Parameterization of the circle

Question

Is $x = r\cos θ$, $y = -r\sin θ$ a good parameterization of the circle $x^2+y^2=r^2$? I know that parameterization $x = r\cosθ$, $y = r\sinθ$ is common but I'm wondering if this is okay too.

Answer 1

Yes, you can always check your if your parameterization is correct by inserting it in the circle equation, so $x^2+y^2$ should be equal to $r^2$, so if we substitute $x$ and $y$, we get $r^2\cos ^2\theta +r^2\sin ^2\theta =r^2(\cos ^2\theta +\sin ^2\theta )=r^2$, which is equal to $r^2$.

Note that there isn't a unique parameterization.

Answer 2

Sure you're just going clockwise instead of counter-clockwise. Beware this may introduce a minus sign in some formulas you're using though