Question

In Pensacola in June, high tide was at noon. The water level at high tide was 12 feet and 2 feet at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in June for Pensacola as a function of time (t).. .

Answer 1

To answer this question, the equation that we will be using is:
 y = A cos bx + c
 where A = amplitude, b = 2 pi/Period, Period = 12 hrs, c = midline,
  x = t and y = f(t)

  A = 1/2 (Xmax - Xmin)
12 - 2 / 2 = 10/2 = 5
  b = 2 pi / 12 = pi/6
  c = 1/2 (Xmax + Xmin)
  12+2/2 = 7
  answer: f(t) = 5 cos pi/6 t + 7