Answer
Radius: $r=4$
$t=0$:
Initial point: $(4,0)$
Orientation: counterclockwise.
One revolution:
$t=\frac{2\pi}{3}$
Work Step by Step
$x=4~cos~3t$
$y=4~sin~3t$
$x^2+y^2=16~cos^23t+16~sin^23t$
$x^2+y^2=16(cos^23t+sin^23t)$
$x^2+y^2=16$
$x^2+y^2=4^2$
Radius: $r=4$
$t=0$:
$x=4~cos~0=4$
$y=4~sin~0=0$
Initial point: $(4,0)$
$t=\frac{\pi}{6}$:
$x=4~cos~\frac{\pi}{2}=0$
$y=4~sin~\frac{\pi}{2}=4$
Point: $(0,4)$
Orientation: counterclockwise.
One revolution:
$3t=2\pi$
$t=\frac{2\pi}{3}$
It is the first value of $t\gt0$ such that $x=4$ and $y=0$ (Starting position)
