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Math Help - need some help with solving a trig equation

  1. #1
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    need some help with solving a trig equation

    ok, i am supposed to solve

    2 sin 2 x = 3(cos 2x + sin x -1) for 0 ≤ x < pi (so in radians)

    please help me out, i suck at these sort of questions

    any help at all? i'm goin to have to move this urgent
    Last edited by andyp999; November 16th 2008 at 10:48 AM.
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  2. #2
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    Quote Originally Posted by andyp999 View Post
    ok i asked this in the trig forum but havnt had a reply for a few hours and i really need to get this done soon

    i am supposed to solve

    2 sin 2 x = 3(cos 2x + sin x -1) for 0 ≤ x < pi (so in radians)

    please help me out, i suck at these sort of questions
    confirm the equation ...

    2\sin(2x) = 3[\cos(2x) + \sin{x} - 1]
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  3. #3
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    sorry for the late reply but yes that is correct
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  4. #4
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    2\sin(2x) = 3[\cos(2x) + \sin{x} - 1]

    4\sin{x}\cos{x} = 3[1 - 2\sin^2{x} + \sin{x} - 1]

    4\sin{x}\cos{x} = 3[2\sin^2{x} + \sin{x}]

    4\sin{x}\cos{x} = 6\sin^2{x} + 3\sin{x}

    0 = 6\sin^2{x} + 3\sin{x} - 4\sin{x}\cos{x}

    0 = \sin{x}[6\sin{x} + 3 - 4\cos{x}]

    \sin{x} = 0 at x = 0

    that was the "easy" solution ... the next is a pain in the @$$ ...

    6\sin{x} + 3 - 4\cos{x} = 0

    6\sin{x} = 4\cos{x} - 3

    36\sin^2{x} = 16\cos^2{x} - 24\cos{x} + 9

    36(1 - \cos^2{x}) = 16\cos^2{x} - 24\cos{x} + 9

    36 - 36\cos^2{x} =   16\cos^2{x} - 24\cos{x} + 9

    0 = 52\cos^2{x} - 24\cos{x} - 27

    \cos{x} = \frac{6 \pm 3\sqrt{43}}{26}

    one of these two solutions is extraneous ... the solution that works is not pretty, you'll need a calculator to determine x.

    x = \arccos\left(\frac{6 - 3\sqrt{43}}{26}\right)

    which makes me ask the question ... were you allowed to use a calculator in solving this equation in the first place?
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  5. #5
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    yes i was allowed a calculator haha
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  6. #6
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    Quote Originally Posted by andyp999 View Post
    yes i was allowed a calculator haha
    not funny.
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  7. #7
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    sorry did u not kno? sorry if i caused you problems
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