The average depth of water at the end of a dock is 6 ft. This varies 2 ft in both directions with the ride. Suppose there is a high tide at 4 am. If the tide goes from low to high every 6 hours, write a cosine function describing the depth of the water as a function of time with t=4 corresponding to 4AM.

Question

The average depth of water at the end of a dock is 6 ft.  This varies 2 ft in both directions with the ride.  Suppose there is a high tide at 4 am.  If the tide goes from low to high every 6 hours, write a cosine function describing the depth of the water as a function of time with t=4 corresponding to 4AM.

My work:

y=2cos((pi/6(x-d))+6

Ok all I need help is with finding the phase shift.  I am having trouble with finding it.  Please be detailed.  Thanks in advance

Reiny · Answer

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