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Math Help - Simplifying?

  1. #1
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    Simplifying?

    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.
    Last edited by mr fantastic; September 20th 2010 at 06:51 PM. Reason: Clarified.
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  2. #2
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    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}.
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  3. #3
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    Ok I understand it until the sin(sin^-1(x)). How does that turn into x specifically?
    Last edited by mr fantastic; September 20th 2010 at 06:57 PM. Reason: Clarity, new question moved to new thread in appropriate subforum.
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  4. #4
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    Quote Originally Posted by DannyMath View Post
    Ok I understand it until the sin(sin^-1(x)). How does that turn into x specifically?
    By definition, f(f^{-1}(x)) = f^{-1}(f(x)) = x.
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  5. #5
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    Oh yes of course, thank you for the clarification!
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