When we consider a power series expansion of a special function such as \begin{equation} \sin z = z -\frac{1}{3!} z^3 + \frac{1}{5!} z^5 + \dots \end{equation} we can notice an interesting fact. If the variable $z$ were to have any kind dimensions (e.g. length, $L$) then the power series expansion of that special function would add together terms with different dimensions ($L$, $L^3$, $L^5$, etc.). Since this is impossible, it implies that the argument of such special functions must always be dimensionless. This fact provides a quick check in many long algebraic manipulations. (The one exception to this rule is the logarithm function. Why?)