4. For 0t4, the path of a particle is parametrized by r(t)=cos(t)sin(t),(sin(t))2,sin(t) (a) Show that the path of the particle is a closed loop. (b) Let C be the curve on which the particle travels. How many times does the particle traverse C from t=0 to t=4? Justify your answer. (c) Write down, but don't evaluate, an integral whose value is the length of C. (d) Write down, but don't evaluate, an integral whose value is the distance traveled by the particle