Answer
Discontinuous at $\frac{\pi}{2} + k\pi$, where $k$ is an integer.
Work Step by Step
The discontinuities of $f(x) = sec(x)$ exist where $sec(x)$ does not exist. Because $sec(x) = \frac{1}{cos(x)}$, discontinuities exist where $cos(x)=0$. $cos(x)=0$ at $\frac{\pi}{2} + k\pi$, where $k$ is an integer.
