I have the following system:

$$ \begin{aligned} \dot x &= -y \\ \dot y &= x \end{aligned} $$

Given that $(x\_i^n,y\_i^n)$ are the points obtained for $i=1,2\dots n^2$ using a time-step $h=1/n$ starting at the initial point $(x\_0,y\_0)=(1,0)$.  

I am struggling to find the following limit:
$$\lim\limits\_{n \to \infty} (x\_n^n,y\_n^n)$$
I can intutively think of the above limit ending up somewhere on the unit circle but I am unable to obtain the value of the exact limit. Pardon if its too simple, but I am surely missing out something. Please help out, thanks in advance.