How to define sawtooth function in lua?

Question

Trigonometry

There is a code in lua and there are variables Y and T in it, T - time, increases every tick when it reaches a certain threshold - resets to 0, I need a line like Y = a+(b*math.sin( T*c+ d)), only that when connected to a conditional oscilloscope, a sawtooth graph is drawn

Answer 1

depending on how it will be applied, this can also be done
through the Fourier series:

and simply:
x(t) = t - math.floor(t)