What would the inverse function of #y=sin x# look like?

1 Answer
marfre
Jul 11, 2018

See answer below

Explanation:

Given: #y = sin x#

In order for a function to have an inverse it must pass both the vertical line test and the horizontal line test:

Graph of #sin x#:
graph{sin x [-6.283, 6.283, -2, 2]}

In order for the #y = sin x# function to have an inverse, we need to limit the domain to #[-pi/2, pi/2] => "range " [-1, 1]#

The inverse function is #y = arcsin x = sin^-1 x:#
graph{arcsin x [-4, 4, -2, 2]}

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