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Math Help - Polar Equation

  1. #1
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    Polar Equation

    can anyone help me:

    Convert the polar equation r^2=3 cos(2x)
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  2. #2
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    Quote Originally Posted by winsome View Post
    can anyone help me:

    Convert the polar equation r^2=3 cos(2x)
    I assume that you mean convert to cartesians.

    Remember that x = r\cos{\theta}, y = r\sin{\theta} and x^2 + y^2 = r^2.


    So r^2 = 3\cos{2\theta}

    r^2 = 3(\cos^2{\theta} - \sin^2{\theta})

    r^2 = 3\left[\left(\frac{x}{r}\right)^2 - \left(\frac{y}{r}\right)^2\right]

    r^2 = 3\left[\frac{x^2}{r^2} - \frac{y^2}{r^2}\right]

    r^2 = \frac{3x^2 - 3y^2}{r^2}

    r^4 = 3x^2 - 3y^2

    (x^2 + y^2)^2 = 3x^2 - 3y^2

    x^4 + 2x^2y^2 + y^4 = 3x^2 - 3y^2
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