# How do you convert r(4sintheta - cos theta) = 1 into cartesian form?

Jun 3, 2016

$4 y - x = 1$

#### Explanation:

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

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

Hence $r \left(4 \sin \theta - \cos \theta\right) = 1$ can be written as

$4 r \sin \theta - r \cos \theta = 1$ or

$4 y - x = 1$