Find the parametric equations

Question

Find parametric equations for the position of a particle moving along a circle as described. (Enter your answers as comma-separated lists of equations. Use t as the parameter.) The particle travels clockwise around a circle centered at the origin with radius 8 and completes a revolution in 8𝜋 seconds. (Assume the particle starts at (0, 8) at t = 0.)

Answer 1

ω = 2π/P = 2π/8π = 1/4

Since the particle starts at (0, 8) and moves clockwise, then the position of the particle is

(8 sin t/4, 8 cos t/4)

You could write this as (8 cos(-t/4+π/2), 8 sin(-t/4+π/2) to show the fact that the particle starts at (0, 8) and moves clockwise - the negative reflects the clockwise movement - expansion of this gives you the result above; alternatively, if you think of how the sin and cos functions behave, the result above jumps out at you.