Chapter 9: Q. 43 (page 583)

Identify and graph each polar equation. Verify your graph using a graphing utility
$r = 4 - 2 \cos θ$

Short Answer

Expert verified

$r = 4 - 2 \cos θ$

Step by step solution

Step 1. The given information is

$r = 4 - 2 \cos θ$

Step 2. Replace θ by -θ

$r = 4 - 2 \cos (- θ) r = 4 - 2 \cos θ$

Test is satisfied, graph is symmetric with respect to polar axis.

Step 3. Replace θ by π-θ

$r = 4 - 2 \cos (π - θ) r = 4 + 2 \cos θ$

Graph may or may not be symmetric with

$θ = \frac{π}{2}$

Step 4. Replace r by -r

$r = 4 - 2 \cos θ - r = 4 - 2 \cos θ r = - 4 + 2 \cos θ$

Graph may or may not be symmetric with respect to pole

Making the graph we get

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Identify and graph each polar equation. Verify your graph using a graphing utility
$r = 4 - 2 \cos θ$

Short Answer

Step by step solution

Step 1. The given information is

Step 2. Replace θ by -θ

Step 3. Replace θ by π-θ

Step 4. Replace r by -r

Making the graph we get

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Identify and graph each polar equation. Verify your graph using a graphing utilityr=4-2cosθ

Short Answer

Step by step solution

Step 1. The given information is

Step 2. Replace θ by -θ

Step 3. Replace θ by π-θ

Step 4. Replace r by -r

Making the graph we get

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

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Study anywhere. Anytime. Across all devices.

Identify and graph each polar equation. Verify your graph using a graphing utility
$r = 4 - 2 \cos θ$