II. 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 4-axis, and the origin, as shown on the right. 1. Find polar coordinates (r, 0) for the intersec- tion A of C₁ and C3, where r, 0 > 0. 2. 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. 3. Find the area of the unshaded region inside C3 but outside C₁. k 0
II. 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 4-axis, and the origin, as shown on the right. 1. Find polar coordinates (r, 0) for the intersec- tion A of C₁ and C3, where r, 0 > 0. 2. 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. 3. Find the area of the unshaded region inside C3 but outside C₁. k 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:II. 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.
1. Find polar coordinates (r,0) for the intersec-
tion A of C₁ and C3, where r, 0 > 0.
2. 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.
3. Find the area of the unshaded region inside C3
but outside C₁.
k
A
0
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