Chapter 1 - Functions - 1.4 Trigonometric Functions and Their Inverse - 1.4 Exercises - Page 48: 8

All $x$ except $x = \frac{\pi}{2}+k\pi,k\in\mathbb{Z}$.

$y = sec(x) = \dfrac{1}{cos(x)}$ We need to find where $cos(x) = 0$, which is $x = \frac{\pi}{2} + k\pi$, where $k$ is an integer. Therefore, the domain is all $x$ except $x = \frac{\pi}{2} + k\pi$.