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