3. Suppose that the positions of two particles at the time t are given by r(t) = 2 cos(t) sin(t)i + sin(t)j r(t) = sin(t)i + cos(t)j Define x,(t), y(t) by r(t) = x(t)i + y(t)j for i E {1,2}. (a) Express the set X = {t ER: y(t) = y2(t)} in abbreviated form. Note that X is infinite. (b) Use your answer to (a) to find the set C of t-values for which there are collisions between the particles. (c) Find the two places in R2 at which the collisions you found in (b) occur.