Answer
See graph and explanations.
Work Step by Step
Step 1. Start from function $y=sin(x)$ (purple) which has a period of $2\pi$ to obtain $y=csc(x)$ (not shown to avoid mixing with the final result) in the interval of $(0,2\pi)$ using reciprocal properties.
Step 2. Start from $y=csc(x)$ and reflect the curve with respect to the y-axis to get the red curve for $y=csc|x|$
See graph and explanations.
