Determine whether the following statements are true and give an explanation or counterexample.

a. The equations x = -cos t, y = -sin t, for 0 ≤ t ≤ 2π, generate a circle in the clockwise direction.

b. An object following the parametric curve x = 2 cos 2πt, y = 2 sin 2πt circles the origin once every 1 time unit.

c. The parametric equations x = t, y = t², for t ≥ 0, describe the complete parabola y = x².

d. The parametric equations x = cos t, y = sin t, for -π/2 ≤ t ≤ π/2, describe a semicircle.

e. There are two points on the curve x = -4 cos t, y = sin t, for 0 ≤ t ≤ 2π, at which there is a vertical tangent line.