$\displaystyle r^2\sin2\vartheta=-2$

can someone help me solve this?

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- Jul 16th 2010, 12:55 PMDannbrpolar to rectangular equation
$\displaystyle r^2\sin2\vartheta=-2$

can someone help me solve this? - Jul 16th 2010, 01:18 PMeumyang
I assume you want to convert the polar equation into a rectangular one.

$\displaystyle r^2\sin 2\theta=-2$

Use the double angle identity:

$\displaystyle \begin{aligned}

r^2 (2\sin \theta \cos \theta) &= -2 \\

2(r \sin \theta)(r \cos \theta) &= -2 \\

2yx &= -2 \\

xy &= -1

\end{aligned}$