# How do you graph inverse trigonometric functions?

Oct 29, 2014

Since the graphs of $f \left(x\right)$ and $f ' \left(x\right)$ are symmetric about the line $y = x$, start with the graph of a trigonometric function with an appropriate restricted domain, then reflect it about the line $y = x$.

(Caution: Their domains must be restricted to an appropriate interval so that their inverses exist.)

Let us sketch the graph of $y = {\sin}^{- 1} x$.

The graph of $y = \sin x$ on $\left[- \frac{\pi}{2} , \frac{\pi}{2}\right]$ looks like:

By reflecting the graph above about the line $y = x$,

The curve in purple is the graph of $y = {\sin}^{- 1} x$.

The graphs of other inverse trigonometric functions can be obtained similarly.

I hope that this was helpful.