Answer
$x = 3~sin~4t$
$y = 3~cos~3t$
$0 \leq t \leq 6.5$
We can see the graph in the window $[-6,6]$ by $[-4,4]$
Work Step by Step
$x = 3~sin~4t$
$y = 3~cos~3t$
$0 \leq t \leq 6.5$
When $t = 0$:
$x = 3~sin~0 = 0$
$y = 3~cos~0 = 3$
When $t = \frac{\pi}{12}$:
$x = 3~sin~\frac{4\pi}{12} = 2.6$
$y = 3~cos~\frac{3\pi}{12} = 2.12$
When $t = \frac{\pi}{6}$:
$x = 3~sin~\frac{4\pi}{6} = 2.6$
$y = 3~cos~\frac{3\pi}{6} = 0$
When $t = \frac{\pi}{4}$:
$x = 3~sin~\frac{4\pi}{4} = 0$
$y = 3~cos~\frac{3\pi}{4} = -2.12$
When $t = \frac{\pi}{3}$:
$x = 3~sin~\frac{4\pi}{3} = -2.6$
$y = 3~cos~\frac{3\pi}{3} = -3$
When $t = \frac{\pi}{2}$:
$x = 3~sin~\frac{4\pi}{2} = 0$
$y = 3~cos~\frac{3\pi}{2} = 0$
When $t = \frac{2\pi}{3}$:
$x = 3~sin~\frac{8\pi}{3} = 2.6$
$y = 3~cos~\frac{6\pi}{3} = 3$
When $t = \frac{3\pi}{4}$:
$x = 3~sin~\frac{12\pi}{4} = 0$
$y = 3~cos~\frac{9\pi}{4} = 2.12$
When $t = \frac{5\pi}{6}$:
$x = 3~sin~\frac{20\pi}{6} = -2.6$
$y = 3~cos~\frac{15\pi}{6} = 0$
When $t = \pi$:
$x = 3~sin~4\pi = 0$
$y = 3~cos~3\pi = -3$
When $t = \frac{7\pi}{6}$:
$x = 3~sin~\frac{28\pi}{6} = 2.6$
$y = 3~cos~\frac{21\pi}{6} = 0$
When $t = \frac{5\pi}{4}$:
$x = 3~sin~\frac{20\pi}{4} = 0$
$y = 3~cos~\frac{15\pi}{4} = 2.12$
When $t = \frac{7\pi}{3}$:
$x = 3~sin~\frac{28\pi}{3} = -2.6$
$y = 3~cos~\frac{21\pi}{3} = -3$
When $t = \frac{3\pi}{2}$:
$x = 3~sin~\frac{12\pi}{2} = 0$
$y = 3~cos~\frac{9\pi}{2} = 0$
When $t = \frac{7\pi}{4}$:
$x = 3~sin~\frac{28\pi}{4} = 0$
$y = 3~cos~\frac{21\pi}{4} = -2.12$
When $t = 2\pi$:
$x = 3~sin~8\pi = 0$
$y = 3~cos~6\pi = 3$
When $t = 6.5$:
$x = 3~sin~26 = 2.29$
$y = 3~cos~19.5 = 2.39$
We can see the graph in the window $[-6,6]$ by $[-4,4]$
