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Math Help - (simple) trigonometric equation

  1. #1
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    (simple) trigonometric equation

    Is it possible to find closed form solutions to this simple trigonometric equation?

    \sin x = a \sin 3x

    where a is a constant.
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  2. #2
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    Re: (simple) trigonometric equation

    Doh!

    \sin x &= &3a\sin x-4a \sin^3x \\ (1-3a)\sin x &=& -4a \sin^3x  \\ \frac{3a-1}{4a} &=& \sin^2x \\ x = \arcsin \sqrt{\frac{3a-1}{4a}}
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  3. #3
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    Re: (simple) trigonometric equation

    \sin{x} = 3a\sin{x} - 4a\sin^3{x}

    4a\sin^3{x} + (1-3a)\sin{x} = 0

    \sin{x}[4a\sin^2{x} + (1-3a)] = 0

    \sin{x} = 0

    \sin^2{x} = \frac{3a-1}{4a}

    \sin{x} = \pm \sqrt{\frac{3a-1}{4a}}
    Thanks from niaren
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