Although Chip's answer already suffices to address the question, I would like to quote here a relevant part of the dialog by Theo Gray and Jerry Glynn in their book Exploring Mathematics with Mathematica; as there does not seem to be an easily accessible online version or preview of the book anywhere, I hope the quotation is useful:
Theo: Satisfied? Mathematica also knows about a whole bunch of other functions, such as trigonometric functions. One of the weird
things about Mathematica that tends to annoy people for a while is
that you have to use square brackets and capital letters. For
Jerry: In other words, you're saying I can't type
sin 1.2 with no parentheses, or
sin[1.2]. I must
Sin[1.2], exactly as you did. That seems like a real
Theo: Yes, you have to type
Sin[1.2], exactly. There are good reasons for both requirements, and we'll see why in later chapters.
If you use one of the variations you suggested above, Mathematica
will warn you that you are probably making a mistake. All of your
variations are legal Mathematica input, but they don't mean what you
want. (For example,
sin(1.2) means the variable named
Jerry: OK, I'll live with the funny brackets for now.
Jerry: …now, what about square brackets? Why can't I use
Sin(x) instead of
Theo: Good question! There is, in fact, a good reason. Ordinary mathematical notation is inconsistent here. Round parentheses are
used to mean two completely different things in traditional notation:
first, order of evaluation; second, function arguments. Consider the
k(b + c). Does this mean
k times the quantity
b + c,
or does it mean the function
k with the argument
b + c? Unless
you know from somewhere else that
k is a function, or that
k is a
variable, you can't tell. It's a mistake to use the same symbols to
mean these two completely different things, and Mathematica corrects
this mistake by using round parentheses only for order of evaluation,
and square brackets only for function arguments.
Jerry: That's a nice point. I never thought of that before. It shows how easily we adapt to nonsense. Aside from that, are you
saying that mathematicians have been sloppy for centuries? That's a
pretty strong statement!
Theo: Yes. Although I'm all in favor of interesting, quirky languages for writing novels and poetry (English comes to mind), it's
really a bad idea to use an ambiguous language for something like
mathematics. One of the great contributions of computer science to
the world has been a powerful set of tools for thinking about what
makes a language "good".
An alternative would be to insist on using a
* for all
k(b + c) would always mean the function
and if you wanted it to mean multiplication you would have to use
k*(b + c). We decided it was better to remove an inconsistency than
to force people to use an extra symbol. Another option would have
been to have Mathematica "know" what was a variable and what was a
function. This turns out to have serious consequences, and it's
really not a good idea.
Jerry: Well, I didn't expect a lecture!
Theo: Sorry. Let's get back to the matter at hand. For functions, you use square brackets. Let's use the
together with some round parentheses, to see how they fit:
Sin[1.2 (3 + 4)] (4 + 5)
Jerry: This means, Find the sine of 1.2 times 7 and multiply that answer by 9.