# How do you find the asymptotes for f( x ) = tan(x)?

Apr 18, 2018

$\tan x$ has vertical asymptotes at $x = \left(\frac{\pi}{2}\right) + n \pi$

#### Explanation:

Determine the values of $x$ for which $\tan x$ doesn't exist.

Recall that $\tan x = \sin \frac{x}{\cos} x .$ If $\cos x = 0 , \tan x$ does not exist due to division by zero.

We know $\cos x = 0$ for $x = \left(\frac{\pi}{2}\right) + n \pi$ where $n$ is any integer.

Therefore, $\tan x$ has vertical asymptotes at $x = \left(\frac{\pi}{2}\right) + n \pi$.

No horizontal asymptotes exist for the tangent function, as it increases and decreases without bound between the vertical asymptotes.