How do you simplify #Sin(arccos x)#?

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Answer 1 · 2016-06-24T03:13:20

sin x

arccos x --> arc x
sin (arccos x) --> sin x

Answer 2 · 2016-06-24T04:32:52

#+-sqrt(1-x^2)#.

Let a = arc cos x. Then, cos a = x = cos (-a).

So, a might be in anyone of the four quadrants.

Accordingly, the given expression

#sin a=+-sqrt(1-cos^2 a)=+-sqrt(1-x^2)#.