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Math Help - express sin x/2 in terms of cos x

  1. #1
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    express sin x/2 in terms of cos x

    express sin x/2 in terms of cos x

    I have the answer, but how would you approach this problem?

    Thanks.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by white_cap View Post
    express sin x/2 in terms of cos x

    I have the answer, but how would you approach this problem?

    Thanks.
    use the half angle formula. you know it right?
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  3. #3
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    Is there a way to do this question using only double angle formulas? Our class has not done the half angle formula yet.

    I googled the half angle formula, and it worked wonders. Thanks

    So i'm assuming you can't do this with only the double angle formula?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by white_cap View Post
    Is there a way to do this question using only double angle formulas? Our class has not done the half angle formula yet.

    I googled the half angle formula, and it worked wonders. Thanks

    So i'm assuming you can't do this with only the double angle formula?
    yes, there is a way to use double angles.

    Let \theta = \frac x2, so now the problem is to express \sin \theta in terms of \cos 2 \theta

    start with the double angle formula for cosine:

    \cos 2 \theta = 1 - 2 \sin^2 \theta

    now solve for \sin \theta, when you're finished, replace all the \theta's with \frac x2 and viola! (you'll realize this is just the half angle formula. your sly professor just had you derive it yourself)
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