## Precalculus (10th Edition)

$\theta=k\pi$, where k is an integer
Since $\csc(\theta)=\frac{1}{\sin\theta}$, then it is undefined when the denominator (which is $\sin{\theta}$) is $0$. Recall that $\sin\theta=0$ if $\theta=k\pi$, where $k$ is an integer. Therefore, the function is undefined when $\theta=k\pi$, where k is an integer.