Consider the circle C₁ : r = 4, and the limaçon C₂ r = 3-2 sin 0. Note that both C₁ and C₂ are symmetric about the -axis. Let A and B be the points of intersection of C₁ and C₂. Let R₁ be the region within C₁ but outside C2, and R2 be the region within both C₁ and C₂, as shown on the right. 1. Find polar coordinates (r,) for A and B, where r> 0 and 0 € [0, 2π]. 2. Set up (and do not evaluate) the definite integral/s that will give the following. a. perimeter of R₁ b. area of R₂. B KIN R₁ R₂ 0 A

Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.4: Analytic Proofs
Problem 28E
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Consider the circle Cı : r = 4, and the limaçon
C2 : r = 3 – 2 sin 0. Note that both C1 and C2
are symmetric about the -axis. Let A and B be
the points of intersection of C1 and C2. Let R1
be the region within C1 but outside C2, and R2
be the region within both C1 and C2, as shown on
the right.
R1
1. Find polar coordinates (r, 0) for A and B,
where r > 0 and 0 E [0, 27].
R2
В
A
2. Set up (and do not evaluate) the definite
integral/s that will give the following.
a. perimeter of R1
b. area of R2.
Transcribed Image Text:Consider the circle Cı : r = 4, and the limaçon C2 : r = 3 – 2 sin 0. Note that both C1 and C2 are symmetric about the -axis. Let A and B be the points of intersection of C1 and C2. Let R1 be the region within C1 but outside C2, and R2 be the region within both C1 and C2, as shown on the right. R1 1. Find polar coordinates (r, 0) for A and B, where r > 0 and 0 E [0, 27]. R2 В A 2. Set up (and do not evaluate) the definite integral/s that will give the following. a. perimeter of R1 b. area of R2.
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