Periodic functions like sin(x) are the solutions to differential equations like dy/dx = -y that describe for example, oscillations of springs, to name but one of an extremely large number of dynamical systems that behave this way.
> So it should not be approximated in that way.
We can’t conclude a dynamic approximation is a bad approach based purely on the fact the underlying function isn’t dynamic.
The function might nevertheless be easily approximated via dynamics — as in the case of predicting sine from seeing the recent history.