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Chapter 9: Q. 71 (page 584)

In Problems 71鈥�80, graph each polar equation. Verify your graph using a graphing utility.

r=21-cos胃

Short Answer

Expert verified

The graph of the polar equation r=21-cos胃is:

Step by step solution

01

Step 1. Given

The polar equation: r=21-cos胃

02

Step 2. The polar axis

Replace 胃by-胃,

r=21-cos(-胃)=21-cos胃

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

03

Step 3. The line

Replace 胃by蟺-胃,

r=21-cos(蟺-胃)=21-(cos蟺.cos胃+sin蟺sin胃)=21+cos胃

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

04

Step 4. The pole

Replace rby-r,

-r=21-cos胃r=-21-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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