[Math] Find a parameterization for the circle of radius 2 in the xy-plane, centered at the origin, clockwise

Question

Find a parameterization for the circle of radius $2$ in the $xy$-plane, centered at the origin, clockwise.

I know to use $2\cos(t)$ and $-2\sin(t)$ but I'm not sure what to do after that

Answer 1

You're basically done! Setting

$x(t) = 2\cos t, \tag{1}$

and

$y(t) = -2\sin t, \tag{2}$

note that

$x^2(t) + y^2(t) = 4 \cos^2 t + 4 \sin^2 t = 4(\cos^2 t + \sin^2 t) = 4, \tag{3}$

which shows that (1)-(2) describe a circle of radius $2$ centeted at $(0, 0)$. Note also that, starting at $t = 0$ and increasing $t$, the point $(x(t), y(t))$ rotates about $(0, 0)$ in a clockwise direction; thus (1), (2) meet the specifications for your circle, parametrized by $t$.

Hope this helps. Cheerio,

and as always,

Fiat Lux!!!