Explanation Given Information: The provided function is y = 6 cos ( 3 4 x − 240 ° ) . Formula Used: For a given function y = A s c t ( B x + Q ) , where s c t = sin / cos / tan Here, A = Amplitude , Period = 360 B and Phase = Q B Calculation: Consider the provided function: y = 6 cos ( 3 4 x − 240 ° ) Now, compare the provided function y = 6 cos ( 3 4 x − 240 ° ) with the function y = A s c t ( B x + Q ) . So, it can be concluded that, Amplitude = 6 And, period = 360 3 4 = 360 ⋅ 4 3 = 480 And, phase = − 240 3 4 = − 320 Thus, the amplitude is 5 , period is 480 ° and phase is 320 ° right in the given function y = 6 cos ( 3 4 x − 240 ) . Graph: Consider the provided function: y = 6 cos ( 3 4 x − 240 ) Now, obtain the values of y by assuming corresponding values of x as: Substitute x = 0 in the function y = 6 cos ( 3 4 x − 240 ) . y = 6 cos ( 3 4 ⋅ 0 − 240 ) = − 6 ⋅ 0.5 = − 3 Substitute x = 30 in the function y = 6 cos ( 3 4 x − 240 ) . y = 6 cos ( 3 4 ⋅ 30 − 240 ) = 6 ⋅ cos ( − 217.5 ) = − 6 ⋅ 0.7933 = − 4.7601 Substitute x = 60 in the function y = 6 cos ( 3 4 x − 240 ) . y = 6 cos ( 3 4 ⋅ 60 − 240 ) = 6 ⋅ cos ( − 195 ) = − 6 ⋅ 0

11th Edition

ISBN: 9781285199191

Author: Dale Ewen, C. Robert Nelson

Publisher: Cengage Learning

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Chapter 14.2, Problem 22E

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To calculate: The period and amplitude and phase of the given expression y=6cos(34x−240°) and graph the provided function.

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Chapter 14.2, Problem 21E

Chapter 14.2, Problem 23E

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Chapter 14 Solutions

Elementary Technical Mathematics

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The period and amplitude and phase of the given expression y = 6 cos ( 3 4 x − 240 ° ) and graph the provided function.

Solution Summary: The author compares the provided function y=6mathrmcos(34x-240°) with the given function.

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To calculate: The period and amplitude and phase of the given expression y=6cos(34x−240°) and graph the provided function.

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Chapter 14 Solutions