For a short time after a wave is created by wind, the height of the wave can be modeled using y = a sin , where a is the amplitude and t is the period of the wave in seconds.
write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
amplitude: 4, period = phase shift = vertical shift = -2

Following are calcultion of the wave equation:

Given:

To find:

function=?

Solution:

Using formula:

Where  

T=period

c=phase shift

b=vertical shift

Putting the value in the above given function:

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  y = 4sin((t+4π/3)/2) -2

Step-by-step explanation:

The generic form is ...

  y = A·sin(B(t -C)) +D

where ...

You have ...

Putting these values into the above form gives ...

  y = 4sin((t+4π/3)/2) -2

A graph is shown in the attachment.

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