Question

The average depth of the water in a port on a tidal river is 4 m. At low tide, the depth of the water is 2 m. One cycle is completed approx every 12 h. a) find an equation of the depth d(t) metres, with respect to the average depth, as a function of the time, t hours, after low tide, which occurred at 15:00.

Answer 1

Since it asks for depth wrt average, we do not need the 4 m average but only how much it departs from average

at t = 0, d = -2 (low tide, 2 feet below average)

d = -2 cos 2 pi t/T
since T = 12 hours is given
d = -2 cos (pi t/6)

Answer 2

ok thanks a lot for your help :D