Consider the following position functions r and R for two objects.

a. Find the interval [c, d] over which the R trajectory is the same as the r trajectory over [a, b].

b. Find the velocity for both objects.

c. Graph the speed of the two objects over the intervals [a, b] and [c, d], respectively.

r(t) = (cos t, 4 sin t), [a, b] = [0, 2π],

R(t) = (cos 3t, 4 sin 3t) on [c, d]