Can someone explain the parametrization of this circle

Question

Question:

Parametrise the circle $(x-2)^2 + (y-3)^2 = 4$ with radius $2$ centered at $(2,3)$, such that the imaginary particle tracing this circle is travelling in the clockwise direction and at time $t=0$ is at $(0,3)$

My lecturer wrote down:

$x = 2 + 2 \cos(-2 t + \pi)$

$y = 3 + 2 \sin(-2 t + \pi)$

I don't understand how she got the $-2t$ within $\cos$ and $\sin$, I understand the negative sign (clockwise) but not the $2$ (within the trig).

Answer 1

You are right to wonder. The $2$ is arbitrary. That constant adjusts the speed of the particle. There is nothing in the problem statement that leads to that value. It's correct, but so would any other constant.