Precalculus (6th Edition) Blitzer

Step 1. As $sec(\frac{\pi}{2} x)=\frac{1}{cos(\frac{\pi}{2} x)}$, we can use the original function $y=-3cos(\frac{\pi}{2} x)$to obtain the reciprocal function $y=-3sec(\frac{\pi}{2} x)$. Step 2. The original function has zeros at $x=\pm1,\pm3, ...$ which become vertical asymptotes of the new function. Step 3. Using the reciprocal property, we can obtain the new function $y=-3sec(\frac{\pi}{2} x)$, shown as the red curves in the figure.