Answer
See graph and explanations.
Work Step by Step
Step 1. As $csc(\frac{x}{2})=\frac{1}{sin(\frac{x}{2})}$, we can use the original function $y=-\frac{1}{2}sin(\frac{x}{2})$to obtain the reciprocal function $y=-\frac{1}{2}csc(\frac{x}{2})$.
Step 2. The original function has zeros at $x=0,\pm 2\pi,\pm 4\pi, ...$ which become vertical asymptotes of the new function.
Step 3. Using the reciprocal property, we can obtain the new function $y=-\frac{1}{2}csc(\frac{x}{2})$, shown as the red curve in the figure.
