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Math Help - product to sum

  1. #1
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    product to sum

    If I have 10sin pi/6 cos pi/6 and need to move it to a sum. I am using 1/2[sin(u+v)+sin(u-v)], do I put the "10" in front of both sin? ex.
    1/2[10sin(u+v)+10sin(u-v)]??
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by dashreeve View Post
    If I have 10sin pi/6 cos pi/6 and need to move it to a sum. I am using 1/2[sin(u+v)+sin(u-v)], do I put the "10" in front of both sin? ex.
    1/2[10sin(u+v)+10sin(u-v)]??
    well yes..
    A\sin\alpha\cos\beta = A\left(\frac{1}{2}\left[\sin(\alpha+\beta) + \sin(\alpha+\beta)\right]\right) = \left(\frac{1}{2}\left[A\sin(\alpha+\beta) + A\sin(\alpha+\beta)\right]\right)
    since you can distribute it..

    but i noticed that the angles for cos and sin is the same..
    you can just use \sin (2A) = 2\sin A\cos A
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  3. #3
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    thank you very much
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  4. #4
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    Hello, dashreeve!

    You're doing fancy Trig and you can't do simple algebra?


    I have . 10\sin\frac{\pi}{6}\cos\frac{\pi}{6} .and need to move it to a sum.

    I am using: \sin u\cos v \;=\;\frac{1}{2}\bigg[\sin(u+v)+\sin(u-v)\bigg]

    Do I put the "10" in front of both sin?

    . . \frac{1}{2}\bigg[10\sin(u+v)+10\sin(u-v)\bigg]

    We have: . 10\cdot\underbrace{\sin(u)\cos(v)} . . . Leave the 10 "out front" !!

    . . 10\cdot\overbrace{ \left(\frac{1}{2}\bigg[\sin(u + v) + \sin(u-v)\bigg]\right)} . . . . Got it?


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    By the way . . . 10\sin\frac{\pi}{6}\cos\frac{\pi}{6} \;=\;5\,\left(2\sin\frac{\pi}{6}\cos\frac{\pi}{6}\  right) \;=\;5\sin\frac{\pi}{3}

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  5. #5
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    I did get ti right, just slower than you guys (you're very smart). I need to think of it more in algebraic terms I guess. In essence I just distributed the 10 earlier than necessary and caused myself more work. Thanks again.
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