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Math Help - solve equation

  1. #1
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    solve equation

    1.solve for x in sinx tanx+ tanx-2sinx+cosx=0 for 0<orequalx<or equal 2\pi rads

    2. find the exact value of (\frac{7\pi}{6})
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  2. #2
    MHF Contributor red_dog's Avatar
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    Here is the graph of the function in the left side of the equation.

    The equation has one solution between 3 and 4.
    Attached Thumbnails Attached Thumbnails solve equation-equation.jpg  
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  3. #3
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    my bad
    Last edited by mathaddict; July 29th 2009 at 11:43 PM.
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  4. #4
    MHF Contributor red_dog's Avatar
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    Quote Originally Posted by mathaddict View Post
    (1)
    sin^2 x +cos^2 x + sin x -2 sin x cos x =0

    sin x (1- 2 cos x )=0


    \sin x(1-2\cos x)=-1
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  5. #5
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    More information please

    Hello william

    What do you mean? This doesn't make sense.
    Quote Originally Posted by william View Post
    ...
    2. find the exact value of (\frac{7\pi}{6})
    If you mean 'Find the exact value of \sin(\tfrac{7\pi}{6})', then the answer is that \sin(\pi+A) = -\sin A, and \sin(\tfrac{\pi}{6}) = \tfrac12. So...?

    Grandad
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  6. #6
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    Quote Originally Posted by red_dog View Post
    Here is the graph of the function in the left side of the equation.

    The equation has one solution between 3 and 4.
    By a numerical method, I got x=3.4968, correct to 4 d.p. Are you sure we have the correct question here?

    Grandad
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  7. #7
    MHF Contributor red_dog's Avatar
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    I tried another way, but that doesn't lead to an exact solution.

    \sin x-2\sin x\cos x+1=0

    2\sin\frac{x}{2}\cos\frac{x}{2}\left(\sin^2\frac{x  }{2}+\cos^2\frac{x}{2}\right)-

    -4\sin\frac{x}{2}\cos\frac{x}{2}\left(\cos^2\frac{x  }{2}-\sin^2\frac{x}{2}\right)+\left(\sin^2\frac{x}{2}+\  cos^2\frac{x}{2}\right)^2=0

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

    Divide by \cos^4\frac{x}{2} and let \tan\frac{x}{2}=t

    t^4+6t^3+2t^2-2t+1=0

    (t+1)(t^3+5t^2-3t+1)=0

    t=-1 which is not good because x\neq\frac{(2k+1)\pi}{2}

    t^3+5t^2-3t+1=0 which has an irational solution.
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