The formula for inductive reactance is X_{L}=2πfL

I understand why the inductive reactance increases as the inductance and frequency increase but I am not sure why "2π" is included in the formula. I suspect that π must represent the average rate of change of the amplitude of the sine wave. By calculating the average by using four values of sine, I get 4.2 units of amplitude per second but if I use eight values of sine, I get 3.6 units of amplitude per second. My guess is that were I to use ninety values of sine, the average would be very close to the numerical value of π. I assume that "2" is in the formula because the peak amplitude occurs twice in each cycle.

My question is: What is the average rate of change of the amplitude of a sine wave?