Explanation Given Information: The provided function is y = 12 cos ( 4 x + 180 ° ) . 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 = 12 cos ( 4 x + 180 ° ) Now, compare the provided function y = 12 cos ( 4 x + 180 ° ) with the function y = A s c t ( B x + Q ) . So, it can be concluded that, Amplitude = 12 And, period = 360 4 = 90 And, phase = 180 4 = 45 Thus, The amplitude is 12 , period is 90 ° and phase is 45 ° left in the given function y = 12 cos ( 4 x + 180 ) . Graph: Consider the provided function: y = 12 cos ( 4 x + 180 ) Now, obtain the values of y by assuming corresponding values of x as: Substitute x = 0 in the function y = 12 cos ( 4 x + 180 ) . y = 12 cos ( 4 ⋅ 0 + 180 ) = − 12 ⋅ 1 = − 12 Substitute x = 30 in the function y = 12 cos ( 4 x + 180 ) . y = 12 cos ( 4 ⋅ 30 + 180 ) = 12 cos ( 300 ) = 12 ⋅ 0.5 = 6 Substitute x = 60 in the function y = 12 cos ( 4 x + 180 ) . y = 12 cos ( 4 ⋅ 60 + 180 ) = 12 cos ( 420 ) = 12 ⋅ 0

11th Edition

ISBN: 9781285199191

Author: Dale Ewen, C. Robert Nelson

Publisher: Cengage Learning

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Chapter 14.2, Problem 20E

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To calculate: The period and amplitude and phase of the given expression y=12cos(4x+180°) and graph the provided function.

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Chapter 14.2, Problem 19E

Chapter 14.2, Problem 21E

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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 = 12 cos ( 4 x + 180 ° ) and graph the provided function.

Solution Summary: The author calculates the period, amplitude, and phase of the given expression y=12mathrmcos(4x+180°).

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To calculate: The period and amplitude and phase of the given expression y=12cos(4x+180°) and graph the provided function.

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Chapter 14 Solutions