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Math Help - solving trigonometric equations

  1. #1
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    solving trigonometric equations

    I've been stuck trying to figure this one out for a while...

    sin(2A) + sin(4A) = 0
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  2. #2
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    Quote Originally Posted by nathanand View Post
    I've been stuck trying to figure this one out for a while...

    sin(2A) + sin(4A) = 0
    Let u = 2A

    sin(u) + sin(2u) = 0

    2sin(u)cos(u) + sin(u) = 0

    sin(u)(2cos(u)+1) = 0

    Either sin(u) = sin(2A) = 0 so A=0


    or 2cos(u) = -1 \rightarrow cos(u) = -\frac{1}{2}

    and so u = \frac{2\pi}{3} thus 2A = \frac{2\pi}{3} <br />
\rightarrow A = \frac{\pi}{3}

    bear in mind this graph will repeat every \pi radians instead of every 2\pi radians
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  3. #3
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    Thanks for the help!
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