Answer:
A and C
Step-by-step explanation:
Easiest way is to plug in values of t and trace the graph.
A (x, y) = (sin(t), cos(t))
At t = 0, (x, y) = (0, 1).
At t = π/2, (x, y) = (1, 0).
So the particle starts at (0, 1) and moves clockwise. The period of sin(t) and cos(t) is 2π, so for 0 < t < 2π, the particle makes 1 revolution.
B (x, y) = (-sin(t), cos(t))
At t = 0, (x, y) = (0, 1).
At t = π/2, (x, y) = (-1, 0).
So the particle starts at (0, 1) and moves counterclockwise. The period of sin(t) and cos(t) is 2π, so for 0 < t < 4π, the particle makes 2 revolutions.
C (x, y) = (cos(4πt), sin(4πt))
At t = 0, (x, y) = (1, 0).
At t = 1/8, (x, y) = (0, 1).
So the particle starts at (1, 0) and moves counterclockwise. The period of sin(4πt) and cos(4πt) is 1/2, so for 0 < t < 1, the particle makes 2 revolutions.
D (x, y) = (cos(2πt), -sin(2πt))
At t = 0, (x, y) = (1, 0).
At t = 1/4, (x, y) = (0, -1).
So the particle starts at (1, 0) and moves clockwise. The period of sin(2πt) and cos(2πt) is 1, so for 0 < t < 1, the particle makes 1 revolution.
