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Math Help - identities (trig)

  1. #1
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    identities (trig)

    prove that: cos (sin^(-1) x) = (1-x^2)^(1/2)
    please help. I don't even know where to start.
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  2. #2
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    \sin^{-1}{x} is an angle. Therefore:

    \sin^{-1}{x} = \theta

    \Rightarrow x = \sin{\theta}

    Recall that in right triangle trigonometry:
    \sin{\theta} = \frac{\text{opp}}{\text{hyp}}

    You can find the adj side using the Pythagorean theorem. Now we can find \cos{\theta}, which is:

    \cos{\theta} = \frac{\text{adj}}{\text{hyp}}
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  3. #3
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    Quote Originally Posted by dee18 View Post
    prove that: cos (sin^(-1) x) = (1-x^2)^(1/2)
    please help. I don't even know where to start.
    Alternatively, if y = \cos{(\sin^{-1}{x})}, then:

    \Rightarrow y^2 = \cos^2{(\sin^{-1}{x})}

    \Rightarrow y^2 = 1 - \sin^2{(\sin^{-1}{x})}

    \Rightarrow y = \ldots
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