a particle moving in a plane has position at time t given by

x(t) = (2 cos t, sin (2t)) , 0<=t<=Pi

(a) find the position and velocity of the particle at times

t=0, t=(pi/2) and t=pi

(b) find the vector equation of the tangent line to the path of the particle at

t0 = (pi/4)

(c) make a sketch of the path of the particle for 0<=t<=Pi, indicating the relevant positions and velocities from parts (a) and (b) above

(hint: draw the component curves)