# What is the domain and range of inverse trigonometric functions?

Apr 7, 2015

For a trig function, the range is called "Period"

For example, the function $f \left(x\right) = \cos x$ has a period of $2 \pi$; the function $f \left(x\right) = \tan x$ has a period of $\pi$. Solving or graphing a trig function must cover a whole period.

The range depends on each specific trig function.
For example, the inverse function $f \left(x\right) = \frac{1}{\cos x} = \sec x$ has as period $2 \pi$.

Its range varies from (+infinity) to Minimum $1$ then back to (+infinity), between ($- \frac{\pi}{2}$ and $\frac{\pi}{2}$).

Its range also varies from (-infinity) to Max -1 then back to to (-infinity), between ($\frac{\pi}{2}$ and $3 \frac{\pi}{2}$).