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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    It can be written as an infinite series, so yes, a polynomial of infinite degree.

  2. anonymous
    • 5 years ago
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    cant get u!!!!!!!

  3. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    Do you know what a taylor series is, brah?

  5. anonymous
    • 5 years ago
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    no......

  6. anonymous
    • 5 years ago
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    \[\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + ... \]

  7. anonymous
    • 5 years ago
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    When x is measured in radian.

  8. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    Tian do you go to Cambridge? I do.

  10. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    What. The. flutter.

  12. anonymous
    • 5 years ago
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    Newton I hope so

  13. anonymous
    • 5 years ago
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    why?

  14. anonymous
    • 5 years ago
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    I thought you said it wasn't a polynomial?

  15. anonymous
    • 5 years ago
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    Then copypasted some random stuff that is vaguely related at the very most.

  16. anonymous
    • 5 years ago
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    yeah I think sinx isn't polynomial by my first argument

  17. anonymous
    • 5 years ago
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    :@

  18. anonymous
    • 5 years ago
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    the point is that ..............my doubt is not clear yet........clear it!!!!!

  19. anonymous
    • 5 years ago
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    Whatever. I'm not going to argue semantics.

  20. anonymous
    • 5 years ago
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    I think a polynomial should have a finite number of terms.

  21. anonymous
    • 5 years ago
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    sinx isn't polynomial, sin(x) has infinitely many zeroes - no polynomial or rational function has this many zeros.

  22. anonymous
    • 5 years ago
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    Actually, 0 is a polynomial and has infinitely many 0s...

  23. anonymous
    • 5 years ago
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    All we have to do to settle this is to check the definition of a polynomial.

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

  25. anonymous
    • 5 years ago
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    the power must be a whole numbr

  26. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    it isn't a polynomial :)

  29. anonymous
    • 5 years ago
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    a polynomial is : f(x) = x^2 + 3 and etc. This is not :)

  30. anonymous
    • 5 years ago
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    WOW.. did somebody kill somebody?

  31. anonymous
    • 5 years ago
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    lol, why , who's dead ._.

  32. anonymous
    • 5 years ago
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    hopefully not me :P

  33. anonymous
    • 5 years ago
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    sin(x) has infinitely many zeroes - no polynomial or rational function has this many zeros. ^_^

  34. anonymous
    • 5 years ago
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    sooooo, it's not a polynomial lol . I hope you're not confused sid :)

  35. anonymous
    • 5 years ago
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    INew lol , cool down :)

  36. anonymous
    • 5 years ago
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    STOP quoting some nobody off yahoo answers. 0 is a polynomial and has infinitely many 0s.

  37. anonymous
    • 5 years ago
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    ._. I'm not , I'm talking

  38. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    u guys r more confuse thn me............

  40. anonymous
    • 5 years ago
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    LOL!

  41. anonymous
    • 5 years ago
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    LOL

  42. anonymous
    • 5 years ago
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    hold on sid :)

  43. anonymous
    • 5 years ago
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    clear my doubt..........

  44. anonymous
    • 5 years ago
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    we apologize for the vagueness, just a second ^_^

  45. anonymous
    • 5 years ago
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    INew, first calm down lol

  46. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    eat ice cream ^_^

  48. anonymous
    • 5 years ago
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    just because our answers sounded alike, doesn't mean we have copied them INew :)

  49. anonymous
    • 5 years ago
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    many answers sound alike, and ofcourse they will since all lead to the same explanation and theorem

  50. anonymous
    • 5 years ago
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    Maybe not yours, but the guy before copied 2 paragraphs directly, so please don't patronise me.

  51. anonymous
    • 5 years ago
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    fight..........killl..............

  52. anonymous
    • 5 years ago
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    oh come on, let's not take it that way :)

  53. anonymous
    • 5 years ago
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    no sid, that's not my style, I take things calmly :)

  54. anonymous
    • 5 years ago
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    that guy is still onlyn!!!!!

  55. anonymous
    • 5 years ago
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    Alright now, sid, read INew's post and tell me if you understood it or not okay?

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

  57. anonymous
    • 5 years ago
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    and INew, don't waste your energy in useless arguments, preserve it for better things ^_^

  58. anonymous
    • 5 years ago
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    what is 'Inew'

  59. anonymous
    • 5 years ago
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    INew = INewton lol

  60. anonymous
    • 5 years ago
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    oh........sry!!!

  61. anonymous
    • 5 years ago
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    read the recent post made by INew :)

  62. anonymous
    • 5 years ago
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    So Newton, Could you write the exact definition down?

