Simplifying?

**DannyMath** · September 20th 2010, 06:06 PM

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.

**Prove It** · September 20th 2010, 06:24 PM

Remember that $\cos{\theta} = \sqrt{1 - \sin^2{\theta}}$ (from the Pythagorean Identity).

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

$= \sqrt{1 - x^2}$ .