Question

What is the domain and range of inverse trigonometric functions?

Answer 1

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

For example, the function `f(x) = cos x` has a period of `2pi`; the function `f(x) = 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(x) = 1/(cos x) = sec x` has as period `2pi`.

Its range varies from (+infinity) to Minimum `1` then back to (+infinity), between (`-pi/2` and `pi/2`).

Its range also varies from (-infinity) to Max -1 then back to to (-infinity), between (`pi/2` and `3pi/2`).