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
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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