Find parametric equations for the path of a particle that moves along the circle described by $x^2 + (y - 1)^2 = 9$ 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 $(3, 1)$. $0 \le t \le 2\pi$.
$x = 3 + 3\cos(t), y = 1 - 3\sin(t)$
(b) Three times around counterclockwise, starting at $(3, 1)$. $0 \le t \le 6\pi$.
$x = 3 + 3\cos(2t), y = 1 + 3\sin(2t)$
(c) Halfway around counterclockwise, starting at $(0, 4)$. $0 \le t \le \pi$.
$x = -3\sin(t), y = 4 - 3\cos(t)$
Enhanced Feedback
Please try again, keeping in mind that the parametric equations for a circle centered at $(h, k)$ are $x = h + r\cos(t)$ and $y = k + r\sin(t)$ when $0 \le t \le 2\pi$.
