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Math Help - factorising trigonometric function

  1. #1
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    factorising trigonometric function

    for -180 </= θ </= 180, solve

    3sin^2(θ) - sin(θ)cos(θ) - 4cos^2(θ) = 0

    i can't factorise the middle term to separate the sine and cosine
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  2. #2
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    Re: factorising trigonometric function

    Quote Originally Posted by tomoshaw View Post
    for -180 </= θ </= 180, solve
    3sin^2(θ) - sin(θ)cos(θ) - 4cos^2(θ) = 0
    i can't factorise the middle term to separate the sine and cosine

    Oh, come on. You can factor 3x^2-xy-4y^2~?
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  3. #3
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    Re: factorising trigonometric function

    Let sin\theta=x and cos\theta=y

    Substitute these into the equation and you get
    3x^2-xy-4y^2

    Edit: Plato beat me to it.
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  4. #4
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    Re: factorising trigonometric function

    This is how i originally tried to tackle it. I'm either blind or I need to be posting on a key stage 2 board but i just can't see how that factorises and I know it's really simple.
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  5. #5
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    Re: factorising trigonometric function

    i see it factorises to

    (3x-4y)(x+y)

    but i thought you could only have 1 trigonometric term in each factor?
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  6. #6
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    Re: factorising trigonometric function

    No, you can have whatever is needed in each factor. Now by setting each factor equal to 0, you end up with two simpler equations to solve for theta.
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