How do turn this to cartesian equation? (1 Viewer)

fabl · Apr 28, 2015

r(t) = [2sin(t)cos(t)]i + 2sin^2(t)j

x(t) =2sin(t)cos(t)] y(t)=2sin^2(t)

??

InteGrand · Apr 28, 2015

fabl said:
r(t) = [2sin(t)cos(t)]i + 2sin^2(t)j

x(t) =2sin(t)cos(t)] y(t)=2sin^2(t)

??

$y=2\sin^2 t \Rightarrow \frac{y}{2}=\sin ^2 t$

$\therefore x^2 = 4\sin^2 t \cos^2 t$

$= 4\sin^2 t \cdot(1-\sin^2 t)$

$= 4\cdot \frac{y}{2}\cdot \left(1-\frac{y}{2} \right)$

$= 2y \left(1-\frac{y}{2} \right)$
$= y \left(2-y\right)$

braintic · Apr 28, 2015

Now that you have a solution, the asker should try to confirm that the domain and range of the Cartesian equation match the domain and range defined by the parametric equations.

[ Alternative solution: write x=sin2t, rewrite y in terms of cos2t, then use sin^2 (2x) + cos^2 (2x) = 1 ]

How do turn this to cartesian equation? (1 Viewer)

fabl

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InteGrand

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braintic

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