## Precalculus (10th Edition)

odd multiples of $\dfrac{\pi}{2}$
Since $\tan(\theta)=\dfrac{\sin\theta}{\cos\theta}$, then it is undefined when the denominator (which is $\cos{\theta}$) is $0$. Recall that $\cos\theta=0$ if $\theta=\frac{\pi}{2}(2k+1)$, where $k$ is an integer. Therefore, the tangent function is undefined when $\theta=\frac{\pi}{2}(2k+1)$, where $k$ is an integer (which are odd multiples of $\frac{\pi}{2}$).