A curve is given by the parametric equations: $x=cos(t) , y=sin(2t)$ , how do you find the cartesian equation?

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Answer 1 · 2016-07-04T20:40:51

$y^2=4x^2(1-x^2)$

$x = cos(t)->x^2=cos^2(t)$
$y = sin(2t)=2cos(t)sin(t)->y^2=4cos^2(t)sin^2(t)$

but $cos^2(t)+sin^2(t) = 1$

then

$y^2=4x^2(1-x^2)$

A curve is given by the parametric equations: x=cos(t) , y=sin(2t)x=cos(t) , y=sin(2t), how do you find the cartesian equation?