The position of a particle is given by the parametric equations
x = 1 + sin pi*t - cos pi*t
y = 3*sin pi*t + 2*cos pi*t
(a) Describe the graph of these parametric equations as t ranges over all real numbers. (In other words, find all possible positions of the particle.)
(b) Describe the motion of the particle as t ranges from 0 to 2.
(c) Find a parametrization such that the overall graph of this parametrization from t = 0 to t = 2 matches the graph of part (b), but the motion of the particle is different.
it is clearly an ellipse. By eliminating t, you get
(3-3x+y)^2 + (2x+y-2)^2 = 25