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Math Help - Trigonometric equations

  1. #1
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    Trigonometric equations

    Im having a little trouble answering these problems.

    Note: Q represents the symbol that looks like a zero with a line across. (Not sure what its called.

    1.) 1 - 2 sin(Q) = sin(Q) - sqrt(3)
    2.) 2 (sin^2)(Q) = 1 - sin (Q)
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  2. #2
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    Quote Originally Posted by ceasar_19134 View Post
    1.) 1 - 2 sin(Q) = sin(Q) - sqrt(3)
    2.) 2 (sin^2)(Q) = 1 - sin (Q)
    Call Q=x, we have

    1-2\sin x=\sin x-\sqrt3\implies3\sin x=1+\sqrt3

    Can you do it from there?

    2\sin^2x+\sin x-1=0\implies(\sin x+1)(2\sin x-1)=0

    Can you?
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ceasar_19134 View Post
    Note: Q represents the symbol that looks like a zero with a line across. (Not sure what its called.)

    1.) 1 - 2 sin(Q) = sin(Q) - sqrt(3)
    It's \theta and it's pronounced "theta." We can stick with Q's though.

    1 - 2sin(Q) = sin(Q) - \sqrt{3}

    -3sin(Q) = -1 - \sqrt{3}

    sin(Q) = \frac{1}{3} + \frac{\sqrt{3}}{3}

    This has no "nice" solution. So
    Q \approx 1.14494~rad

    -Dan
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