On the subject of annoying ambiguities in mathematical notations, I would like to point out the ridiculous convention of inverse function notation. Is there an

On the subject of annoying ambiguities in mathematical notations, I would like to point out the ridiculous convention of inverse function notation. Is there any sensible rationale for sin^(-1)(x) meaning arcsin(x) while sin^2(x) means (sin(x))^2?