These are highly useful properties in some contexts. That said, cos(0) being the unit prior to any rotation is also nice. (But the definition of a rotation in Cartesian coordinates contains exactly as many sines as cosines; and that generalizes to 3 dimensions where complex numbers do not.)
I’d like to put in a word for sine:
These are highly useful properties in some contexts. That said, cos(0) being the unit prior to any rotation is also nice. (But the definition of a rotation in Cartesian coordinates contains exactly as many sines as cosines; and that generalizes to 3 dimensions where complex numbers do not.)