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Math Help - determining Sin x as Cos x = sqrt 3/2

  1. #1
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    determining Sin x as Cos x = sqrt 3/2

    Hello I need help in determining Sin x as Cos x = sqrt 3/2.

    What should I know to be able to do this. and how?
    I would like a fully detailed explanation if possible.
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  2. #2
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    Hello, Meowet!

    \text{If }\cos x = \frac{\sqrt{3}}{2}\text{, find }\sin x

    We have: . \cos x \:=\:\frac{\sqrt{3}}{2} \:=\:\frac{adj}{hyp}

    x is a in a right triangle with: . adj = \sqrt{3},\;hyp = 2

    The triangle looks like this:
    Code:
                            *
                         *  *
                  2   *     *
                   *        *
                *           *
             * x            *
          *  *  *  *  *  *  *
                  √3

    Pythagorus says: . \text{(opp)}^2 + \text{(adj)}^2 \:=\:\text{(hyp)}^2

    So we have: . \text{(opp)}^2 + (\sqrt{3})^2 \:=\:2^2 \quad\Rightarrow\quad \text{(opp)}^2 + 3 \:=\:4

    . . Hence: . \text{(opp)}^2 \:=\:1 \quad\Rightarrow\quad \text{opp} \:=\:1


    Therefore: . \sin x \;=\;\frac{opp}{hyp} \;=\;\frac{1}{2}

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