Chapter 4.5, Problem 72PE

The monthly high temperature for Atlantic City. New Jersey, peaks at an average high of $86°$ in July and goes down to an average high of $64°$ in January. Assume that this pattern for monthly high temperatures continues indefinitely and behaves like a cosine wave.

a. Write a function of the form $H\left(t\right)=A\cos \left(Bt-C\right)+D$ to model the average high temperature. The value $H\left(t\right)$ is the average high temperature for month $t$ , with January as $t=0.$

b. Graph the function from part (a) on the interval $\left[0,13\right]$ and plot the points $\left(0,64\right),\left(6,86\right)$ and $\left(12,64\right)$ to check the accuracy of your model.