Question

is sinx a polynomial........?????????

Answer 1

It can be written as an infinite series, so yes, a polynomial of infinite degree.

Answer 2

cant get u!!!!!!!

Answer 3

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.

Answer 4

Do you know what a taylor series is, brah?

Answer 5

no......

Answer 6

\[\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + ... \]

Answer 7

When x is measured in radian.

Answer 8

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.

Answer 9

Tian do you go to Cambridge? I do.

Answer 10

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 :)

Answer 11

What. The. flutter.

Answer 12

Newton I hope so

Answer 13

why?

Answer 14

I thought you said it wasn't a polynomial?

Answer 15

Then copypasted some random stuff that is vaguely related at the very most.

Answer 16

yeah I think sinx isn't polynomial by my first argument

Answer 17

:@

Answer 18

the point is that ..............my doubt is not clear yet........clear it!!!!!

Answer 19

Whatever. I'm not going to argue semantics.

Answer 20

I think a polynomial should have a finite number of terms.

Answer 21

sinx isn't polynomial, sin(x) has infinitely many zeroes - no polynomial or rational function has this many zeros.

Answer 22

Actually, 0 is a polynomial and has infinitely many 0s...

Answer 23

All we have to do to settle this is to check the definition of a polynomial.

Answer 24

Sin x may not be a polynomial (in your baby, non-cantab definitions), but the reasoning given is incorrect.

Answer 25

the power must be a whole numbr

Answer 26

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.

Answer 27

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.

Answer 28

it isn't a polynomial :)

Answer 29

a polynomial is : f(x) = x^2 + 3 and etc. This is not :)

Answer 30

WOW.. did somebody kill somebody?

Answer 31

lol, why , who's dead ._.

Answer 32

hopefully not me :P

Answer 33

sin(x) has infinitely many zeroes - no polynomial or rational function has this many zeros.
^_^

Answer 34

sooooo, it's not a polynomial lol . I hope you're not confused sid :)

Answer 35

INew lol , cool down :)

Answer 36

STOP quoting some nobody off yahoo answers. 0 is a polynomial and has infinitely many 0s.

Answer 37

._. I'm not , I'm talking

Answer 38

based on knowledge and experience. Hey it's okay to make mistakes, don't get all boiled up for a question, calm down

Answer 39

u guys r more confuse thn me............

Answer 40

LOL!

Answer 41

LOL

Answer 42

hold on sid :)

Answer 43

clear my doubt..........

Answer 44

we apologize for the vagueness, just a second ^_^

Answer 45

INew, first calm down lol

Answer 46

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

Answer 47

eat ice cream ^_^

Answer 48

just because our answers sounded alike, doesn't mean we have copied them INew :)

Answer 49

many answers sound alike, and ofcourse they will since all lead to the same explanation and theorem

Answer 50

Maybe not yours, but the guy before copied 2 paragraphs directly, so please don't patronise me.

Answer 51

fight..........killl..............

Answer 52

oh come on, let's not take it that way :)

Answer 53

no sid, that's not my style, I take things calmly :)

Answer 54

that guy is still onlyn!!!!!

Answer 55

Alright now, sid, read INew's post and tell me if you understood it or not okay?

Answer 56

My first post was wrong (apparently). But I didn't make a mistake, I just never needed to know the exact definition.

Answer 57

and INew, don't waste your energy in useless arguments, preserve it for better things ^_^

Answer 58

what is 'Inew'

Answer 59

INew = INewton lol

Answer 60

oh........sry!!!

Answer 61

read the recent post made by INew :)

Answer 62

So Newton, Could you write the exact definition down?

Answer 63

and thank you for your help tian ^_^ ,all of you have been a great help to sid, but let's calm down now

Answer 64

so finally.........sinx is a polynomial or not....with reasons!!!

Answer 65

lol, sin x is not a polynomial since it tends to go to infinity. A polynomial = has a finite number of zeros.

Answer 66

It doesn't go to infinity? It has an infinite number of terms.

Answer 67

contradiction comes.........i m frustrated!!!!!!!!!!!!!

Answer 68

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

Answer 69

sid dear, calm down , don't panic :)

Answer 70

f(x) = 0

INFINITE NUMBER OF ZEROS BUT POLYNOMIAL OF DEGREE ZERO.

Answer 71

LOL! INew shut the caps =D

Answer 72

come to india .............and kill me!!!!!!!

Answer 73

I'll slap you instead to wake u up

Answer 74

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

Answer 75

both of u ......as a unit...........give me the final nd the CORRECT answer!!!!!!!

Answer 76

wtf I'm not a her

Answer 77

SID! LOL

Answer 78

INEW, eat ICE CREAM and stay away from bananas!

Answer 79

lolzzzzzzz!!!!!!!!!!........sry 4 dat

Answer 80

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.

Answer 81

lol, I liked how you've put it "baby" polynomial, so sid do you get it now?

Answer 82

so sinx is not a polynomial bcos it has infinite roots!!!!!!!is it.......

Answer 83

yes :)

Answer 84

NO. It is of an infinite degree, with an infinite number of terms. NOT because of infinite roots.

Answer 85

same scenario as long as he got the picture lol

Answer 86

But by your logic, f(x) = 0 isn't a polynomial.

Answer 87

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

Answer 88

Protip: Taylor series isn't advanced.

Answer 89

INew, let's not get him into the series maze ._. from now, just simply explain it in a simple way LOL

Answer 90

I am taking taylor series next week

Answer 91

so, it's sorta advanced for him?

Answer 92

at some point u guyz would also have been as i m today!!!!!!dont forget........

Answer 93

Lol, don't worry :)

Answer 94

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.

Answer 95

did I make it easier? ^_^

Answer 96

so now you tell me, is it a polynomial? :)

Answer 97

|;

Answer 98

no ...it is not