anonymous
  • anonymous
is sinx a polynomial........?????????
Mathematics
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anonymous
  • anonymous
is sinx a polynomial........?????????
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
It can be written as an infinite series, so yes, a polynomial of infinite degree.
anonymous
  • anonymous
cant get u!!!!!!!
anonymous
  • anonymous
sinx isn't polynomial which only works for sin(x), is to notice that sin(x) has infinitely many zeroes - no polynomial or rational function has this many zeros.

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anonymous
  • anonymous
Do you know what a taylor series is, brah?
anonymous
  • anonymous
no......
anonymous
  • anonymous
\[\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + ... \]
anonymous
  • anonymous
When x is measured in radian.
anonymous
  • anonymous
Sin x is a trigonometric function. A polynomial is in the form ax^n+bx^n-1+...+cx+d A rational function is the quotient of two polynomials. e^x is not a rational function, but it is an exponential function because it is in the form a^x where is a constant, and e is a constant.
anonymous
  • anonymous
Tian do you go to Cambridge? I do.
anonymous
  • anonymous
Use the taylor's polynomial for sin(x) to find the rates of convergence of the following Taylor expansion of sin(x) about x=0 is sin(x) = x - x^3 / 3! + x^5 / 5! - x^7 / 7! + ... so sin(x) / x = 1 - x^2 / 3! + ... In the limit that x goes to zero, [sin(x)/x] = 1 - (0)^2 / 3! + ... = 1 Second way...extra:) hehe Consider a trigonometric circle with its center O and a tangent to this circle at A Let M be any point on The ciricle, and project M on the x-asis and name it H and let T be the tangent Thetha which is from A to T http://img534.imageshack.us/img534/1252/… As you realize in the picture Area of Triangle OAT = half tan thetha and Area of triangular sector OAM = thetha / 2 and Area of OHM : sin thetha = MH /OM (where OM =1 cz its a trigonometic circle ) ==> MH = Sin thetha ==> Area of OHM = (sin theha cos theha) /2 Therefore we can conclude that Area of OHM is smaller than OAM which is smaller than triangle OAT ==> (sing thetha cos thetha) /2 < thetha/2 < (tan thetha) / 2 multiply this by ( thetha / sin thehta) ==> we get cos theha < thetha / sin thetha < 1/cos thetha let thetha tend to zero that is cos thetha = cos 0 = 1 ==> 1- < lim tetha /sin thetha as thetha goes to zero < 1+ ==> lim sin thetha / tjhetha as thjetha goes to 0 = 1 PS: Dont forget that lim sin thetha / thetha as thetha tends to zero = lim thetha / sin thetha as thetha tends to zero ! Hope i helped you :)
anonymous
  • anonymous
What. The. flutter.
anonymous
  • anonymous
Newton I hope so
anonymous
  • anonymous
why?
anonymous
  • anonymous
I thought you said it wasn't a polynomial?
anonymous
  • anonymous
Then copypasted some random stuff that is vaguely related at the very most.
anonymous
  • anonymous
yeah I think sinx isn't polynomial by my first argument
anonymous
  • anonymous
:@
anonymous
  • anonymous
the point is that ..............my doubt is not clear yet........clear it!!!!!
anonymous
  • anonymous
Whatever. I'm not going to argue semantics.
anonymous
  • anonymous
I think a polynomial should have a finite number of terms.
anonymous
  • anonymous
sinx isn't polynomial, sin(x) has infinitely many zeroes - no polynomial or rational function has this many zeros.
anonymous
  • anonymous
Actually, 0 is a polynomial and has infinitely many 0s...
anonymous
  • anonymous
All we have to do to settle this is to check the definition of a polynomial.
anonymous
  • anonymous
Sin x may not be a polynomial (in your baby, non-cantab definitions), but the reasoning given is incorrect.
anonymous
  • anonymous
the power must be a whole numbr
anonymous
  • anonymous
Whatever, I don't have time to argue with people who get their arguments of wikipedia and yahoo answers. this is like when 48/2(9+3) was asked. Yes, wolfram says something so it's right. People need to learn what REAL mathematicians do and stop this nonsense.
anonymous
  • anonymous
Polynomial has to be of finite degree, so I made a mistake (not that definitions change how I do mathematics, so it's irrelevant). But the person who argued with me copied their argument DIRECTLY from yahoo answers and made some glaring mistakes. I don't have time for this pellet any more.
anonymous
  • anonymous
it isn't a polynomial :)
anonymous
  • anonymous
a polynomial is : f(x) = x^2 + 3 and etc. This is not :)
anonymous
  • anonymous
WOW.. did somebody kill somebody?
