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Thread: Sketch the curve and eliminate the parameter

  1. #1
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    Sketch the curve and eliminate the parameter

    I can't figure out how to eliminate the parameter or best way to sketch the curve

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  2. #2
    MHF Contributor
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    Re: Sketch the curve and eliminate the parameter

    In the first quadrant

    $y = \sin^3(t)$

    $y=(1-\cos^2(t))^{3/2}$

    $\cos^2(t) = x^{2/3}$

    $y = \left(1 - \left(\sqrt[3]{x}\right)^2\right)^{3/2}$

    I leave you to come up with the sketch.

    we also have

    $y = \left(1 - \left(\sqrt[3]{(-x)}\right)^2\right)^{3/2}$ in the second quadrant

    $y = -\left(1 - \left(\sqrt[3]{(-x)}\right)^2\right)^{3/2}$ in the third quadrant

    $y = -\left(1 - \left(\sqrt[3]{(-x)}\right)^2\right)^{3/2}$ in the fourth quadrant
    Thanks from topsquark and HallsofIvy
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