Answer
$x = 2~cos~t$
$y = 3~sin~2t$
$0 \leq t \leq 6.5$
We can see the graph in the window $[-6,6]$ by $[-4,4]$
Work Step by Step
$x = 2~cos~t$
$y = 3~sin~2t$
$0 \leq t \leq 6.5$
When $t = 0$:
$x = 2~cos~0 = 2$
$y = 3~sin~[2(0)] = 0$
When $t = \frac{\pi}{4}$:
$x = 2~cos~\frac{\pi}{4} = 1.41$
$y = 3~sin~[2(\frac{\pi}{4})] = 3$
When $t = \frac{\pi}{3}$:
$x = 2~cos~\frac{\pi}{3} = 1$
$y = 3~sin~[2(\frac{\pi}{3})] = 2.6$
When $t = \frac{\pi}{2}$:
$x = 2~cos~\frac{\pi}{2} = 0$
$y = 3~sin~[2(\frac{\pi}{2})] = 0$
When $t = \frac{2\pi}{3}$:
$x = 2~cos~\frac{2\pi}{3} = -1$
$y = 3~sin~[2(\frac{2\pi}{3})] = -2.6$
When $t = \frac{3\pi}{4}$:
$x = 2~cos~\frac{3\pi}{4} = -1.41$
$y = 3~sin~[2(\frac{3\pi}{4})] = -3$
When $t = \pi$:
$x = 2~cos~\pi = 2$
$y = 3~sin~(2\pi) = 0$
When $t = \frac{5\pi}{4}$:
$x = 2~cos~\frac{5\pi}{4} = -1.41$
$y = 3~sin~[2(\frac{5\pi}{4})] = 3$
When $t = \frac{3\pi}{2}$:
$x = 2~cos~\frac{3\pi}{2} = 0$
$y = 3~sin~[2(\frac{3\pi}{2})] = 0$
When $t = \frac{7\pi}{4}$:
$x = 2~cos~\frac{7\pi}{4} = 1.41$
$y = 3~sin~[2(\frac{7\pi}{4})] = -3$
When $t = 2\pi$:
$x = 2~cos~2\pi = 2$
$y = 3~sin~(4\pi) = 0$
When $t = 6.5$:
$x = 2~cos~6.5 = 1.95$
$y = 3~sin~13 = 1.26$
We can see the graph in the window $[-6,6]$ by $[-4,4]$
