Chapter 9: Q 36. (page 731)

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

Short Answer

Expert verified

The required equation is ${(x - 1)}^{2} + y^{2} = 1$ .

Step by step solution

Step 1. Given information.

The given equation in polar coordinates is:

$r = 2 \cos θ$

Step 2. Find the equation in rectangular coordinates.

$r = 2 \cos θ$

First, multiply both sides byr,

$r^{2} = 2 r \cos θ r^{2} = 2 x [Since r \cos θ = x] x^{2} + y^{2} = 2 x [S i n c e r^{2} = x^{2} + y^{2}]$

Now add $- 2 x$ on both sides of the equation,

role="math" localid="1649264450788" $x^{2} + y^{2} - 2 x = 2 x - 2 x x^{2} + y^{2} - 2 x = 0$

Complete the square in x,

${(x - 1)}^{2} + y^{2} - 1 = 0$

now add 1 on both sides of the equation,

${(x - 1)}^{2} + y^{2} - 1 + 1 = 0 + 1 {(x - 1)}^{2} + y^{2} = 1$

Therefore, the equation in rectangular coordinates is ${(x - 1)}^{2} + y^{2} = 1$ .

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the equation in rectangular coordinates.

One App. One Place for Learning.

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In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.r=2cosθ

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

Applied Mathematics

Mechanics Maths

Decision Maths

Geometry

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

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