2. Consider the circle C₁ : r = 1 and the roses C₂:r = cos 20 and C3 r = 2 cos 20, each of which is sym- metric with respect to the polar axis, the-axis, and the origin, as shown on the right. a. Find polar coordinates (r,) for the intersec- tion A of C₁ and C3, where r, 0 > 0. b. Set-up (do not evaluate) a sum of three def- inite integrals that give the perimeter of the yellow-shaded region inside both C₁ and C3 but outside C₂. c. Find the area of the unshaded region inside C3 but outside C₁.
2. Consider the circle C₁ : r = 1 and the roses C₂:r = cos 20 and C3 r = 2 cos 20, each of which is sym- metric with respect to the polar axis, the-axis, and the origin, as shown on the right. a. Find polar coordinates (r,) for the intersec- tion A of C₁ and C3, where r, 0 > 0. b. Set-up (do not evaluate) a sum of three def- inite integrals that give the perimeter of the yellow-shaded region inside both C₁ and C3 but outside C₂. c. Find the area of the unshaded region inside C3 but outside C₁.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 14T
Related questions
Question
#2
![2. Consider the circle C₁ : r = 1 and the roses C₂:r =
cos 20 and C3 r = 2 cos 20, each of which is sym-
metric with respect to the polar axis, the -axis, and
the origin, as shown on the right.
a. Find polar coordinates (r,) for the intersec-
tion A of C₁ and C3, where r, 0 > 0.
b. Set-up (do not evaluate) a sum of three def-
inite integrals that give the perimeter of the
yellow-shaded region inside both C₁ and C3 but
outside C₂.
c. Find the area of the unshaded region inside C3
but outside C₁.
KIN
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6089656-79f3-4afc-988e-4e6cb47ce17b%2F62dba21a-3fa9-4611-bb8d-3f12f87d06ad%2Fxx4079o_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider the circle C₁ : r = 1 and the roses C₂:r =
cos 20 and C3 r = 2 cos 20, each of which is sym-
metric with respect to the polar axis, the -axis, and
the origin, as shown on the right.
a. Find polar coordinates (r,) for the intersec-
tion A of C₁ and C3, where r, 0 > 0.
b. Set-up (do not evaluate) a sum of three def-
inite integrals that give the perimeter of the
yellow-shaded region inside both C₁ and C3 but
outside C₂.
c. Find the area of the unshaded region inside C3
but outside C₁.
KIN
0
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