I need to find out if these vector functions meet eachother at some point, where they share the same t value. And if they do, i need the x/y values of where they meet.
Any help is greatly appreciated!
The t variables can be set as one wishes, tm and tr that is.
The system of equations $$\begin{split} 2t&= 2\cos t \\ \frac{6}{t+4}&=2\sin t \end{split}$$ has no solutions. Indeed, by squaring the equations and adding them, we see that a solution would satisfy $$t^2+\frac{9}{(t+4)^2}=1\tag{1}$$ which is an algebraic equation. On the other hand, $t=\cos t$ is transcendental equation; its only root is not an algebraic number.
Okay, I don't actually know a proof of the preceding claim, but it's easy enough to check that neither of two real roots of (1) satisfies $\cos t=t$. One of them is $\approx -0.51$, which obviously fails. The other, $\approx 0.78$, comes close, but its cosine is about $0.71$.