If curve is parametrized using $x=r\cos(t), y=r\sin(t)$, then is the entire curve graphed by reading through $0 \le t \lt 2 \pi$?

Question

If curve is parametrized using $x=r\cos(t), y=r\sin(t)$, then is the entire curve graphed by reading through $0 \le t \lt 2 \pi$? Particularly, when no other details about $t$'s range have been given. $r$ is fixed.

This sounds intuitive, but just to make sure I'm not missing something.

Answer 1

You are missing nothing.

$\{(r \cos t,r \sin t):t \in [0, 2 \pi]\}=\{(x,y) \in \mathbb R^2: x^2+y^2=r^2\}$.