TITLE: When do I write $\sin(x)$ and when $\sin x$?
QUESTION [7 upvotes]: I sometimes see $\sin x$ and sometimes $\sin(x)$. Are the parenteses needed since the sine is a function or is it more an operator that can be premultiplied to the variable? Or are people just lazy?

REPLY [9 votes]: There's no mathematical difference in when to write parentheses or not, as long as there is no doubt how much of the thing that follows "$\sin$" is part of the argument.
Part of the syntactic role of parentheses is to make clear that the thing to the left of them is actually a function rather than something rather than something to be multiplied. The need for this is greater when the name of the function is just a letter ("$f$" or "$g$" could also conceivably be used as names of constants, for example), but on the other hand "$\sin$" is so unambiguously a function that we usually don't need parentheses to remind the reader that that's what it is.
... except in situations like $\sin(t+1)$ where "$\sin t + 1$" would have meant $(\sin t)+1$.
Omitting the parentheses in unambiguous cases makes the expression slightly easier to read at a glance then there are many other levels of parentheses around.