Explanation Given Information: The provided function is y = 5 cos ( 2 x + 60 ° ) . 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 = 5 cos ( 2 x + 60 ° ) Now, compare the provided function y = 5 cos ( 2 x + 60 ° ) with the function y = A s c t ( B x + Q ) . So, it can be concluded that, Amplitude = 5 And, period = 360 2 = 180 And, phase = 60 2 = 30 Thus, the amplitude is 5 , period is 180 ° and phase is 30 ° left in the given function y = 5 cos ( 2 x + 60 ) . Graph: Consider the provided function: y = 5 cos ( 2 x + 60 ) Now, obtain the values of y by assuming corresponding values of x as: Substitute x = 0 in the function y = 5 cos ( 2 x + 60 ) . y = 5 cos ( 2 ⋅ 0 + 60 ) = 5 ⋅ 0.5 = 2.5 Substitute x = 30 in the function y = 5 cos ( 2 x + 60 ) . y = 5 cos ( 2 ⋅ 30 + 60 ) = 5 ⋅ cos ( 120 ) = − 5 ⋅ 0.5 = − 2.5 Substitute x = 60 in the function y = 5 cos ( 2 x + 60 ) . y = 5 cos ( 2 ⋅ 60 + 60 ) = 5 ⋅ cos ( 180 ) = − 5 ⋅ 1 = − 5 Substitute x = 90 in the function y = 5 cos ( 2 x + 60 )

11th Edition

ISBN: 9781285199191

Author: Dale Ewen, C. Robert Nelson

Publisher: Cengage Learning

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Chapter 14.2, Problem 18E

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To calculate: The period and amplitude and phase of the given expression y=5cos(2x+60°) and graph the provided function.

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Chapter 14.2, Problem 17E

Chapter 14.2, Problem 19E

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The period and amplitude and phase of the given expression y = 5 cos ( 2 x + 60 ° ) and graph the provided function.

Solution Summary: The author calculates the period, amplitude, and phase of the given expression y=5mathrmcos(2x+60°).

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To calculate: The period and amplitude and phase of the given expression y=5cos(2x+60°) and graph the provided function.

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Chapter 14 Solutions