I'm a little rusty on my trig and I'm faced with this:

Simplify cos(sin^-1(x))

the -1 just means the inverse.

I've looked the answer up and I know it's sqrt(1-x^2) but I don't remember how to get that. Any help is appreciated.

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- Sep 20th 2010, 06:06 PMDannyMathSimplifying?
I'm a little rusty on my trig and I'm faced with this:

Simplify cos(sin^-1(x))

the -1 just means the inverse.

I've looked the answer up and I know it's sqrt(1-x^2) but I don't remember how to get that. Any help is appreciated. - Sep 20th 2010, 06:24 PMProve It
Remember that $\displaystyle \cos{\theta} = \sqrt{1 - \sin^2{\theta}}$ (from the Pythagorean Identity).

So $\displaystyle \cos{(\sin^{-1}{x})} = \sqrt{1 - [\sin{(\sin^{-1}{x})}]^2}$

$\displaystyle = \sqrt{1 - x^2}$. - Sep 20th 2010, 06:45 PMDannyMath
Ok I understand it until the sin(sin^-1(x)). How does that turn into x specifically?

- Sep 20th 2010, 06:59 PMmr fantastic
- Sep 20th 2010, 07:06 PMDannyMath
Oh yes of course, thank you for the clarification! :)