## Precalculus (10th Edition)

$x=-\frac{3\pi}{2},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{2}$
If $x=-\frac{3\pi}{2},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{2}$, $\tan{x}=\frac{\sin{x}}{\cos{x}}$ has vertical asymptotes because $\cos{x}=0$ at those values, hence the denominator is $0$, therefore $\tan{x}$ is undefined at those values. (see graph)