Unit vectors for similar oblate spheroidal coordinates and vector transformation

The unit vectors transformation between the Cartesian and the novel similar oblate spheroidal coordinates, and vice versa, is derived. It facilitates transformation of vector fields between these two types of orthogonal coordinates and can advantageously simplify solutions of problems exhibiting oblate spheroidal geometry. Several examples demonstrate the use of the derived relations. Generalized sine and cosine applicable in the similar oblate spheroidal coordinate system are introduced as well.