Chapter 10.5, Problem 28E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding Points of Intersection In Exercises 27-34, find the points of intersection of the graphs of the equations. r = 3 ( 1 + sin θ ) r = 3 ( 1 − sin θ )

To determine

To Find: The point of intersection of graphs.

Explanation

Given:

Formula Used:

r=3(1+sinÎ¸),r=3(1âˆ’sinÎ¸)

Calculation:

Polar equations are given: r=3(1+sinÎ¸),r=3(1âˆ’sinÎ¸)

Solve simultaneously and get,

â‡’3(1+sinÎ¸)=3(1âˆ’sinÎ¸)

â‡’2sinÎ¸=0

Î¸=0,Ï€,2Ï€

Substitute Î¸=0 in r=3(1+sinÎ¸) and get,

r=3(1+sin0)

â‡’r=3

Therefore, the point of intersection is (3,0).

Substitute the value of Î¸=2Ï€ in r=3(1+sinÎ¸) and get,

r=3(1+sin2Ï€)

â‡’r=3

Therefore, the another point of intersection is (3,2Ï€)

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