Explanation Given Information: The provided function is y = 10 cos ( 1 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 = 10 cos ( 1 4 x + 180 ° ) Now, compare the provided function y = 10 cos ( 1 4 x + 180 ° ) with the function y = A s c t ( B x + Q ) . So, it can be concluded that, Amplitude = 10 And, period = 360 1 4 = 360 ⋅ 4 = 1440 And, phase = 180 1 4 = 180 ⋅ 4 = 720 Thus, the amplitude is 10 , period is 1440 ° and phase is 720 ° left in the given function y = 10 cos ( 1 4 x + 180 ) . Graph: Consider the provided function: y = 10 cos ( 1 4 x + 180 ) Now, obtain the values of y by assuming corresponding values of x as: Substitute x = 0 in the function y = 10 cos ( 1 4 x + 180 ) . y = 10 cos ( 1 4 ⋅ 0 + 180 ) = 10 ⋅ cos ( 180 ) = − 10 ⋅ 1 = − 10 Substitute x = 30 in the function y = 10 cos ( 1 4 x + 180 ) . y = 10 cos ( 1 4 ⋅ 30 + 180 ) = 10 ⋅ cos ( 187.5 ) = − 10 ⋅ 0.9914 = − 9.914 Substitute x = 60 in the function y = 10 cos ( 1 4 x + 180 ) . y = 10 cos ( 1 4 ⋅ 60 + 180 ) = 10 ⋅ cos ( 195 ) = − 10 ⋅ 0

Bundle: Elementary Technical Mathematics, Loose-leaf Version, 12th + WebAssign Printed Access Card, Single-Term

12th Edition

ISBN: 9781337890199

Author: Dale Ewen

Publisher: Cengage Learning

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Chapter 14.2, Problem 23E

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To calculate: The period and amplitude and phase of the given function y=10cos(14x+180°) and graph the provided function.

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Chapter 14.2, Problem 22E

Chapter 14.2, Problem 24E

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Chapter 14 Solutions

Bundle: Elementary Technical Mathematics, Loose-leaf Version, 12th + WebAssign Printed Access Card, Single-Term

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The period and amplitude and phase of the given function y = 10 cos ( 1 4 x + 180 ° ) and graph the provided function.

Solution Summary: The author calculates the period, amplitude, and phase of the given function y=10mathrmcosleft.

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To calculate: The period and amplitude and phase of the given function y=10cos(14x+180°) and graph the provided function.

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Chapter 14 Solutions