Question

True or False The graphs of

$y=\tan x,y=cotx,y=secx,andy=cscx$

each have infinitely many vertical asymptotes.

Short answer

It is true that the graphs of $y=\tan x,y=cotx,y=secx,andy=csx$each have infinitely many vertical asymptotes.

Step-by-step solution

Step 1. Given Information

The given functions are $y=\tan x,y=cotx,y=secx,andy=csx.$

We have to state whether it is true or false that each function have infinitely many vertical asymptotes.

Step 2. Finding whether the statement is true or false

The function $y=\tan x$has asymptotes at$\pm \frac{n\mathrm{\pi }}{2}$. Hence it has infinite asymptotes.

The function $y=cotx$has asymptotes at $\pm n\mathrm{\pi }.$Hence it has infinite asymptotes.

The function $y=secx$has asymptotes at $\pm \frac{n\mathrm{\pi }}{2}.$Hence it has infinite asymptotes.

The function $y=cscx$has asymptotes at $\pm n\mathrm{\pi }.$Hence it has infinite asymptotes.

Thus, the statement is true.