Suppose that the average temperature in Lincoln, NE in degrees Fahrenheit $t$ months after January 1, 2016 (that is, January 1 corresponds to $t=0$) is given by the following equation: $$T(t) = -50\cos\big(\frac{\pi}{6}t\big)+ 70.$$

(a) Which of the following is the graph of $T(t)$ on the interval $[0,12]$? Select A B C D None of the graphs above

(b) According to your answer in part (a), how many times in the course of 2016 does our model say the temperature should be $75$ degrees. times.

(c) Find all values of $t$ on the interval $[0,12]$ for which the temperature in Lincoln, NE is predicted by this model to be $75$ degrees. Enter your answer as a comma separated list. Use radian measure and round your answer to at least four significant digits. .

Hint: