Explanation Given Information: The provided function is y = 4 sin ( 3 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 = 4 sin ( 3 x + 180 ° ) Now, compare the provided function y = 4 sin ( 3 x + 180 ° ) with the function y = A s c t ( B x + Q ) . So, it can be concluded that, Amplitude = 4 And, period = 360 3 = 120 And, phase = 180 3 = 60 Thus, the amplitude is 4 , period is 120 ° and phase is 60 ° left in the given function y = 4 sin ( 3 x + 180 ) . Graph: Consider the provided function: y = 4 sin ( 3 x + 180 ) Now, obtain the values of y by assuming corresponding values of x as: Substitute x = 0 in the function y = 4 sin ( 3 x + 180 ) . y = 4 sin ( 3 ⋅ 0 + 180 ) = 4 sin ( 180 ) = 0 Substitute x = 30 in the function y = 4 sin ( 3 x + 180 ) . y = 4 sin ( 3 ⋅ 30 + 180 ) = 4 sin ( 270 ) = − 4 ⋅ 1 = − 4 Substitute x = 60 in the function y = 4 sin ( 3 x + 180 ) . y = 4 sin ( 3 ⋅ 60 + 180 ) = 4 sin ( 360 ) = 4 ⋅ 0 = 0 Substitute x = 90 in the function y = 4 sin ( 3 x + 180 )

11th Edition

ISBN: 9781285199191

Author: Dale Ewen, C. Robert Nelson

Publisher: Cengage Learning

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Chapter 14.2, Problem 17E

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To calculate: The period and amplitude and phase of the given expression y=4sin(3x+180°) and graph the provided function.

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Chapter 14.2, Problem 16E

Chapter 14.2, Problem 18E

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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 = 4 sin ( 3 x + 180 ° ) and graph the provided function.

Solution Summary: The author calculates the period and amplitude and phase of the given expression y=4mathrmsin(3x+180°).

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To calculate: The period and amplitude and phase of the given expression y=4sin(3x+180°) and graph the provided function.

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Chapter 14 Solutions