True, however that doesn't mean x represents an angle. It means you can put a geometric interpretation on an abstract formula. e^ix = cos x + i sin x regardle

True, however that doesn't mean x represents an angle. It means you can put a geometric interpretation on an abstract formula. e^ix = cos x + i sin x regardless of what x represents - if you were doing electrical engineering it might be time, for example. Interpretation is often strongly motivated by what "comes first" in the order in which you learn things, so the whole debate is a bit subjective anyway. Another common example: at school we learn the integral is the area under the curve. At university we learn the area under the curve is the integral. The integral is the "real" thing and the area is just a convenient geometric interpretation, which actually makes no sense for many (most?) integrals. At school we learn it "backwards" purely because it's easier that way, and visual aids are helpful. I think something similar applies to sin and cos.