To achieve the formula that rotates a point theta degrees around an arbitrary rotation axis, We take arbitrary pointon the rotation axis(we know that it's a fixed point), Now being the function that rotates the pointctheta degrees around the rotation axis, we can find a linear transformation such that , Soxbeing the corresponding transformation matrix for we haveAThis also proves that rotation is an affine transformation(a linear transformation followed by a translation) , and BTW similar approach can be used to achieve formulas for other affine transformations that have a fixed point(like shear, reflection and scaling)