# polar to rectangular equation

• Jul 16th 2010, 01:55 PM
Dannbr
polar to rectangular equation
$r^2\sin2\vartheta=-2$

can someone help me solve this?
• Jul 16th 2010, 02:18 PM
eumyang
I assume you want to convert the polar equation into a rectangular one.
$r^2\sin 2\theta=-2$

Use the double angle identity:
\begin{aligned}
r^2 (2\sin \theta \cos \theta) &= -2 \\
2(r \sin \theta)(r \cos \theta) &= -2 \\
2yx &= -2 \\
xy &= -1
\end{aligned}