I’ve a question for the math folks out there:
What does sin(x)2 mean, or is it ambiguous notation?
I’m taking an informal poll of the internet (or at least, of the six people who actively read this site). If you’d be so kind, please put your answer in the comments.
I’ve got my answer, and I’ll give next week month, but I’d really like your thoughts first.
Definitely (sin(x))2. Though I know it is sometimes written sin2(x). Though does it really matter if the author makes clear the convention and sticks to it?
Comment by Ben — 04.13.2009 @
Dammit. Apparently, html tags don’t work in the comments section. Assume the 2’s are superscripted.
– Travis sez: I went and fixed your superscripts for ya!
Comment by Ben — 04.13.2009 @
i’m with ben on this one. it isn’t unambiguous to me….
Comment by sam — 04.13.2009 @
Ambiguous.
Comment by Anonymous — 04.13.2009 @
Isn’t that a half angle? But yeah, what Ben said. The x is not squared. The sin of x, however, is squared.
Comment by Megan — 04.13.2009 @
Since brackets are around the argument, I agree; it would definitely be (sin(x))^2. Normally for a simple argument (a single variable or value), the brackets are omitted. In that case, sin x^2 would be ambiguous.
Comment by EverardXavier — 04.13.2009 @
I wonder why mathematicians insist on omitting brackets and parentheses as often as they do, be sin, cos, tan, log sinh, or whatever. I think the only time more paratheses or brackets make things confusing is when I’m writing a program in Lisp.
Comment by Ben — 04.14.2009 @
Not ambiguous: it equals (sin (x))^2. Once that bracket closes on the argument, anything after that is done to the value of the function at x. The only possibility of ambiguity here is because, as Ben said, mathematicians like to omit brackets around arguments, which makes it possible for this to mean sin(x^2). But once you put those brackets in you are explicitly denoting an argument and therefore a closing bracket indicates the end of the function.
On my scientific calculator in degree mode, when I type sin(30)^2 it returns 0.25 (i.e. the square of 1/2, which is sin(30)), not 0 (i.e. sin(30^2)=sin(900)).
@Megan (5): Half angle? Isn’t that sin(x/2)?
Comment by Blake — 04.14.2009 @
I think its ambiguous. I would assume the writer probably meant (sin (x))^2 but without the parenthesis, you can’t really know for sure.
I’m all about sin2(x)
Because of the parenthesis around the x, I would also assume the writer does not intend for the x to be squared, otherwise the exponent would be inside the parenthesis or left out completely.
In any event, I do not like that notation.
Comment by Heather — 04.15.2009 @
so if you know there’s only like 6 of us… why bother, really?
Comment by JBu92 — 04.18.2009 @
like surely the money you’re spending on the domain name could be put to better use?
and yeah, it’s (sin(x))^2. when in doubt, plug it in to a calculator lol
Comment by JBu92 — 04.18.2009 @
As a High School Math teacher, I find myself trying to build a bridge between common people, and the power of math as an analytical tool that guides our interactions with the world around us, and to that purpose any ambiguity is very, very bad. This ambiguity arises from a differences between the esoteric informed, and the lay people who are operating out of the limits of their knowledge. Because to a student, or just to someone who studies math because of its usefulness in describing the universe and is not concerned with eccentricities, sin (x)^2 would very clearly state sin x^2, because that’s how () works it defines a group that other terms may apply to, for the term x they can be there, (x), or not, x, it makes no difference, working with parenthesis is a skill introduced in middle school/junior high, some places even late elementary, trig functions generally come later. Furthermore the most direct and obvious way of communicating the square of the function sin x would be sin^2 x or (sin x)^2. The rule that when the parenthesis close around the argument anything outside applies to the sin function is the rule as many have been taught perhaps in a trig, college trig, or modern algebra class. But it’s this “new” (as in new to the learner) rule about parenthesis in the context of an a trig argument, that must be taught as a counterpoint to the initial interpretation that creates the ambiguity. So is this “ambiguity?” This closing argument rule in the context of trig functions actually doesn’t come up in the high school trig books I’ve seen, but it is taught in the context of composition of functions in an algebra 2 class.
Comment by Adam — 04.19.2009 @
As a high school senior in AP Calculus..I would interpret that as the sine of x2. I agree with Heather; I’m used to the sin2(x) notation. So it’s ambiguous to me.
Comment by Jayna — 04.20.2009 @