# Thread: polar to rectangular equation

1. ## polar to rectangular equation

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

can someone help me solve this?

2. 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}