So lets say we were trying to compute a circle on a graph screen(like matlab), why would it be more convenient to compute this IVP instead rather than directly using trigonometric equations?
So my question is why abide from solving $x=r\cos(\theta)$ and $y=r\sin(\theta)$ point by point using some iteration scheme and rather solve this system of ODE's numerically with initial values $\begin{equation}\begin{cases}\dot{x}=-y,&& x(0)=r\\ \dot{y}=x, && y(0)=0\end{cases}\end{equation}$ by forward euler method, backward euler method, or trapezoidal method?