# Where are the vertical asymptotes of f(x) = tan x?

The asymptotes are at $x = \frac{\pi}{2} + k \pi , x \in \mathbb{Z}$
The vertical asymptotes of a function are usually located in points, where the function is undefined. In this case since $\tan x = \sin \frac{x}{\cos} x$, the asymptotes are located where $\cos x = 0$ (denominator of a fraction cannot be zero) which leads to the answer: $x = \frac{\pi}{2} + k \pi , x \in \mathbb{Z}$