anonymous
  • anonymous
lol, why , who's dead ._.
anonymous
  • anonymous
hopefully not me :P
anonymous
  • anonymous
sin(x) has infinitely many zeroes - no polynomial or rational function has this many zeros. ^_^
anonymous
  • anonymous
sooooo, it's not a polynomial lol . I hope you're not confused sid :)
anonymous
  • anonymous
INew lol , cool down :)
anonymous
  • anonymous
STOP quoting some nobody off yahoo answers. 0 is a polynomial and has infinitely many 0s.
anonymous
  • anonymous
._. I'm not , I'm talking
anonymous
  • anonymous
based on knowledge and experience. Hey it's okay to make mistakes, don't get all boiled up for a question, calm down
anonymous
  • anonymous
u guys r more confuse thn me............
anonymous
  • anonymous
LOL!
anonymous
  • anonymous
LOL
anonymous
  • anonymous
hold on sid :)
anonymous
  • anonymous
clear my doubt..........
anonymous
  • anonymous
we apologize for the vagueness, just a second ^_^
anonymous
  • anonymous
INew, first calm down lol
anonymous
  • anonymous
Sin(x) has an infinite degree which (apparently) makes it not a polynomial. Also, it has infinite zeros, so can'y be a polynomial. Source: Yahoo answers
anonymous
  • anonymous
eat ice cream ^_^
anonymous
  • anonymous
just because our answers sounded alike, doesn't mean we have copied them INew :)
anonymous
  • anonymous
many answers sound alike, and ofcourse they will since all lead to the same explanation and theorem
anonymous
  • anonymous
Maybe not yours, but the guy before copied 2 paragraphs directly, so please don't patronise me.
anonymous
  • anonymous
fight..........killl..............
anonymous
  • anonymous
oh come on, let's not take it that way :)
anonymous
  • anonymous
no sid, that's not my style, I take things calmly :)
anonymous
  • anonymous
that guy is still onlyn!!!!!
anonymous
  • anonymous
Alright now, sid, read INew's post and tell me if you understood it or not okay?
anonymous
  • anonymous
My first post was wrong (apparently). But I didn't make a mistake, I just never needed to know the exact definition.
anonymous
  • anonymous
and INew, don't waste your energy in useless arguments, preserve it for better things ^_^
anonymous
  • anonymous
what is 'Inew'
anonymous
  • anonymous
INew = INewton lol
anonymous
  • anonymous
oh........sry!!!
anonymous
  • anonymous
read the recent post made by INew :)
anonymous
  • anonymous
So Newton, Could you write the exact definition down?
anonymous
  • anonymous
and thank you for your help tian ^_^ ,all of you have been a great help to sid, but let's calm down now
anonymous
  • anonymous
so finally.........sinx is a polynomial or not....with reasons!!!
anonymous
  • anonymous
lol, sin x is not a polynomial since it tends to go to infinity. A polynomial = has a finite number of zeros.
anonymous
  • anonymous
It doesn't go to infinity? It has an infinite number of terms.
anonymous
  • anonymous
contradiction comes.........i m frustrated!!!!!!!!!!!!!
anonymous
  • anonymous
Example : \[f(x) = x^2 -1\] = (x-1)(x+1) where the zeros are x = 1, -1 <-- finite numbers of zeros but sin x keeps on oscillating b/w -1 and 1 and never stops, so that's why it's not a polynomial
anonymous
  • anonymous
sid dear, calm down , don't panic :)
anonymous
  • anonymous
f(x) = 0 INFINITE NUMBER OF ZEROS BUT POLYNOMIAL OF DEGREE ZERO.
anonymous
  • anonymous
LOL! INew shut the caps =D
anonymous
  • anonymous
come to india .............and kill me!!!!!!!
anonymous
  • anonymous
I'll slap you instead to wake u up
anonymous
  • anonymous
lol, hush now, we're going to explain it, if you don't get me, then INew will explain it, if you don't get her , then someone else, alright? now hush LOL
anonymous
  • anonymous
both of u ......as a unit...........give me the final nd the CORRECT answer!!!!!!!
anonymous
  • anonymous
wtf I'm not a her
anonymous
  • anonymous
SID! LOL
anonymous
  • anonymous
INEW, eat ICE CREAM and stay away from bananas!
anonymous
  • anonymous
lolzzzzzzz!!!!!!!!!!........sry 4 dat
anonymous
  • anonymous
In mathematics, a BABY polynomial is an expression of finite length, containing variables and constants. The Fundamental Theorem of Algebra says that a BABY polynomial of degree n can be written as the product of n linear factors. Sin(x) is a taylor series of infinite length, and therefore not a BABY polynomial.
