Yes, trigonometry should be avoided whenever possible (which is much more than people often expect) in favor of vector methods in pretty much every context. If

Yes, trigonometry should be avoided whenever possible (which is much more than people often expect) in favor of vector methods in pretty much every context. If someone wants a single number for representing a rotation, consider using the stereographic projection (instead of angle measure), which takes only 1 division to go back and forth to cartesian coordinates. Floating point is fine for modern hardware though.