Answer
$x = t+cos~t$
$y = sin~t$
$t$ in $[0,2\pi]$
We can see the graph below:
Work Step by Step
$x = t+cos~t$
$y = sin~t$
$t$ in $[0,2\pi]$
When $t = 0$:
$x = 0 + cos~0 = 1$
$y = sin~0 = 0$
When $t = \frac{\pi}{4}$:
$x = \frac{\pi}{4} + cos~\frac{\pi}{4} = \frac{\pi}{4} + \frac{\sqrt{2}}{2} = 1.49$
$y = sin~\frac{\pi}{4} = \frac{\sqrt{2}}{2} = 0.707$
When $t = \frac{\pi}{2}$:
$x = \frac{\pi}{2} + cos~\frac{\pi}{2} = \frac{\pi}{2}+0 = 1.57$
$y = sin~\frac{\pi}{2} = 1$
When $t = \frac{3\pi}{4}$:
$x = \frac{3\pi}{4} + cos~\frac{3\pi}{4} = \frac{3\pi}{4} -\frac{\sqrt{2}}{2} = 1.65$
$y = sin~\frac{3\pi}{4} = \frac{\sqrt{2}}{2} = 0.707$
When $t = \pi$:
$x = \pi + cos~\pi = \pi-1 = 2.14$
$y = sin~\pi = 0$
When $t = \frac{5\pi}{4}$:
$x = \frac{5\pi}{4} + cos~\frac{5\pi}{4} = \frac{5\pi}{4} -\frac{\sqrt{2}}{2} = 3.22$
$y = sin~\frac{5\pi}{4} = -\frac{\sqrt{2}}{2} = -0.707$
When $t = \frac{3\pi}{2}$:
$x = \frac{3\pi}{2} + cos~\frac{3\pi}{2} = \frac{3\pi}{2}+0 = 4.71$
$y = sin~\frac{3\pi}{2} = -1$
When $t = \frac{7\pi}{4}$:
$x = \frac{7\pi}{4} + cos~\frac{7\pi}{4} = \frac{7\pi}{4} +\frac{\sqrt{2}}{2} = 6.20$
$y = sin~\frac{7\pi}{4} = -\frac{\sqrt{2}}{2} = -0.707$
When $t = 2\pi$:
$x = 2\pi + cos~2\pi = 2\pi+1 = 7.28$
$y = sin~0 = 0$
We can see the graph below:
