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pset3[1] - 18.02 Problem Set 3 Due Thursday March 5 at 1:00...

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18.02 Problem Set 3 Due Thursday, March 5 at 1:00 PM in 2-106 Reading The material for this problem set is covered in section SD of the 18.02 Notes, Exercises and Solutions , and sections 19.4, 19.5, 19.6, 19.7 of Simmons, Calculus with Analytic Geometry, 2nd Edition . Part A (10 points) Exercises from the Supplementary Notes and Exercises. Please turn in the 10 underlined problems for 1 point each, the others are for more practice: (2C) : 2C-1, 2C-2, 2C-3 , 2C-4 (2D) : 2D-1, 2D-2, 2D-3 , 2D-4 , 2D-6 , 2D-7 (2E) : 2E-1, 2E-2 , 2E-4 (2F) : 2F-1 , 2F-2, 2F-5 (2H) : 2H-1, 2H-3 , 2H-4 , 2H-5 Part B (25 points) 1. (8 points, lecture 10) Consider a triangle in the plane, with angles α, β, γ . Assume that that the radius of its incircle (the circle tangent to all three sides) is 1. (a) By decomposing the triangle into six right triangles having the incenter as a common vertex, express the area A of the triangle in terms of α , β , and γ . The use your result to show that A can be expressed as a function of the two variables α and β by the formula A = cot α 2 + cot β 2 + tan
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