Chapter 6.6, Problem 33AE

Tides The length of time between consecutive high tides is 12 hours and 25 minutes. According to the National Oceanic and Atmospheric Administration, on Saturday, March 28, 2015, in Charleston, South Carolina, high tide occurred at $2:12$ AM ( hours) and low tide occurred at $8:18$ AM ( $8.3$ hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was $5.27$ feet, and the height of the water at low tide was $0.87$ foot.

(a) Approximately when will the next high tide occur?

(b) Find a sinusoidal function of the form $y=A\sin (\omega x-\varphi )+B$ that models the data.

(c) Use the function found in part $\left(b\right)$ to predict the height of the water at 11 AM on March 28, 2015.