Question

On September 17, 2008, high tide in Portland was at midnight. The water level at high tide was 10.3 feet; later, at low tide, it was 0.3 feet. Assuming the next high tide is exactly at 12 noon and that the height of the water is given by a sine or cosine curve, find a formula for the water level in Portland as a function of time, where yy is the water level in feet, and tt is the time measured in hours from midnight.

Answer 1

Since at time 0 (midnight) the tide is at the highest, the tide is modeled by a cosine function.
The amplitude is
a = (10.3 - 0.3) / 2 = 5
The period is 12 hours
b = 2π / 12 = π/6
The vertical shift is
10.3 - 5 = 5.3

The equation then is
y = 5 cos (π/6 t) + 5.3