What is the correct derivation for the Rotation Matrix?

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This might seem like a basic question, but I've been stuck on this for a bit.

Upon looking at many different sources, I found 2 derivations of the rotation matrix.

  1. One of them considers a point at a distance of r from the origin and rotates it by a certain angle theta and derives the matrix by comparing the projections of the original point and the new, rotated point.
  2. The other one considers coordinate axes of unit length which are rotated by a certain angle theta and derives the rotation matrix by projecting the new x and y axes onto the original ones.

Which one of them is the correct derivation? What significance does each method have?