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Math Help - New Trigo-equation

  1. #1
    Super Member dhiab's Avatar
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    New Trigo-equation

    Solve in R : \sqrt{-3-\cos ^{2}(x)+3\sin (5x)}=1-\sin (x)
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  2. #2
    MHF Contributor red_dog's Avatar
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    Condition: -3-\cos^2x+3\sin 5x\geq 0

    But 3(\sin 5x-1)\leq 0 and -\cos^2x\leq 0.

    Then \sin 5x=1 and \cos x=0.

    Also the right side member must be 0: 1-\sin x=0

    \sin 5x=16\sin^5x-20\sin^3x+5\sin x

    If \sin x=1 then \sin 5x=1.

    So \sin x=1\Rightarrow x=\frac{\pi}{2}+2k\pi
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  3. #3
    Senior Member pacman's Avatar
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    from red_dog: ,

    when k = 0, then x = pi/2,

    k = 1, x = 7pi/2.

    The graph confirms the rightfullness of red_dog's Solution.



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