Chapter 8.2, Problem 41E

(a)

To determine

To graph: The function for tap water temperature $t$ days after the beginning of a year is approximated by the formula $T=59+14\cos \left[\frac{2\pi }{365}(t-208)\right],0\le t\le 365$.

(b)

To determine

The temperature $t$ on February 14 i.e. for $t=45$, where the tap water temperature $t$ days after the beginning of a year is approximated by the formula $T=59+14\cos \left[\frac{2\pi }{365}(t-208)\right],0\le t\le 365$.

(c)

To determine

The coldest and warmest tap water temperature, where the temperature is approximated by the formula $T=59+14\cos \left[\frac{2\pi }{365}(t-208)\right],0\le t\le 365$.

(d)

To determine

The day at which the minimum temperature occurs, where the temperature is approximated by the formula $T=59+14\cos \left[\frac{2\pi }{365}(t-208)\right],0\le t\le 365$.

(e)

To determine

The day at which the maximum temperature occurs, where the temperature is approximated by the formula $T=59+14\cos \left[\frac{2\pi }{365}(t-208)\right],0\le t\le 365$.

(f)

To determine

The days at which the average tap water temperature $59°$ is achieved, where the temperature is approximated by the formula $T=59+14\cos \left[\frac{2\pi }{365}(t-208)\right],0\le t\le 365$.