Can vector algebra completely replace trigonometry?

Question

Mathematics

Can vector algebra completely replace trigonometry?

Answer 1

I will put it differently: in those places where angles are not explicitly needed, trigonometry is most likely redundant, and indeed the question can very often be solved using vector algebra. In most tasks of game development and 3D graphics, this is exactly the case.
Well, I will be so categorical as to say "completely." There was somehow a task: there is an articulated quadrilateral, a spring is stretched diagonally. Can this design (as a first approximation) imitate the clutch pedal of a car? And then even the Logitech G27 clutch pedal is not too convincing. I solved it numerically and with trigonometry, although you can try it analytically and with vector algebra.
PS. The main arguments against are simplicity and the accumulation of errors. But accumulation can sometimes be bypassed without resorting to trigonometry - for example, using quaternions instead of rotation matrices in 3D or normalizing a vector in 2D.

Answer 2

How?

Answer 3

Be more specific, what do you want to achieve?