Chapter 8.2, Problem 81E

Medicine The temperature T (in degrees Fahrenheit) of a patient t hours after arriving at the emergency room of a hospital at 10:00 p.m. is given by

$T\left(t\right)=98.6+4\cos \frac{\pi t}{36},\text{ 0}\le \text{t}\le \text{18}$.

Find the patient’s temperature at (a) 10:00 p.m., (b) 4:00 a.m., and (c) 10:00 a.m. (d) At what time do you expect the patient’s temperature to return to normal $\left(98.6°\right)$

? Explain your reasoning.