Question

Name the trigonometric functions that have asymptotes.

Short answer

The trigonometric functions are$\tan x,secx,cscx,secx$

Step-by-step solution

Given information

Given trigonometric function

Checking the asymptotes

For $y=\tan x$, the asymptotes are $x=\dots ,-\frac{3\pi }{2},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{2},\dots$

For $y=cotx$, the asymptotes are $x=\dots ,-2\pi ,-\pi ,0,\pi ,2\pi ,\dots$

For $y=cscx$, the asymptotes are $x=\dots ,-2\pi ,-\pi ,0,\pi ,2\pi ,\dots$

For$y=secx$, the asymptotes are$x=\dots ,-\frac{3\pi }{2},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{2},\dots$