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Chapter 9: Q. 64 (page 584)

In Problems 61鈥�66, graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph.

r=3;r=2+2cos胃

Short Answer

Expert verified

The graph of the polar equations on the same polar grid is:

Step by step solution

01

Step 1. Given

The polar equations:

r=3;r=2+2cos胃

02

Step 2. Substitute the values and equate them.

Substitute the values of rand equate them.

3=2+2cos胃2cos胃=1cos胃=12胃=cos-1(12)=蟺3,5蟺3

The point of intersection is (3,蟺3),(3,5蟺3)

03

Step 3. Sketch the graph of r=3

Sketch the graph of r=3

04

Step 4. Polar axis

Replace 胃by-胃

r=2+2cos(-胃)=2+2cos胃

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

05

Step 5. The line

Replace 胃by 蟺-胃

r=2+2cos(蟺-胃)=2+2(cos蟺.cos胃+sin蟺.sin胃)=2+2((-1)cos胃+0)=2-2cos胃

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

06

Step 6. The pole

Replace rby-r

-r=2+2cos胃r=-2-2cos胃

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

07

Step 7. Sketch the graph r=2+2 cos θ

Graph the polar function r=2+2cos胃on the same polar grid.

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Most popular questions from this chapter

To test if the graph of a polar equation may be symmetric with respect to the line胃=蟺2,replace 胃by ______.

find each quantity if v=3i-5jand w=-2i+3j

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Find zw and zw. Leave the answers in polar form.

z=1-iw=1-3i

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