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Tides are cyclical phenomena caused by the gravitational pull of the sun and the moon. On a particular retaining wall, the ocean generally reaches the 3 m mark at high tide. At low tide, the water reaches the 1 m mark. Assume that high tide occurs at 12:00 p.m. and at 12:00 a.m., and that low tide occurs at 6:00 p.m. and 6:00 a.m. What is the height of the water at 10:30 a.m.?

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Since the phenomenon is cyclical, we can model with a sinusoid.

Taking 12am to be t=0, and marking the horizontal axis in 1 hour increments we have the maximum occurring at t=0, so it seems reasonable to model with the cosine.

The amplitude is the maximal distance from the midline, or we can use `A=("highest"-"lowest")/2` so `A=(3-1)/2=1`

The midline is the arithmetic mean of the...

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