Question

find a parametrization of the circle of radius 6 in the xy - plane, centered at the origin, oriented counterclockwise. the point (6,0) should correspond to t = 0. use t as the parameter for all of your answers.
x(t) =
y(t) =
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Explanation:

Step1: Recall circle - parametric form

The general parametric equations for a circle of radius $r$ centered at the origin with counter - clockwise orientation are $x(t)=r\cos(t)$ and $y(t)=r\sin(t)$.

Step2: Substitute the radius value

Given $r = 6$, we substitute $r$ into the parametric equations. So $x(t)=6\cos(t)$ and $y(t)=6\sin(t)$. When $t = 0$, $x(0)=6\cos(0)=6$ and $y(0)=6\sin(0)=0$, which satisfies the given condition.

Answer:

$x(t)=6\cos(t)$
$y(t)=6\sin(t)$