# How do you convert r^2sin2t=2 into cartesian form?

Jun 3, 2016

In Cartesian form ${r}^{2} \sin 2 t = 2$ can be written as
$x y = 1$, which is the equation of a hyperbola.

#### Explanation:

The relation between a polar coordinate $\left(r , t\right)$ and Cartesian coordinates $\left(x , y\right)$ is given by $x = r \cos t$ and $y = r \sin t$

Also note that ${r}^{2} = {x}^{2} + {y}^{2}$ and $\frac{y}{x} = \tan \theta$

Hence ${r}^{2} \sin 2 t = 2$ can be written as

${r}^{2} \times 2 \sin t \cos t = 2$ or $r \sin t \times r \cos t = 1$

or $x y = 1$, which is the equation of a hyperbola.

graph{xy=1 [-10, 10, -5, 5]}