II. Consider the circle C₁ : r = 4, and the limaon C₂: r = 3-2 sine. Note that both C₁ and C₂ are symmetric about the 4-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 def- inite integral/s that will give the follow- ing. a. perimeter of R₁ b. area of R₂. B KIN R₁ R₂ A 0
II. Consider the circle C₁ : r = 4, and the limaon C₂: r = 3-2 sine. Note that both C₁ and C₂ are symmetric about the 4-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 def- inite integral/s that will give the follow- ing. a. perimeter of R₁ b. area of R₂. B KIN R₁ R₂ A 0
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.4: Analytic Proofs
Problem 32E
Related questions
Question
![II. Consider the circle C₁ : r = 4, and the limaon
C₂ r = 3-2 sin 8. 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, 0) for A and
B, where r> 0 and 0 € [0, 2π].
2. Set up (and do not evaluate) the def-
inite integral/s that will give the follow-
ing.
a. perimeter of R₁
b. area of R₂.
B
KIN
R₁
R₂
/A
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe91a9957-4253-47da-9fb0-7d570bdaf52a%2F8c216044-7129-47b3-a608-3e3a2cde7286%2F39m3dla_processed.png&w=3840&q=75)
Transcribed Image Text:II. Consider the circle C₁ : r = 4, and the limaon
C₂ r = 3-2 sin 8. 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, 0) for A and
B, where r> 0 and 0 € [0, 2π].
2. Set up (and do not evaluate) the def-
inite integral/s that will give the follow-
ing.
a. perimeter of R₁
b. area of R₂.
B
KIN
R₁
R₂
/A
0
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