Answer
See graph.
Work Step by Step
1. Given $y=-cot(2x+\frac{\pi}{2})$, we can identify: period$=\frac{2\pi}{2}=\pi$, phase shift$=-\frac{\pi}{4}$.
2. To graph $y=-cot(2x+\frac{\pi}{2})$, start with one period of $y=cot(x)$, compress horizontally by a factor of $2$, shift $\frac{\pi}{4}$ to the left, then reflect across the x-axis. Repeat the resulting curve horizontally a few times to cover the entire window.
3. See graph.