Answer
$y = -\frac{1}{2}~csc~(x+\frac{\pi}{2})$
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/c31b7456-9136-4932-b837-cd73024f8143/result_image/1531458876.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T010809Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=2f993d41a0d1ef4cb0fdee90f3b9e6d2eee7f682e5688ac7aa44f3c11d30efbe)
Work Step by Step
$y = -\frac{1}{2}~csc~(x+\frac{\pi}{2})$
When $x = -\frac{\pi}{2}$, then $y = -\frac{1}{2}~csc~0$ (which is undefined)
When $x = 0$, then $y = -\frac{1}{2}~csc~\frac{\pi}{2} = -\frac{1}{2}$
When $x = \frac{\pi}{2}$, then $y = -\frac{1}{2}~csc~\pi$ (which is undefined)
When $x = \pi$, then $y = -\frac{1}{2}~csc~\frac{3\pi}{2} = \frac{1}{2}$
When $x = \frac{3\pi}{2}$, then $y = -\frac{1}{2}~csc~2\pi$ (which is undefined)
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/c31b7456-9136-4932-b837-cd73024f8143/steps_image/small_1531458876.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T010809Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=2e65c6140b3c23855aefe984b4133082dbfee5812407cdfbfd9278192bacc5e6)