Suggested languages for you:

Americas

Europe

Q56.

Expert-verified
Found in: Page 593

### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# Polar Equations to Rectangular Equations Convert the polar equation to rectangular coordinates $r=2\mathrm{csc}\theta$

The rectangular equation is $y=2$

See the step by step solution

## Step 1. Given information

An equation is given in polar coordinate system as $r=2\mathrm{csc}\theta$

## Step 2. Concept used

Use conversion formulae from rectangular coordinates into polar coordinates as-

$\begin{array}{l}x=r\mathrm{cos}\theta \\ y=r\mathrm{sin}\theta \end{array}$

Substitute the value in the formulae. And simplify them.

## Step 3. Calculation

Formulae used,

$y=r\mathrm{sin}\theta$

Substitute the values in the formulae,

$\begin{array}{l}r=\frac{2}{\mathrm{sin}\theta }\\ y=r\mathrm{sin}\theta \\ \therefore y=2\end{array}$

It is a line