That is important... I think it can be derived by using the "series expansions" for each one, taking angle as "x" in radians for a unit circle:One thing I did find out that is interesting about this issue is that at the limit as the angle m approaches 0, the difference between the length of the tangent and the length of the arc approaches 8 times the difference between the length of the arc and the length of the chord.

Limit = (tan(x)-x)/(x-2sin(x/2)) = 8 + 3.3x

^{2}+ ...

Yeah, Miles' analysis is flawed there, I did try to explain that to him. Which is why I had to get into a re-derivation of circular motion.