How do you find the vertical, horizontal and slant asymptotes of: tan(x)?

Jul 25, 2016

Only vertical asymptotes $x = \left(2 n + 1\right) \frac{\pi}{2} , n = 0. \pm 1 , \pm 2 , \pm 3 , \ldots$, in both positive and negative directions of y=axis.

Explanation:

y = tan x is periodic with period $\pi$

As $x \to \left(2 n + 1\right) \frac{\pi}{2} \pm , n = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$,

$x \to - + \infty$.

$\left(2 n + 1\right) \frac{\pi}{2} \pm$ is used to indicate the limits,

for approach from higher and lower values, respectively.

So, the graph is asymptotic with

$x = \left(2 n + 1\right) \frac{\pi}{2} , n = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots ,$3

in both positive and negative directions of y-axis