Hi. I need some help getting the cusp for c,d,e I could not quite get why c) results in an empty set, I did not manage to solve for d) and how to equate the cos and sin of the derivative for e) to get the actual value of t

Q94. Cusps and smoothness. Decide whether each of the following parametric curves r : R - R' is smooth. For those that are not smooth, find any cusps. (a) r(t) = e-ti+ +3j. ( b) r(t) = tsi + tj (c) r(t) = cos(t)i + sin(3t)j. (d) r(t) = cos(2t)i + sin(t)j. (e) r(t) = (2 cos(t) + cos(2t) )i + (2 sin(t) - sin(2t) )j