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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 54E
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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
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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