Answer
$x = 4~sin~4t$
$y = 3~sin~5t$
$0 \leq t \leq 6.5$
We can see the graph in the window $[-6,6]$ by $[-4,4]$
Work Step by Step
$x = 4~sin~4t$
$y = 3~sin~5t$
$0 \leq t \leq 6.5$
When $t = 0$:
$x = 4~sin~0 = 0$
$y = 3~sin~0 = 0$
When $t = \frac{\pi}{12}$:
$x = 4~sin~\frac{4\pi}{12} = 3.46$
$y = 3~sin~\frac{5\pi}{12} = 2.90$
When $t = \frac{\pi}{6}$:
$x = 4~sin~\frac{4\pi}{6} = 3.46$
$y = 3~sin~\frac{5\pi}{6} = 1.5$
When $t = \frac{\pi}{5}$:
$x = 4~sin~\frac{4\pi}{5} = 2.35$
$y = 3~sin~\frac{5\pi}{5} = 0$
When $t = \frac{\pi}{4}$:
$x = 4~sin~\frac{4\pi}{4} = 0$
$y = 3~sin~\frac{5\pi}{4} = -2.12$
When $t = \frac{\pi}{3}$:
$x = 4~sin~\frac{4\pi}{3} = - 3.46$
$y = 3~sin~\frac{5\pi}{3} = -2.60$
When $t = \frac{2\pi}{5}$:
$x = 4~sin~\frac{8\pi}{5} = -3.8$
$y = 3~sin~\frac{10\pi}{5} = 0$
When $t = \frac{\pi}{2}$:
$x = 4~sin~\frac{4\pi}{2} = 0$
$y = 3~sin~\frac{5\pi}{2} = 3$
When $t = \frac{2\pi}{3}$:
$x = 4~sin~\frac{8\pi}{3} = 3.46$
$y = 3~sin~\frac{10\pi}{3} = -2.6$
When $t = \frac{3\pi}{4}$:
$x = 4~sin~\frac{12\pi}{4} = 0$
$y = 3~sin~\frac{15\pi}{4} = -2.12$
When $t = \frac{4\pi}{5}$:
$x = 4~sin~\frac{16\pi}{5} = -2.35$
$y = 3~sin~\frac{20\pi}{5} = 0$
When $t = \frac{5\pi}{6}$:
$x = 4~sin~\frac{20\pi}{6} = - 3.46$
$y = 3~sin~\frac{25\pi}{6} = 1.5$
When $t = \pi$:
$x = 4~sin~4\pi = 0$
$y = 3~sin~5\pi = 0$
When $t = \frac{7\pi}{6}$:
$x = 4~sin~\frac{28\pi}{6} = 3.46$
$y = 3~sin~\frac{35\pi}{6} = -1.5$
When $t = \frac{5\pi}{4}$:
$x = 4~sin~\frac{20\pi}{4} = 0$
$y = 3~sin~\frac{25\pi}{4} = 2.12$
When $t = \frac{7\pi}{3}$:
$x = 4~sin~\frac{28\pi}{3} = - 3.46$
$y = 3~sin~\frac{35\pi}{3} = 2.60$
When $t = \frac{3\pi}{2}$:
$x = 4~sin~\frac{12\pi}{2} = 0$
$y = 3~sin~\frac{15\pi}{2} = -3$
When $t = \frac{7\pi}{4}$:
$x = 4~sin~\frac{28\pi}{4} = 0$
$y = 3~sin~\frac{35\pi}{4} = 2.12$
When $t = 2\pi$:
$x = 4~sin~8\pi = 0$
$y = 3~sin~10\pi = 0$
When $t = 6.5$:
$x = 4~sin~26 = 3.05$
$y = 3~sin~32.5 = 2.65$
We can see the graph in the window $[-6,6]$ by $[-4,4]$
