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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 72 (page 584)

In Problems 71鈥�80, graph each polar equation. Verify your graph using a graphing utility.
$r = \frac{2}{1 - 2 \cos 胃}$

Short Answer

Expert verified

The graph of the polar equation $r = \frac{2}{1 - 2 \cos 胃}$ is:

Step by step solution

01

Step 1. Given

The polar equation: $r = \frac{2}{1 - 2 \cos 胃}$

02

Step 2. The polar axis

Replace $胃 b y - 胃$ ,

$r = \frac{2}{1 - 2 \cos (- 胃)} = \frac{2}{1 - 2 \cos 胃}$

The test is satisfied, so the graph is symmetric with respect to the polar axis.

03

Step 3. The line

Replace $胃 b y 蟺 - 胃$ ,

$r = \frac{2}{1 - 2 \cos (蟺 - 胃)} = \frac{2}{1 - 2 (\cos 蟺 . \cos 胃 + \sin 蟺 \sin 胃)} = \frac{2}{1 + \cos 胃}$

The test fails, so the graph may or may not be symmetric with respect to the line $胃 = \frac{蟺}{2}$

04

Step 4. The pole

Replace $r b y - r$ ,

$- r = \frac{2}{1 - 2 \cos 胃} r = - \frac{2}{1 - 2 \cos 胃}$

The test fails, so the graph may or may not be symmetric with respect to the pole.

05

Step 5. Graph the equation

Sketch the graph of the polar equation,

06

Step 6. Verify the graph

Verify the graph using graphing utility.

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Most popular questions from this chapter

The standard equation of a circle with center at $(- 2, 5)$ and radius $3$ is ______ .

In Problems55鈥�66, the rectangular coordinates of a point are given. Find polar coordinates for each point.

$(0, 2)$

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(6, 150 掳)$

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(- 2, 0)$

Match the graph with the polar equation

$r \sin 胃 = 2$

See all solutions

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