Question

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

Explanation:

Step1: Recall standard circle parametrization

The standard counter - clockwise parametrization of a circle of radius $r$ centered at the origin is $x = r\cos t$ and $y = r\sin t$. For a clockwise orientation, we change the sign of the parameter in the trigonometric functions. Here $r = 6$.

Step2: Determine $x(t)$

Since the circle is clockwise and centered at the origin with radius $r = 6$, when $t = 0$ we want to start at $(0,6)$. Using the clock - wise parametrization, $x(t)=6\sin t$.

Step3: Determine $y(t)$

For the same circle, $y(t)=6\cos t$.

Answer:

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