[doubleunplussed]

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.

[omrjml]

Of course sine can appear in the solution for dynamical systems but the function itself is not dynamical. When evaluating sin(x) you do not need to know about the previous state.

[zmgsabst]

That is true, the problem is with the conclusion you drew from that fact:

> 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.

[freemint]

sin(x) only arises as solution in second order systems. So d^2x/dt^2 = -x

[doubleunplussed]

Sorry, you're absolutely correct. Brain fart. The equation I wrote actually is for an exponential, whoops.