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Math Help - trigonometry

  1. #1
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    trigonometry

    sin6x+3sin4x.cos2x=0
    find solution set

    sin6x+3/2(sin6x+sin2x)=0
    5sin6x+3sin2x=0

    I got stuck here.
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  2. #2
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    Re: trigonometry

    Quote Originally Posted by kastamonu View Post
    sin6x+3sin4x.cos2x=0
    find solution set

    sin6x+3/2(sin6x+sin2x)=0
    5sin6x+3sin2x=0

    I got stuck here.
    Is it sin(2x) or sin^2(x)?

    -Dan
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  3. #3
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    Re: trigonometry

    write

    sin 6x = sin( 4x + 2x) = ......
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    Re: trigonometry

    sin2x
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    Re: trigonometry

    Quote Originally Posted by Idea View Post
    write

    sin 6x = sin( 4x + 2x) = ......
    I couldn't get anything.
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  6. #6
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    Re: trigonometry

    \sin (4x+2x)=\sin  4x \cos  2x +\cos  4x \sin  2x
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  7. #7
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    Re: trigonometry

    Let y = 2x so we have 5.sin(3y) + 3.sin(y) = 0

    where sin(3y) = sin(2y+y) = sin(2y).cos(y) + cos(2y).sin(y)

    = 2.sin(y).cos^2(y) + sin(y).(1-2.sin^2(y))

    = 2.sin(y)(1-sin^2(y)) + sin(y) - 2.sin^3(y)

    = 3.sin(y) - 4.sin^3(y)
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  8. #8
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    Re: trigonometry

    Plug that in for sin(3y). Then, let u = \sin(y). You wind up with a cubic equation in u. Solve for u (you have something for the form au-bu^3=0, so u(a-bu^2)=0 implies u=0 or a-bu^2=0). Once you solve for u, you have u = \sin(y), so take arcsin of both sides. Then, you have y = 2x.
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    Re: trigonometry

    you could also linearize the equation

    \sin  2x (4+ 5\cos  4x)=0

    giving two sets of solutions

    \sin  2x=0

    \cos  4x=-4/5
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  10. #10
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    Re: trigonometry

    Thanks.
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