1- Suppose that the position of one particle at time t is given by

x₁ = 2sin(t),y₁ = 2cos(t),0 t 2

and the position of a second particle is given by

x₂ = 2 + cos(t),y₂ = 1 + sin(t),0 t 2.

a. How many points of intersection are there?

=??? points of intersection

b. Are any of these points of intersection collision points? In other words, are the particles ever at the same place at the same time?

Yes

If so, find the collision points. (Enter your answers as a comma-separated list of ordered pairs. If an answer does not exist, enter DNE.)

=???

2- Find parametric equations for the path of a particle that moves along the circle x² + (y 3)² = 16

in the manner described. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.)

(a) Once around clockwise, starting at (4, 3). 0 t 2.

=???

(b) Four times around counterclockwise, starting at (4, 3). 0 t 8.

=???

(c) Halfway around counterclockwise, starting at (0, 7). 0 t .

=????