# Thread: Sketch the curve and eliminate the parameter

1. ## 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. ## Re: Sketch the curve and eliminate the parameter

$y = \sin^3(t)$

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

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

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

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