Please determine the amplitude, period(in hours), and determine the mid-line (write in an equation)?

Question

At midnight the water at a particular beach is at high tide. At the same time a gauge at the end of a pier reads 10 feet. Low tide is reached at 6 AM when the gauge reads 4ft.

Answer 1

Amplitude = A = (high - Low)/2 = 3

Time from peak (crest) to low (trough) = 1/2 Period = 12:00 - 6:00 = 6 hours

Period P = 12 hours

Frequency  b = 2Π /P = π/6

 

If high tide is 3 ft and low tide is -3ft, then equation is

 y(t) = A cos bt

 

Since the high tide is actually at 10 ft and low tide is at 4 ft, then equation is

y(t) = A cos bt + 7