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Chapter 9: Q. 68 (page 584)

In Problems 67鈥�70, the polar equation for each graph is either r=a+bcos胃or r=a+bsin胃,a>0. Select the correct equation and find the values of aand b.

Short Answer

Expert verified

The correct equation for the graph isr=3-3cos胃

And the value of a is3 and bis-3

Step by step solution

01

Step 1. Given

The graph:

The polar equations:

r=a+bcos胃r=a+bsin胃

02

Step 2. Test for r=a+b cos θ

Substitute the point (6,蟺)from the graph in the equation,

6=a+bcos(蟺)6=a-b

Substitute another point (3,蟺2)in the equation,

3=a+bcos(蟺2)3=a

03

Step 3. Find the values of a,b

The value of a=3

Substitute a=3in the equation,

a-b=63-b=6b=-3

The value of b is -3

04

Step 4. Find the equation

Substitute a=3;b=-3in the suitable equation,

r=3-3cos胃

The polar equation of the given graph is r=3-3cos胃

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Most popular questions from this chapter

In Problems 39鈥�54, the polar coordinates of a point are given. Find the rectangular coordinates of each point.

(6.3,3.8)

Identify and graph each polar equation. Verify your graph using a graphing utility.

r=3胃

Match the graph with the polar equation.

r=2sin胃

If P=-3,1andQ=x,4, find all numbers x such that the vector represented by PQ鈬赌has length 5.

Write the expression in the standard form a+ib.

3cos80掳+isin80掳3
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