## anonymous 5 years ago is sinx a polynomial........?????????

1. anonymous

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

2. anonymous

cant get u!!!!!!!

3. 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.

4. anonymous

Do you know what a taylor series is, brah?

5. anonymous

no......

6. anonymous

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

7. anonymous

When x is measured in radian.

8. 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.

9. anonymous

Tian do you go to Cambridge? I do.

10. 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 :)

11. anonymous

What. The. flutter.

12. anonymous

Newton I hope so

13. anonymous

why?

14. anonymous

I thought you said it wasn't a polynomial?

15. anonymous

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

16. anonymous

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

17. anonymous

:@

18. anonymous

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

19. anonymous

Whatever. I'm not going to argue semantics.

20. anonymous

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

21. anonymous

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

22. anonymous

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

23. anonymous

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

24. anonymous

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

25. anonymous

the power must be a whole numbr

26. 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.

27. 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.

28. anonymous

it isn't a polynomial :)

29. anonymous

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

30. anonymous

WOW.. did somebody kill somebody?

31. anonymous

lol, why , who's dead ._.

32. anonymous

hopefully not me :P

33. anonymous

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

34. anonymous

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

35. anonymous

INew lol , cool down :)

36. anonymous

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

37. anonymous

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

38. anonymous

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

39. anonymous

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

40. anonymous

LOL!

41. anonymous

LOL

42. anonymous

hold on sid :)

43. anonymous

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

44. anonymous

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

45. anonymous

INew, first calm down lol

46. 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

47. anonymous

eat ice cream ^_^

48. anonymous

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

49. anonymous

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

50. anonymous

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

51. anonymous

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

52. anonymous

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

53. anonymous

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

54. anonymous

that guy is still onlyn!!!!!

55. anonymous

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

56. anonymous

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

57. anonymous

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

58. anonymous

what is 'Inew'

59. anonymous

INew = INewton lol

60. anonymous

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

61. anonymous

62. anonymous

So Newton, Could you write the exact definition down?

63. anonymous

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

64. anonymous

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

65. anonymous

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

66. anonymous

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

67. anonymous

68. 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

69. anonymous

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

70. anonymous

f(x) = 0 INFINITE NUMBER OF ZEROS BUT POLYNOMIAL OF DEGREE ZERO.

71. anonymous

LOL! INew shut the caps =D

72. anonymous

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

73. anonymous

I'll slap you instead to wake u up

74. 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

75. anonymous

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

76. anonymous

wtf I'm not a her

77. anonymous

SID! LOL

78. anonymous

INEW, eat ICE CREAM and stay away from bananas!

79. anonymous

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

80. 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.

81. anonymous

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

82. anonymous

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

83. anonymous

yes :)

84. anonymous

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

85. anonymous

same scenario as long as he got the picture lol

86. anonymous

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

87. 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

88. anonymous

89. anonymous

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

90. anonymous

I am taking taylor series next week

91. anonymous

so, it's sorta advanced for him?

92. anonymous

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

93. anonymous

Lol, don't worry :)

94. 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.

95. anonymous

did I make it easier? ^_^

96. anonymous

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

97. anonymous

|;

98. anonymous

no ...it is not

99. anonymous

excellent ^_^

100. anonymous

x^2 goes to infinity.

101. anonymous

here comes confusion

102. anonymous

lol, wait, did you understand what I have said?

103. anonymous

hold on INew

104. anonymous

gud nyt!!!!!!!

105. anonymous

sweet drms.............!!!!!1

106. anonymous

lol good night

107. anonymous

:(

108. anonymous

INew, you're right, >_< my bad lol

109. 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 ^_^

110. 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.

111. anonymous

well we're all humans, and we all make mistakes that we learn from right? :)

112. anonymous

"Who hasn't made a mistake, hasn't tried anything new" -Albert Einstein ^_^

113. anonymous

:-)

114. anonymous

when you face such situations, yelling and screaming won't solve the problem, calm down and take it with reason :)

115. anonymous

promise me no more overreacting?

116. anonymous

yeah right

117. anonymous

Indeed. It's just, the first time I've been wrong, ever. Kind of a shock to the system. I'll try.

118. anonymous

again, human LOL, you should see MY mistakes. I subtract instead of adding and the vice versa LOL

119. anonymous

well, not anymore, just rarely happens now ^_^"

120. anonymous

you make a mistake, fix it, period =P just no more cursing or any of that stuff lol

121. 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*'

122. anonymous

123. anonymous

you said that you were a she last time ._.

124. anonymous

or were my eyes twisted x_x

125. anonymous

Hmm. I think I may have said it (sarcasticaly :( ). Hence my pseudonym (and real name, actually, if you can see it).

126. anonymous

oh yeah, LOL. My dearest apologies ^_^

127. anonymous

anyhow, I'm off to bed now, good night :) don't let me catch you cursing or overreacting next time =P

128. anonymous

lol, OK, bye