anonymous
  • anonymous
lol, I liked how you've put it "baby" polynomial, so sid do you get it now?
anonymous
  • anonymous
so sinx is not a polynomial bcos it has infinite roots!!!!!!!is it.......
anonymous
  • anonymous
yes :)
anonymous
  • anonymous
NO. It is of an infinite degree, with an infinite number of terms. NOT because of infinite roots.
anonymous
  • anonymous
same scenario as long as he got the picture lol
anonymous
  • anonymous
But by your logic, f(x) = 0 isn't a polynomial.
anonymous
  • anonymous
listen u guyz .....u may be a cambridgian or etc.etc........i m a scul going boy............new to maths..........dont kno so advance concepts...lyk taylor series.etc.etc
anonymous
  • anonymous
Protip: Taylor series isn't advanced.
anonymous
  • anonymous
INew, let's not get him into the series maze ._. from now, just simply explain it in a simple way LOL
anonymous
  • anonymous
I am taking taylor series next week
anonymous
  • anonymous
so, it's sorta advanced for him?
anonymous
  • anonymous
at some point u guyz would also have been as i m today!!!!!!dont forget........
anonymous
  • anonymous
Lol, don't worry :)
anonymous
  • anonymous
Alright, listen If you plot a graph for sin x, you'll notice it oscillating between -1 and 1 and never stops, as in never dies, it goes to infinity On the other hand, when you plot a simple function such as f(x) = x^2 or f(x) = ax + bx + c ( which is a polynomial ) you'll have a line, parabola or curve. A polynomial is : (ax + bx + c), does sin(x) have this form? if yes, then it's a polynomial, if not, then it isn't.
anonymous
  • anonymous
did I make it easier? ^_^
anonymous
  • anonymous
so now you tell me, is it a polynomial? :)
anonymous
  • anonymous
|;
anonymous
  • anonymous
no ...it is not
anonymous
  • anonymous
excellent ^_^
anonymous
  • anonymous
x^2 goes to infinity.
anonymous
  • anonymous
here comes confusion
anonymous
  • anonymous
lol, wait, did you understand what I have said?
anonymous
  • anonymous
hold on INew
anonymous
  • anonymous
gud nyt!!!!!!!
anonymous
  • anonymous
sweet drms.............!!!!!1
anonymous
  • anonymous
lol good night
anonymous
  • anonymous
:(
anonymous
  • anonymous
INew, you're right, >_< my bad lol
anonymous
  • anonymous
what's with the long face? :) cheer up, he got it and you have given awesome "advanced" explanations, but it was too much for his level. I thought they were great ^_^
anonymous
  • anonymous
Lol. I was wrong to start with, so rather than admit it, I spent pretty much the rest of the argument crying and pointing out tiny mistakes. Pretty disappointing, really.
anonymous
  • anonymous
well we're all humans, and we all make mistakes that we learn from right? :)
anonymous
  • anonymous
"Who hasn't made a mistake, hasn't tried anything new" -Albert Einstein ^_^
anonymous
  • anonymous
:-)
anonymous
  • anonymous
when you face such situations, yelling and screaming won't solve the problem, calm down and take it with reason :)
anonymous
  • anonymous
promise me no more overreacting?
anonymous
  • anonymous
yeah right
anonymous
  • anonymous
Indeed. It's just, the first time I've been wrong, ever. Kind of a shock to the system. I'll try.
anonymous
  • anonymous
again, human LOL, you should see MY mistakes. I subtract instead of adding and the vice versa LOL
anonymous
  • anonymous
well, not anymore, just rarely happens now ^_^"
anonymous
  • anonymous
you make a mistake, fix it, period =P just no more cursing or any of that stuff lol
anonymous
  • anonymous
We'll see. :D. One thing before this topic dies, in case you didn't see my correction, there is a little error here: 'if you don't get me, then INew will explain it, if you don't get *her*'
anonymous
  • anonymous
^_^" my bad, aha..
anonymous
  • anonymous
you said that you were a she last time ._.
anonymous
  • anonymous
or were my eyes twisted x_x
anonymous
  • anonymous
Hmm. I think I may have said it (sarcasticaly :( ). Hence my pseudonym (and real name, actually, if you can see it).
anonymous
  • anonymous
oh yeah, LOL. My dearest apologies ^_^
anonymous
  • anonymous
anyhow, I'm off to bed now, good night :) don't let me catch you cursing or overreacting next time =P
anonymous
  • anonymous
lol, OK, bye

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