Answer
$y = -4~csc~\frac{1}{2}x$
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/df0b924c-7e57-49e2-973a-5c5086930b9b/result_image/1531666791.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T003501Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=6cfd5049933604e0cf085466a9bd40ff5d5839e5531f65e9157488e52bdd7e88)
Work Step by Step
$y = -4~csc~\frac{1}{2}x$
When $x = -2\pi$, then $y = -4~csc~(-\pi)~~$ (which is undefined)
When $x = -\pi$, then $y = -4~csc~(-\frac{\pi}{2}) = 4$
When $x = 0$, then $y = -4~csc~0~~$ (which is undefined)
When $x = \pi$, then $y = -4~csc~(\frac{\pi}{2}) = -4$
When $x = 2\pi$, then $y = -4~csc~\pi~~$ (which is undefined)
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/df0b924c-7e57-49e2-973a-5c5086930b9b/steps_image/small_1531666791.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T003501Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=efb67582d8bfc07602b6a2a6c569510968a1d8c9971b1f45eedd565994c3098b)