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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.

13. Write an equation for the given function given the period, phase shift, and vertical shift. cotangent function, period =pi phase shift = -1/3 pi, vertical shift = 2

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Answer:

y = 4sin((t+4π/3)/2) -2

Step-by-step explanation:

The generic form is   y = A·sin(B(t -C)) +D  

where  A is the amplitude

B is 2π/period

C is the phase shift

D is the vertical shift

You have   A = 4

period = 4π, so B = (2π)/(4π) = 1/2

C = -4π/3

D = -2

Putting these values into the above form gives:  

 y = 4sin((t+4π/3)/2) -2

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