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?
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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.
Parentheses make the expression clearer for the expressions like $\sin (xy)$, if you write $\sin xy$, then it may mean $(\sin x).y$. But for only $\sin (x)$ it is enough to write $\sin x$. If there is some possiblilty of ambiguity then it is better to use parentheses.