Short Answer

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r^{2} = \sin θ$

The required equation is ${(x^{2} + y^{2})}^{\frac{3}{2}} = y$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given equation in polar coordinates is:

$r^{2} = \sin θ$

Step 2. Find the equation in rectangular coordinates.

$r^{2} = \sin θ$

First, multiply both sides by r,

$r \cdot r^{2} = r \sin θ r^{3} = y [r \sin θ = y] {(\sqrt{x^{2} + y^{2}})}^{3} = y [r^{2} = x^{2} + y^{2} and r = \sqrt{x^{2} + y^{2}}] {(x^{2} + y^{2})}^{\frac{3}{2}} = y$

Therefore, the equation in rectangular coordinates is ${(x^{2} + y^{2})}^{\frac{3}{2}} = y$ .

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Short Answer

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r^{2} = \sin θ$

Step by Step Solution

Step 1. Given information.

Step 2. Find the equation in rectangular coordinates.

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Calculus

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Short Answer

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.r2=sin θ

Step by Step Solution

Step 1. Given information.

Step 2. Find the equation in rectangular coordinates.

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In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r^{2} = \sin θ$