Answer
a. see the graph.
b. $4\pi $
c. see proof below.
Work Step by Step
a. See the graph above.
b. From the graph, we see that the period is $4\pi $
c. Confirm your finding in part (b) algebraically:
Let $ f(x)=sin(x)+cos(x/2)$ and let k be an integer.
$ f(x+4k\pi)=sin(x+4k\pi)+cos(x/2+2k\pi)=sin(x)+cos(x/2)=f(x)$
So, $4\pi $ is the period.
