3. Suppose that the positions of two particles at the time t are given by r1(t) = 2 cos(t) sin (t)i + sin(t)j r2(t) = sin(t)i + cos(t)j Define xi(t), yi(t) by ri(t) = xi(t)i + yi(t)j for i E {1, 2}. (a) Express the set X = {t E R : y1(t) = y2(t)} in abbreviated form. Note that X is infinite.(b) Use your answer to (a) to nd the set C of tvalues for which there are collisions between the particles. (c) Find the two places in R2 at which the collisions you found in (b) occur