Question

give the parameters of the unit circle or a part of it . describe the motion of the particle in the following problem x=cos(t)^2 and y=sin(t)^2

Answer 1

The parameters of the unit circle are x = cost and y = sint. The particle travels along the path x + y = 1 because cos(t)^2 + sin(t)^2 = 1. The range of sin(t)^2 and cos(t)^2 are both positive or zero, so we x and y are going to both be positive or zero. That means we only graph x + y = 1 in the first quadrant. You can test values of t starting at t = 0 and going up to find the orientation of the parametric line.