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2. Let C be a circle of radius r and let An be the area of the regular n-sided polygon inscribed in C. Now divide the polygon into n congruent isosceles triangles with central angle 0 = 2 b Circle -Inscribed polygon An (a) (Slice) Show that the area of each triangle is r² sin(2). Hint: sin(20) = 2 sin(0) cos(0). b (b) (Approximate) Find an expression for the area An of the polygon (in terms of r and n only) by adding the areas of all the triangles. Hint: There is not much to do here. (c) (Refine) Find the area of the circle by letting the number

2. Let C be a circle of radius r and let An be the area of the regular n-sided polygon inscribed in C. Now divide the polygon into n congruent isosceles triangles with central angle 0 = 2 b Circle -Inscribed polygon An (a) (Slice) Show that the area of each triangle is r² sin(2). Hint: sin(20) = 2 sin(0) cos(0). b (b) (Approximate) Find an expression for the area An of the polygon (in terms of r and n only) by adding the areas of all the triangles. Hint: There is not much to do here. (c) (Refine) Find the area of the circle by letting the number

Advanced Engineering Mathematics
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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2. Let C be a circle of radius r and let An be the area of the regular n-sided polygon inscribed in C. Now divide the polygon into n congruent isosceles triangles with central angle 0 = 2 b Circle An -Inscribed polygon (a) (Slice) Show that the area of each triangle is r² sin(2). Hint: sin(20) = 2 sin(0) cos(0). (b) (Approximate) Find an expression for the area A,, of the polygon (in terms of r and n only) by adding the areas of all the triangles. Hint: There is not much to do here. b (c) (Refine) Find the area of the circle by letting the number A = lim An 12-00
Transcribed Image Text:2. Let C be a circle of radius r and let An be the area of the regular n-sided polygon inscribed in C. Now divide the polygon into n congruent isosceles triangles with central angle 0 = 2 b Circle An -Inscribed polygon (a) (Slice) Show that the area of each triangle is r² sin(2). Hint: sin(20) = 2 sin(0) cos(0). (b) (Approximate) Find an expression for the area A,, of the polygon (in terms of r and n only) by adding the areas of all the triangles. Hint: There is not much to do here. b (c) (Refine) Find the area of the circle by letting the number A = lim An 12-00
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