The depth of the water at the end of a pier changes periodically along with the movement of tides. on a particular day, low tides occur at 12: 00 am and 12: 30 pm, with a depth of 2.5 m, while high tides occur at 6: 15 am and 6: 45 pm, with a depth of 5.5 m. let t = 0 be 12: 00 am. which periodic function, sine or cosine, would be a simpler model for the situation? explain.

Refer to the figure shown below which illustrates the problem.
Low tides occur at a depth of 2.5 m at 12:00 am and 12:30 pm, separated by a period of T = 12.5 hours.
Likewise, high tides occur at a depth of 5.5 m at 6:15 am and 6:45 pm, separated by a period of T = 12.5 hours.

Use a time coordinate of t hours.
The amplitude is (1/2)*(5.5 - 2.5) = 1.5 m.
Use x(t) to denote depth at time t.

Because x(0)=2.5 and x(T/2) = 5.5,, use the periodic function


Verify the model.
x(0) = -1.5 + 4 = 2.5
x(6.25) = 1.5 + 4 = 5.5
x(12.5) = -1.5 + 4 = 2.5

A computer plot for x(t) is shown in the accompanying figure.

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