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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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    @N.S. Saying $\sin^{-1}$ does make sense since we have $\csc$ could also put the other way since we have $\asin$. I try to use the other names in order to avoid negative powers.2012-10-14

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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.

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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.

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    I think $\sin xy$ is quite clearly $\sin(xy)$. The latter just looks ugly.2018-01-22