Mathematical Notation
March 15, 2007 2:29 AM   Subscribe

Mathematics notation help needed please. Given the expresion: cosx(x+1), is this properly interpreted as (x+1)cosx or cos(x^2+x)?
posted by Neiltupper to Education (14 answers total) 1 user marked this as a favorite
Practical experience indicates the second one.
posted by Phire at 2:36 AM on March 15, 2007

The second
posted by handee at 2:48 AM on March 15, 2007

I would have to say it would depend on the layout of the formula and where you got it. As an engineering student, I have different professors for different subjects in math, where one prof. would expect the first answer, and the other prof. would expect the second answer. The spacing in the question would matter as well. Generally speaking, if the only thing written is Cos x(x+1) and this is not a part of a larger equation, i would be inclined to say it is equal to Cos (x^2 + x). if you are unsure, take a look at the other expressions around it and check to see if there is anything that looks like (x+1) Cos x to compare against.

In general mathematic rules expect (x+1)cos x to be written as such, so I would be inclined to agree with the second answer
posted by mrw at 3:37 AM on March 15, 2007

It's ambiguous, and there's no way around that. When I looked at it, the way I interpreted it was (cos(x))(x+1). I tend to see "cosx" as a tightly-bound chunk; if the argument for a trig function is larger than a single letter, then it should be enclosed in parentheses. Styles vary, though, and I agree with mrw that spacing may be a clue to the intended meaning.

This probably goes without saying, but the way to deal with this if it's an isolated expression that's part of homework or something is to use parenthesization to indicate which interpretation you took, and possibly even include a little note acknowledging the ambiguity. No sensible teacher will have a problem with that; admittedly, there are less than sensible teachers out there.

If it's not just an isolated expression then it may be possible to figure out which expression is correct from the context of the problem.
posted by Wolfdog at 4:36 AM on March 15, 2007

I've often wondered about this too, when professors have used similar notation. It always annoyed me that they wouldn't just write Cos(x(x+1)) to save everyone some confusion. I don' t think the order of operations rules would say definitively either way; because the proper notation is to use perentheses around the entire argument, there is no need for a special rule. But yes, I agree with the previous answers - generally, that means Cos(x(x+1)).
posted by whataboutben at 4:43 AM on March 15, 2007

I should note that I think the expression should mean (x+1)cos(x), because I would go by the common sense rule that perentheses can only be omitted in the case of the expression "Cosx". But, like I said, in my experience, professors often mean the other way.
posted by whataboutben at 5:05 AM on March 15, 2007

Best answer: To me, it doesn't mean anything. cos() is a function and a function requires that the parameters be surrounded by parenthesis. "cos x" is just barely acceptable, "cos x(x+1)" is not. It is an ambiguous string and therefore bad notation.
posted by DU at 5:25 AM on March 15, 2007

As everyone else said, it's ambiguous. If you encountered this in a paper or something, I bet it's (x+1) * cos(x), which is a little weird (using x as both an angle and a distance) but at least could make sense if x were in radians and you had a unit circle nearby. cos(x * (x+1)), on the other hand, really doesn't make any sense at all to me; x would have to be in units of square roots of an angle, and why add 1 to that?
posted by dfan at 7:26 AM on March 15, 2007

Response by poster: Right now I lean to whataboutben's response, In reply to Du, your argument (pardon the pun) is valid, but one almost never sees f(x) = (x)^2 (or cos(x) for that matter.

The notation is only ambiguous in the absence of a convention, and my own feeling is that parentheses or brackets or other symbol of inclusion should be used around the argument if any ambiguity arises without them. There I agree with Du
posted by Neiltupper at 7:30 AM on March 15, 2007

Unfortunately (perhaps), common mathematical notation is essentially never unambiguous. It needs to be interpreted contextually, and we don't know as much as you about the context in which you saw cosx(x+1). I must say, however, that I think I have never seen a context in which cosx(x+1) would not have been ambiguous had it appeared!

Because parentheses are usually used for both grouping of additive terms and enclosing the arguments of functions, there is a reasonably common (but by no means universal) instinct to put overall multiplicative factors before functions. Due to this, my best guess is that it means cos(x(x + 1)).
posted by hAndrew at 8:25 AM on March 15, 2007

It doesn't matter what we think it means. The notation is only a way of expressing ideas, and since this is even slightly ambiguous, you shouldn't assume anything at all.

The writer may have gotten it wrong when he encoded his ideas into that notation, and you may get it wrong when you decode it into an idea.

Ask the writer. It's the only way to know.
posted by cmiller at 8:26 AM on March 15, 2007

If you can't ask the writer, point out the ambiguity and do the problem both ways.
posted by kindall at 8:30 AM on March 15, 2007

You should also be able to tell from the context of what you are working on.. You might make a question much easier or harder than it should be, for example.

As kindall suggests, do it both ways. Even then, you should probably indicate the one you think was intended.
posted by Chuckles at 8:55 AM on March 15, 2007

I plugged it into Mathematica's online symbolic integrator and it was interpreted as (x+1)cosx.
posted by JackFlash at 11:26 AM on March 15, 2007

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