Hi, given the ellipse in the xy plane I have to sketch the x(t) & y(t) graphs for the solution. I have included a photo of the problem from the textbook (its problem # 24, the ellipse) as well as my attempt at a solution.
Let $a$ be the radius of the ellipse along the x-axis and $b$ be the radius along the y-axis. Let $(h,k)$ be the center of the ellipse. Then the parametrization of the ellipse is:
$x = h + a\cos t$
$y = k + b\sin t$
Your ellipse has $a=2, b=1, h=2, k=1$
So, $x(t) = 2(1+\cos t)$, $y(t) = 1+\sin t$
Hence, your graph for $x(t)$ looks correct, but your graph of $y(t)$ is not. Reflect $y(t)$ over the line $y=1$ and it will be what you drew.
Thank you very much, I really appreciate it. I was wondering, do I need to label the t axis with values, or are they unknown? At first I put that each complete wavelength took 2pi but for some reason I wasn't sure if there was enough info to determine the time it takes to complete each wavelength