# How do you find the vertical, horizontal and slant asymptotes of: arctanx?

Horizontal asymptotes at $y = \frac{\pi}{2}$ and $y = - \frac{\pi}{2}$.
Of the types of asymptotes a function can have, the graph of arctangent only has horizontal asymptotes. They're located at $y = \frac{\pi}{2}$ and $y = - \frac{\pi}{2}$.
The limited one-to-one graph of tangent that we use to define arctangent has domain $- \frac{\pi}{2} < x < \frac{\pi}{2}$ and has vertical asymptotes at $x = \frac{\pi}{2}$ and $x = - \frac{\pi}{2}$. When we create the inverse function the vertical asymptotes become the horizontal asymptotes.