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Math Help - Solve a trigonometric equation

  1. #1
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    Solve a trigonometric equation

    34*Sin^2[x]+Sin[2*x]-8*Cos^2[x]==4

    Could someone please help me with this equation.
    Thx
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  2. #2
    MHF Contributor red_dog's Avatar
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    34\sin^2x+2\sin x\cos x-8\cos^2x=4(\sin^2x+\cos^2x)\Rightarrow

    \Rightarrow 30\sin^2x+2\sin x\cos x-12\cos^2x=0| \ :2\cos^2x

    15\tan^2x+\tan x-6=0

    Now solve the quadratic.
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  3. #3
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    Quote Originally Posted by antrax1988 View Post
    34*Sin^2[x]+Sin[2*x]-8*Cos^2[x]==4

    Could someone please help me with this equation.
    Thx
    34\sin^2{x} + \sin(2x) - 8\cos^2{x} = 4(\sin^2{x} + \cos^2{x})<br />

    30\sin^2{x} + 2\sin{x}\cos{x} - 12\cos^2{x} =  0

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

    (5\sin{x} - 3\cos{x})(3\sin{x} + 2\sin{x}) = 0

    I leave the rest for you ... set each factor equal to zero and solve.
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  4. #4
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    Thx guys for the help
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