Personally, that again sounds like a very pedantic and obvious point to me. However, I could be wrong so feel free to break down your point further.
My interpretation is that I think you guys are missing the fact that the intent of my original comment is in the context approximations, from which you can see the use of the 'trick' is correct.
To break it down a little further: the trick I am referring to is in practice it's often convenient to scale approximations so that you can use the unit circle for calculations, since you can use the radians as a measurement of arc length. If it's not a unit circle, the angle != arc length, so that convenience is lost.
> Just because it's easy to derive doesn't mean it's immediately obvious
is what I was responding to. My point is this -- there is no derivation happening there. If it was pedantic, obvious and simple to you as you claim, I wonder why you claimed that it was a derivation.
To you the distinction between a definition and a derivation might be a pedantic one, I have doubts on whether that is an universal or even an useful position to have.
