# Convert the polar equation to rectangular coordinates. {eq}r = \frac{2}{\sin(\theta) - \cos(\theta)} {/eq}

## Question:

Convert the polar equation to rectangular coordinates.

{eq}r = \frac{2}{\sin(\theta) - \cos(\theta)} {/eq}

## Polar to Rectangular Conversion:

The rectangular coordinate system and the polar coordinate system are the two types of coordinate systems. The rectangular form can be converted to the polar form and vice versa. It can be done by modifying the given equation and using some other equations. These equations are {eq}x=r \cos \theta {/eq}, {eq}y=r \sin \theta {/eq}, and {eq}{{r}^{2}}={{x}^{2}}+{{y}^{2}} {/eq}.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer!

Multiply both sides of the given polar equation by {eq}(\sin \theta-\cos \theta) {/eq} and simplify the resulting equation.

{eq}\begin{aligned} ...

See full answer below.

#### Learn more about this topic:

Polar Coordinates: Definition, Equation & Examples

from

Chapter 1 / Lesson 16
28K

Understand the definition of polar coordinates, discover the formula for expressing polar coordinates, and learn how to convert cartesian coordinates into polar coordinates with examples.