Chapter 4 - Graphs of the Circular Functions - Summary Exercises on Graphing Circular Functions - Page 181: 5

$y = -4~csc~\frac{1}{2}x$ We can see the graph below.

$y = -4~csc~\frac{1}{2}x$ 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.