Chapter 4, Problem 80RE

The depth of water along a coastal inlet varies with the tides. On a summer day, the water depth at the end of a pier is $23\text{ ft}$ at $6:30\text{ A}\text{.M}\text{.}$ , $21\text{ ft}$ at $12:30\text{ P}\text{.M}$ , and $23\text{ ft}$ at $6:30\text{ P}\text{.M}\text{.}$ Assuming that this pattern continues indefinitely and behaves like a cosine wave, write a function of the form $h\left(t\right)=A\cos \left(Bt-C\right)+D$ . The value $h\left(t\right)$ is the water depth (in feet), $t$ hours after $6:30\text{ A}\text{.M}\text{.}$