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

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

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Answer 1 · 2016-07-04T20:40:51

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

Explanation:

$x = cos (t) \to x^{2} = {cos}^{2} (t)$ $x = cos(t)->x^2=cos^2(t)$
$y = sin (2 t) = 2 cos (t) sin (t) \to y^{2} = 4 {cos}^{2} (t) {sin}^{2} (t)$ $y = sin(2t)=2cos(t)sin(t)->y^2=4cos^2(t)sin^2(t)$

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

then

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

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

1 Answer

Explanation:

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

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Explanation:

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