In any given locality, tap water temperature varies during the year. In Dallas, Texas, the tap water temperature (in degrees Fahrenheit) t days after the beginning of a year is given approximately by the formula

(a) Graph the function in the window [0, 365] by [-10, 75].

(b) What is the temperature on February 14, that is, when t = 45 ?

(c) Use the fact that the value of the cosine function ranges from -1 to 1 to find the coldest and warmest tap water temperatures during the year.

(d) Use the trace feature or the minimum command to estimate the day during which the tap water temperature is coldest. Find the exact day algebraically by using the fact that cos(-π) = -1.

(e) Use the trace feature or the maximum command to estimate the day during which the tap water temperature is warmest. Find the exact day algebraically by using the fact that cos(0) = 1.

(f) The average tap water temperature during the year is 59°. Find the two days during which the average temperature is achieved.

T= 59 + 14 cos 2 365 (t - 208) 0 t 365.