(5 marks). There are two coloured pencils: red and blue. The tip of the red pencil is moving along the r-axis and the tip of the blue pencil is moving along the y-axis. The locations of the tips of the red and blue pencils at time t are given by differentiable functions r(t) and b(t), respectively. We know that r(t) = sin(t)-2. However, we know only that the tip of the blue pencil moves along the positive y-axis with b(0) = b'(0) = 1. We are interested in the areas of the triangles made by the two tips of the pencils and the origin. Let's denote such an area at time t by A(t). For example, at t = 0 the area is equal to A(0) = 1. (Check this to make sure you understand the question!). (a) (2 marks) Find the formula for A(t) in terms of r(t) and b(t). You may want to make sure that your formula gives A(0) = 1. (b) (3 marks) Find the rate of change of the area when t = 0. (5 marks). Prove that there exists a value of r so that COST = COST