Chapter 2, Problem 10P

The average daily temperature for an area can be approximated by the following function,

$T=T_{\text{mean}}+\left(T_{\text{peak}}-T_{\text{mean}}\right)\text{ cos }\left(\omega \left(t-t_{\text{peak}}\right)\right)$

Where $T_{\text{mean}}=$ the average annual temperature, $T_{\text{peak}}=$ the peak temperature, $\omega =$ the frequency of the annual variation $\left(=2\pi \text{/}365\right),\text{ and }{t}_{\text{peak}}=$ day of the peak temperature $\left(\cong 205\text{ d}\right)$. Develop a program that computes the average temperature between two days of the year for a particular city. Test it for (a) January-February $\left(t=0\text{ to 59}\right)$ in Miami, Florida $\left(T_{\text{mean}}=22.1°\text{C};T_{\text{peak}}=28.3°\text{C}\right)$, and (b) July-August $\left(t=180\text{ to 242}\right)$ in Boston, Massachusetts $\left(T_{\text{mean}}=10.7°\text{C;}{T}_{\text{peak}}=22.9°\text{C}\right)$.