Answer
Discontinuities at $kπ$, where $k$ is an integer.
Work Step by Step
The discontinuities of $f(x)=csc(x)$ exist where $csc(x)$ does not exist. Because $csc(x)=\frac{1}{sin(x)}$, discontinuities exist where $sin(x)=0$. $sin(x)=0$ at $kπ$, where $k$ is an integer.
