Textbook Problem

Transportation Workers The number W (In thousands) of scenic and sightseeing transportation workers employed in the United States during 2014 can be modeled by

$W=31.184+8.447\sin \left(0.568t-2.595\right)$

Where t is the time (in months), with t = 1 corresponding to January. Find the average number of scenic and sightseeing transportation workers during the first quarter $\left(0\le t\le 3\right)$. the second quarter $\left(3\le t\le 6\right)$. the entire year $\left(0\le t\le 12\right)$.

(Source: U.S. Bureau of Labor Statistics)