Where f is a function, does $f ab = f(a)b~ \text{or}~ f(ab)$?

Question

I know $\sin ab = \sin(ab)$, but does this apply to other functions?

Answer 1

It is typically the convention that the argument of an univariate function lacking parenthesis is the product of the factors of the term following the symbol until another function symbol is encountered.

$$\begin{align} \cos a \, b + c &= \cos (ab)+c \\ \ln a \cos b &= \ln (a) \cdot \cos (b) \\ {\rm\,f\,}a\,b{\rm\,g\,}c &= {\rm\,f}(ab) {\rm\,g}(c) \end{align} $$

However, it is only typically so, and you can't always rely on an author following the convention.

The best practice is: whenever there may be doubt, use parenthesis to be clear about it.