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Q 53.

Expert-verified
Found in: Page 731

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.$y=-3$

The required equation is $-3\mathrm{csc}\theta$.

See the step by step solution

## Step 1. Given information.

The given equation in rectangular coordinates is:

$y=-3$

## Step 2. Find the equation in rectangular coordinates.

$y=-3$

As we know that in polar coordinates $y=r\mathrm{sin}\theta$, then substitute the value of y ,

$r\mathrm{sin}\theta =-3$

Divide both sides by role="math" localid="1649349326734" $\mathrm{sin}\theta$,

$\frac{r\mathrm{sin}\theta }{\mathrm{sin}\theta }=\frac{-3}{\mathrm{sin}\theta }\phantom{\rule{0ex}{0ex}}r=\frac{-3}{\mathrm{sin}\theta }\phantom{\rule{0ex}{0ex}}r=-3\mathrm{csc}\theta$

Therefore, the equation in polar coordinates is $-3\mathrm{csc}\theta$.