Chapter 4.5, Problem 71PE

The probability of precipitation in Modesto, California, varies from a peak of $0.34\left(34\%\right)$ in January to a low of $0.04\left(4\%\right)$ in July. Assume that the percentage of precipitation varies monthly and behaves like a cosine curve.

a. Write a function of the form $P\left(t\right)=A\cos \left(Bt-C\right)+D$ to model the precipitation probability. The value $P\left(t\right)$ is the probability of precipitation (as a decimal), for month $t$ with January as $t=1$ .

b. Graph the function from part (a) on the interval $\left[0,13\right]$ and plot the points $\left(1,0.34\right),\left(7,0.04\right)$ , and $\left(13,0.34\right)$ to check the accuracy of your model.