It is not as obvious how to determine the rotational operator compared to space and time translations. We may consider a special case (rotations about the x, y, or z -axis) then infer the general result, or use the general rotation matrix directly and tensor index notation with δ ij and ε ijk. To derive the infinitesimal rotation operator, which corresponds to small Δ θ, we use the small angle approximations sin(Δ θ) ≈ Δ θ and cos(Δ θ) ≈ 1, then Taylor expand about r or r i, keep the first order term, and substitute the angular momentum operator components.