Answer
$x = 3~cos~2t$
$y = 3~sin~3t$
$0 \leq t \leq 6.5$
We can see the graph in the window $[-6,6]$ by $[-4,4]$
Work Step by Step
$x = 3~cos~2t$
$y = 3~sin~3t$
$0 \leq t \leq 6.5$
When $t = 0$:
$x = 3~cos~0 = 3$
$y = 3~sin~0 = 0$
When $t = \frac{\pi}{12}$:
$x = 3~cos~\frac{2\pi}{12} = 2.6$
$y = 3~sin~\frac{3\pi}{12} = 2.12$
When $t = \frac{\pi}{6}$:
$x = 3~cos~\frac{2\pi}{6} = 1.5$
$y = 3~sin~\frac{3\pi}{6} = 3$
When $t = \frac{\pi}{4}$:
$x = 3~cos~\frac{2\pi}{4} = 0$
$y = 3~sin~\frac{3\pi}{4} = 2.12$
When $t = \frac{\pi}{3}$:
$x = 3~cos~\frac{2\pi}{3} = -1.5$
$y = 3~sin~\frac{3\pi}{3} = 0$
When $t = \frac{\pi}{2}$:
$x = 3~cos~\frac{2\pi}{2} = -3$
$y = 3~sin~\frac{3\pi}{2} = -3$
When $t = \frac{2\pi}{3}$:
$x = 3~cos~\frac{4\pi}{3} = -1.5$
$y = 3~sin~\frac{6\pi}{3} = 0$
When $t = \frac{3\pi}{4}$:
$x = 3~cos~\frac{6\pi}{4} = 0$
$y = 3~sin~\frac{9\pi}{4} = 2.12$
When $t = \pi$:
$x = 3~cos~2\pi = 3$
$y = 3~sin~3\pi = 0$
When $t = \frac{7\pi}{6}$:
$x = 3~cos~\frac{14\pi}{6} = 1.5$
$y = 3~sin~\frac{21\pi}{6} = -3$
When $t = \frac{5\pi}{4}$:
$x = 3~cos~\frac{10\pi}{4} = 0$
$y = 3~sin~\frac{15\pi}{4} = -2.12$
When $t = \frac{7\pi}{3}$:
$x = 3~cos~\frac{14\pi}{3} = -1.5$
$y = 3~sin~\frac{21\pi}{3} = 0$
When $t = \frac{3\pi}{2}$:
$x = 3~cos~\frac{6\pi}{2} = -3$
$y = 3~sin~\frac{9\pi}{2} = 3$
When $t = \frac{7\pi}{4}$:
$x = 3~cos~\frac{14\pi}{4} = 0$
$y = 3~sin~\frac{21\pi}{4} = -2.12$
When $t = 2\pi$:
$x = 3~cos~4\pi = 3$
$y = 3~sin~6\pi = 0$
When $t = 6.5$:
$x = 3~cos~13 = 2.72$
$y = 3~sin~19.5 = 1.82$
We can see the graph in the window $[-6,6]$ by $[-4,4]$
