Let the path $c(t): \mathbb{R}\rightarrow \mathbb{R}^2$ be defined by $c(t)=(\sin(t)+2, 1/(\sin(t)+2))$
How can I find the location of the path at $t=n\pi$ where $n$ is any integer?
I plugged $\pi$ into $c(t)$ and I got $(0,1/2)$ for all $n$ but $(0,1/2)$ doesn't lie on the curve. I'm not sure what else to do.
Community wiki answer so the question can be marked as answered:
As remarked in a comment, substituting $t=n\pi$ yields $2$ in the first coordinate, not $0$.