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Q 53.

Expert-verified

Calculus

Found in: Page 731

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

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

The required equation is $- 3 \csc θ$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $y = r \sin θ$ , then substitute the value of y ,

$r \sin θ = - 3$

Divide both sides by role="math" localid="1649349326734" $\sin θ$ ,

$\frac{r \sin θ}{\sin θ} = \frac{- 3}{\sin θ} r = \frac{- 3}{\sin θ} r = - 3 \csc θ$

Therefore, the equation in polar coordinates is $- 3 \csc θ$ .

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