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Math Help - [SOLVED] Eliminating more trig parameters (sin & cos)

  1. #1
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    [SOLVED] Eliminating more trig parameters (sin & cos)

    Ok so I thought I'd post this one now that I've been able to work through it a little farther because it didn't quite turn out how I expected graphically...

    original problem:

    Eliminate the parameter to find a Cartesian equation of the curve
    <br />
x = \frac{1}{2}\cos\theta   ,   y = 2\sin\theta   ,   0 <= \theta <= \pi<br />

    My steps:

    2x = \cos\theta and \frac{y}{2} = \sin\theta

    1) 2x^2 + \frac{1}{2}y^2 = 1

    2) \frac{1}{2}y^2 = 1 - 2x^2

    3) y^2 = 2(1-2x^2)

    4) y^2 = 2 - 4x^2

    Solution) y = \sqrt{2-4x^2}

    is this correct? If so how do I graph this appropriately? Do I just graph the function I have for the solution or do I have to plug back in the trigonometric x value?

    Thanks
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  2. #2
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    Quote Originally Posted by buddyp450 View Post

    1) 2x^2 + \frac{1}{2}y^2 = 1
    This is wrong. Can you figure it out?

    And the graph will be an ellipse
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  3. #3
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    solved*
    Last edited by buddyp450; January 25th 2010 at 03:59 PM.
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