# Math Help - Parametric Equations

1. ## Parametric Equations

I need to find the point were the curve crosses itself:

$x=2-\pi \cos(t)$
$y=2t-\pi \sin(t)$

This is really tricky; I can't think of any method to use to solve this (other than plotting points).

I need to find the point were the curve crosses itself:

$x=2-\pi \cos(t)$
$y=2t-\pi \sin(t)$

This is really tricky; I can't think of any method to use to solve this (other than plotting points).
You need to find the parameter values s, t, that satisfy

$2-\pi \cos t=2-\pi \cos s$ and $2t-\pi\sin t=2s-\pi \sin s$

from the first equation you get that $\cos t=\cos s$, hence $s=\pm t+n\cdot 2\pi$.

Now plug that value of s into the second equation and hope for the best...