Chapter 9: Q 41. (page 731)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

The given equation in polar coordinates is:

$r = \sin 2 θ$

Step 2. Find the equation in rectangular coordinates.

$r = \sin 2 θ r = 2 \sin θ \cos θ [\sin 2 θ = 2 \sin θ \cos θ]$

First, multiply both sides byr,

$r^{2} = 2 \cdot r \sin θ \cdot \cos θ r^{2} = 2 \cdot y \cdot \cos θ [r \sin θ = y]$

Again multiply both sides byr,

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

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

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

Short Answer

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=sin2θ

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the equation in rectangular coordinates.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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