How do you graph inverse trigonometric functions?

1 Answer
Oct 29, 2014

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.)


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

The graph of #y=sinx# on #[-pi/2, pi/2]# looks like:

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

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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.