Consider the particle moving along the path given by r(t) = (cos(nt) + πt sin(at), sin(xt) - πt cos(xt)). (a) Draw a sketch of r(t) for 0 < t <3. (b) Compute the vectors 7(1), 7(2), a(1), and a(2), and sketch them on the graph from part (a). (c) Find ar and ay when t = 1 and t = 2. (d) Is the speed of the particle increasing or decreasing when t = 1 and t = 2? Justify your answers.