True, but you are now setting up a false dilemma. The point is not that arbitrary units are hard, nor that any 2 are relatively harder. It is that a consistent unit that is not arbitrary is easier than the arbitrary ones, and usually involves quite a few useful "symetries" (by which I don't mean real symetries, but conceptual linkages).
As for why people think degrees is easier: it is simply because common usage of degrees makes the concept familiar to learners. I totally agree that teaching trig in terms of radians first would be much better.
Comments
True, but you are now setting up a false dilemma. The point is not that arbitrary units are hard, nor that any 2 are relatively harder. It is that a consistent unit that is not arbitrary is easier than the arbitrary ones, and usually involves quite a few useful "symetries" (by which I don't mean real symetries, but conceptual linkages).
As for why people think degrees is easier: it is simply because common usage of degrees makes the concept familiar to learners. I totally agree that teaching trig in terms of radians first would be much better.