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Math Help - find the exact value: cos[sin^-1(2/8)]

  1. #1
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    Red face find the exact value: cos[sin^-1(2/8)]

    thanks
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  2. #2
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    Quote Originally Posted by sarabara View Post
    thanks
    Let \sin^{-1} \frac{1}{4} = \alpha \Rightarrow \sin \alpha = \frac{1}{4}.

    Now get the value of \cos \alpha.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Let \sin^{-1} \frac{1}{4} = \alpha \Rightarrow \sin \alpha = \frac{1}{4}.

    Now get the value of \cos \alpha.
    You can think of this as a right triangle with side opposite \alpha 1 and hypotenuse 4. What is the length of the side near \alpha, the third side of this right triangle?

    You could also use the fact that sin^2(\theta)+ cos^2(\theta)= 1 so that cos(\theta)= \sqrt{1- sin^2(\theta)}
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