine curve is the values of the function for each one-fourth period. Thus, one-fourth of the period will be, 1 4 ( 1 3 ) = 1 12 . That is, the curve starts at 1 2 π and starts repeating 1 3 units to the right of 1 2 π . Since the period is 1 3 , the one complete cycle of the curve ends at 1 2 π + 1 3 . That is, one complete cycle is from x = 1 2 π to x = 1 3 + 1 2 π

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 10.3, Problem 22E

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The value of amplitude, period and displacement for the function y=360cos(6πx−3), sketch the graph of the function and check using a calculator.

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Chapter 10.3, Problem 21E

Chapter 10.3, Problem 23E

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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

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The value of amplitude, period and displacement for the function y = 360 cos ( 6 π x − 3 ) , sketch the graph of the function and check using a calculator.

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The value of amplitude, period and displacement for the function y=360cos(6πx−3), sketch the graph of the function and check using a calculator.

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Chapter 10 Solutions