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Math Help - Using a sum or difference identity

  1. #1
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    Exclamation Using a sum or difference identity

    Question:
    Find exact Value: Sin(15o).

    So I know I can use Sin(45o - 30o) which would be (SinA)(SinB) - (CosA)(CosB): ((sqrt(2)/2)(1/2)) - ((sqrt(2)/2)(sqrt(3)/2)). I get the result: (sqrt(2)-sqrt(6))/4 . But the answer in the answer key is similar, but not this answer. At first it seems undistributed, but after making the attempt to do so, there is a negative in the wrong place. Answer Key: (sqrt(2)(sqrt(3)-1)/4.

    Can someone point out my error? Or if I'm taking the wrong approach to this.
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  2. #2
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    Re: Using a sum or difference identity

    Hello, Vlad781!

    Your formula is wrong.


    Find the exact value: \sin(15^o)

    The identity is: . \sin(A-B) \:=\:\sin A\cos B - \cos A\sin B


    \sin(15) \;=\;\sin(45-30)

    . . . . . =\;\sin45\cos30 - \cos45\sin30

    . . . . . =\;\left(\frac{\sqrt{2}}{2}\right)\left(\frac{ \sqrt{3}}{2}\right) - \left(\frac{\sqrt{2}}{2}\right)\left(\frac{1}{2} \right)

    . . . . . =\;\frac{\sqrt{2}(\sqrt{3}-1)}{4}
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  3. #3
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    Re: Using a sum or difference identity

    Oh, great catch. What can I do to post this as solved? And for future reference how did you get the nice images for the fractions?
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  4. #4
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    Re: Using a sum or difference identity

    Click Reply With Quote to see what Soroban posted. Then you can see how he formatted his response.
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