Question

Which trigonometric function requires a domain restriction of [-pi/2, pi/2] to make it invertable?

Answer 1

Answer:

$y=\tan x$

Step-by-step explanation:

The trigonometric function that needs a domain restriction of $[-\frac{\pi}{2},\frac{\pi}{2} ]$ to make it invertible is $y=\tan x$.

The function $y=\tan x$ will pass the horizontal line test on this interval therefore making it an invertible function on this interval.

This explains why the inverse tangent function, $y=\tan^{-1} x$ has range $[-\frac{\pi}{2},\frac{\pi}{2} ]$.