In Portland, Maine, the tide causes the ocean's height to vary sinusoidally, peaking every 12.4 hours.........

Question

In Portland, Maine, the tide causes the ocean's height to vary sinusoidally, peaking every 12.4 hours. The average high tide (the difference between the height at high and low tides) is 2.7m. Find an equation for the height, h, of the tide as a function of the time, t, in hours of if h = 0 at time t = 0.
Plz elaborate on how you solved it.
Also show all work that you did.
THANK YOU VERY MUCH!

Answer 1

Lets take h = 0 to be the average height of the water. And suppose the tide is rising at t = 0. From t = 0 to t = 12.4 we would have one complete cycle of the sine wave. At t = 12.4 we want the sine of 2π, so the argument of the sine will be 2π/12.4 And we want the amplitude to be 2.7 instead of the normal amplitude of the sine wave which is 2. So the coefficient of the sine would be 2.7/2 = 1.35. That gives us:
h = 1.35sin(2π/12.4)