A turn doesn't have to represent an angle. It can also be a "cycle" in the oscillation. I studied engineering, and pretty much everywhere where we needed the r

A turn doesn't have to represent an angle. It can also be a "cycle" in the oscillation. I studied engineering, and pretty much everywhere where we needed the radian form with Pi, the mental reasoning was "one cycle, or repetition, or loop ot whatever is Pi". Never did Pi have any deeper meaning that helped understand the logic of the problem.