# How do you convert (r^2)(sin2theta)=2 into cartesian form?

##### 1 Answer
Jul 1, 2016

$y = \frac{1}{x}$

#### Explanation:

$\left({r}^{2}\right) \left(\sin 2 \theta\right) = 2$

frim trig we know that

$\sin 2 \theta = 2 \sin \theta \cos \theta$

and in polar coords
$= 2 \cdot \frac{y}{r} \cdot \frac{x}{r} = 2 \frac{x y}{r} ^ 2$

so $\left({r}^{2}\right) \left(2 \frac{x y}{r} ^ 2\right) = 2$

$\setminus \implies x y = 1$ or $y = \frac{1}{x}$