How do you simplify sin(cos−1x)?

1 Answer
sente
May 9, 2016

sin(cos−1(x))=√1−x2

Explanation:

Let's draw a right triangle with an angle of a=cos−1(x).

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As we know cos(a)=x=x1 we can label the adjacent leg as x and the hypotenuse as 1. The Pythagorean theorem then allows us to solve for the second leg as √1−x2.

With this, we can now find sin(cos−1(x)) as the quotient of the opposite leg and the hypotenuse.

sin(cos−1(x))=sin(a)=√1−x21=√1−x2

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