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Thread: 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 $\displaystyle \sin^{-1} \frac{1}{4} = \alpha \Rightarrow \sin \alpha = \frac{1}{4}$.

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

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

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