Question: Problem 3. Problem 2. Using the identities sin(x) = sin(x -2x) and sin(x) = sin(-x - #), show why the following statements are true. 1.

Problem 3.

Problem 2. Using the identities sin(x) = sin(x -2x) and sin(x) = sin(-x - #), show why the following statements are true. 1. aresin(sin(x)) = x - 2x for all & E [3x /2, 5x/2]. 2. arcsin(sin(x)) = -x - * for all r e [-3x/2, -w/2]. Problem 3. Prove the following identities. 1. tan(arcsin(x)) = V1-12 2. sin(arctan(r)) = VI+ +2 Problem 4. Let f(t) = (t-1)2. Suppose that f(t) describes the position of a particle. Is the instanta- neous velocity of of the particle defined at t = 1

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