for a short time after a wave is created by wind the height of the wave can be modeled using y = a sin 2pit/T where a is the amplitude and T is the period of the wave in seconds. Srite an equation for the given function given the amplitude = 4, period = 4pi, phase shift = - 4/3pi, vertical shift = - 2

Question

Mathematics

Nick Lane

20 June, 06:51

for a short time after a wave is created by wind the height of the wave can be modeled using y = a sin 2pit/T where a is the amplitude and T is the period of the wave in seconds. Srite an equation for the given function given the amplitude = 4, period = 4pi, phase shift = - 4/3pi, vertical shift = - 2

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Answers (1)

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Chace Kelley · Answer 1

y = 4 sin (t/2 + 4π/3) - 2

Step-by-step explanation:

General form:

y = a sin (2π/T t)

Given a = 4 and T = 4π:

y = 4 sin (2π / (4π) t)

y = 4 sin (t/2)

Add horizontal shift of - 4π/3 and vertical shift of - 2:

y = 4 sin (t/2 - (-4π/3)) - 2

y = 4 sin (t/2 + 4π/3) - 2