Question

How do you graph inverse trigonometric functions?

Answer 1

Since the graphs of `f(x)` and `f'(x)` 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.)

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

The graph of `y=sinx` on `[-pi/2, pi/2]` 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.

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I hope that this was helpful.