## Trigonometry (11th Edition) Clone

$x = 2t-2~sin~t$ $y = 2-2~cos~t$ $0 \leq t \leq 4\pi$ We can see the graph below.
$x = 2t-2~sin~t$ $y = 2-2~cos~t$ $0 \leq t \leq 4\pi$ When $t = 0$: $x = 2(0)-2~sin~0 = 0$ $y = 2-2~cos~0 = 0$ When $t = \frac{\pi}{6}$: $x = 2(\frac{\pi}{6})-2~sin~\frac{\pi}{6} = 0.047$ $y = 2-2~cos~\frac{\pi}{6} = 0.268$ When $t = \frac{\pi}{4}$: $x = 2(\frac{\pi}{4})-2~sin~\frac{\pi}{4} = 0.157$ $y = 2-2~cos~\frac{\pi}{4} = 0.586$ When $t = \frac{\pi}{3}$: $x = 2(\frac{\pi}{3})-2~sin~\frac{\pi}{3} = 0.362$ $y = 2-2~cos~\frac{\pi}{3} = 1$ When $t = \frac{\pi}{2}$: $x = 2(\frac{\pi}{2})-2~sin~\frac{\pi}{2} = 1.14$ $y = 2-2~cos~\frac{\pi}{2} = 2$ When $t = \frac{2\pi}{3}$: $x = 2(\frac{2\pi}{3})-2~sin~\frac{2\pi}{3} = 2.46$ $y = 2-2~cos~\frac{2\pi}{3} = 3$ When $t = \pi$: $x = 2(\pi)-2~sin~\pi = 6.28$ $y = 2-2~cos~\pi = 4$ When $t = \frac{4\pi}{3}$: $x = 2(\frac{4\pi}{3})-2~sin~\frac{4\pi}{3} = 10.110$ $y = 2-2~cos~\frac{4\pi}{3} = 3$ When $t = \frac{3\pi}{2}$: $x = 2(\frac{3\pi}{2})-2~sin~\frac{3\pi}{2} = 11.425$ $y = 2-2~cos~\frac{3\pi}{2} = 2$ When $t = 2\pi$: $x = 2(2\pi)-2~sin~2\pi = 12.566$ $y = 2-2~cos~2\pi = 0$ When $t = 3\pi$: $x = 2(3\pi)-2~sin~3\pi = 18.850$ $y = 2-2~cos~3\pi = 4$ When $t = 4\pi$: $x = 2(4\pi)-2~sin~4\pi = 25.133$ $y = 2-2~cos~4\pi = 0$ We can see the graph below.