Explanation Given Information: The provided function is y = 10 sin ( 4 x − 120 ° ) . 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 = 10 sin ( 4 x − 120 ° ) Now, compare the provided function y = 10 sin ( 4 x − 120 ° ) with the function y = A s c t ( B x + Q ) . So, it can be concluded that, Amplitude = 10 And, period = 360 4 = 90 And, phase = − 120 4 = − 30 Thus, the amplitude is 10 , period is 90 ° and phase is 30 ° right in the given function y = 10 sin ( 4 x − 120 ) . Graph: Consider the provided function: y = 10 sin ( 4 x − 120 ) Now, obtain the values of y by assuming corresponding values of x as: Substitute x = 0 in the function y = 10 sin ( 4 x − 120 ) . y = 10 sin ( 4 ⋅ 0 − 120 ) = − 10 ⋅ 0.8660 = − 8.660 Substitute x = 30 in the function y = 10 sin ( 4 x − 120 ) . y = 10 sin ( 4 ⋅ 30 − 120 ) = 10 sin ( 0 ) = 10 ⋅ 0 = 0 Substitute x = 60 in the function y = 10 sin ( 4 x − 120 ) . y = 10 sin ( 4 ⋅ 60 − 120 ) = 10 sin ( 120 ) = 10 ⋅ 0

12th Edition

ISBN: 9781337630580

Author: Dale Ewen

Publisher: Cengage Learning

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Chapter 14.2, Problem 19E

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To calculate: The period and amplitude and phase of the given expression y=10sin(4x−120°) and graph the provided function.

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Chapter 14.2, Problem 18E

Chapter 14.2, Problem 20E

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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 = 10 sin ( 4 x − 120 ° ) and graph the provided function.

Solution Summary: The author calculates the period, amplitude, and phase of the given expression y=10mathrmsin(4x-120°).

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To calculate: The period and amplitude and phase of the given expression y=10sin(4x−120°) and graph the provided function.

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Chapter 14 Solutions