The average daytime temperature for a city is given by the function

PHYSICS · Multi-part

Problem

D(t)=5\cos\left(\frac{\pi}{6}t\right)+20\ ^\circ\text{C}

, where

t

is the time in months after January. (1) Sketch the graph of

D

against

t

for

0\leq t\leq24

. (2) Find the average daytime temperature during May. (3) Find the minimum average daytime temperature, and the month in which it occurs.