## Precalculus (10th Edition)

The domain is all real numbers except $\theta=(2k+1)\cdot\frac{\pi}{2}$, where $k$ is an integer.
The denominator cannot be 0, hence $cos(\theta)$ cannot be 0. $cos(\theta)=0$ if and only if $\theta=(2k+1)\cdot\frac{\pi}{2}$, where $k$ is an integer. Therfore the domain is all real numbers except $\theta=(2k+1)\cdot\frac{\pi}{2}$, where $k$ is an integer.