  63. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    so finally.........sinx is a polynomial or not....with reasons!!!

  65. anonymous
    • 5 years ago
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    lol, sin x is not a polynomial since it tends to go to infinity. A polynomial = has a finite number of zeros.

  66. anonymous
    • 5 years ago
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    It doesn't go to infinity? It has an infinite number of terms.

  67. anonymous
    • 5 years ago
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    contradiction comes.........i m frustrated!!!!!!!!!!!!!

  68. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    sid dear, calm down , don't panic :)

  70. anonymous
    • 5 years ago
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    f(x) = 0 INFINITE NUMBER OF ZEROS BUT POLYNOMIAL OF DEGREE ZERO.

  71. anonymous
    • 5 years ago
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    LOL! INew shut the caps =D

  72. anonymous
    • 5 years ago
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    come to india .............and kill me!!!!!!!

  73. anonymous
    • 5 years ago
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    I'll slap you instead to wake u up

  74. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    both of u ......as a unit...........give me the final nd the CORRECT answer!!!!!!!

  76. anonymous
    • 5 years ago
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    wtf I'm not a her

  77. anonymous
    • 5 years ago
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    SID! LOL

  78. anonymous
    • 5 years ago
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    INEW, eat ICE CREAM and stay away from bananas!

  79. anonymous
    • 5 years ago
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    lolzzzzzzz!!!!!!!!!!........sry 4 dat

  80. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    lol, I liked how you've put it "baby" polynomial, so sid do you get it now?

  82. anonymous
    • 5 years ago
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    so sinx is not a polynomial bcos it has infinite roots!!!!!!!is it.......

  83. anonymous
    • 5 years ago
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    yes :)

  84. anonymous
    • 5 years ago
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    NO. It is of an infinite degree, with an infinite number of terms. NOT because of infinite roots.

  85. anonymous
    • 5 years ago
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    same scenario as long as he got the picture lol

  86. anonymous
    • 5 years ago
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    But by your logic, f(x) = 0 isn't a polynomial.

  87. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    Protip: Taylor series isn't advanced.

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

  90. anonymous
    • 5 years ago
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    I am taking taylor series next week

  91. anonymous
    • 5 years ago
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    so, it's sorta advanced for him?

  92. anonymous
    • 5 years ago
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    at some point u guyz would also have been as i m today!!!!!!dont forget........

  93. anonymous
    • 5 years ago
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    Lol, don't worry :)

  94. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    did I make it easier? ^_^

  96. anonymous
    • 5 years ago
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    so now you tell me, is it a polynomial? :)

  97. anonymous
    • 5 years ago
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    |;

  98. anonymous
    • 5 years ago
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    no ...it is not

  99. anonymous
    • 5 years ago
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    excellent ^_^

  100. anonymous
    • 5 years ago
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    x^2 goes to infinity.

  101. anonymous
    • 5 years ago
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    here comes confusion

  102. anonymous
    • 5 years ago
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    lol, wait, did you understand what I have said?

  103. anonymous
    • 5 years ago
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    hold on INew

  104. anonymous
    • 5 years ago
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    gud nyt!!!!!!!

  105. anonymous
    • 5 years ago
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    sweet drms.............!!!!!1

  106. anonymous
    • 5 years ago
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    lol good night

  107. anonymous
    • 5 years ago
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    :(

  108. anonymous
    • 5 years ago
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    INew, you're right, >_< my bad lol

  109. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    well we're all humans, and we all make mistakes that we learn from right? :)

  112. anonymous
    • 5 years ago
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    "Who hasn't made a mistake, hasn't tried anything new" -Albert Einstein ^_^

  113. anonymous
    • 5 years ago
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    :-)

  114. anonymous
    • 5 years ago
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    when you face such situations, yelling and screaming won't solve the problem, calm down and take it with reason :)

  115. anonymous
    • 5 years ago
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    promise me no more overreacting?

  116. anonymous
    • 5 years ago
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    yeah right

  117. anonymous
    • 5 years ago
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    Indeed. It's just, the first time I've been wrong, ever. Kind of a shock to the system. I'll try.

  118. anonymous
    • 5 years ago
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    again, human LOL, you should see MY mistakes. I subtract instead of adding and the vice versa LOL

  119. anonymous
    • 5 years ago
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    well, not anymore, just rarely happens now ^_^"

  120. anonymous
    • 5 years ago
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    you make a mistake, fix it, period =P just no more cursing or any of that stuff lol

  121. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    ^_^" my bad, aha..

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

  124. anonymous
    • 5 years ago
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    or were my eyes twisted x_x

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

  126. anonymous
    • 5 years ago
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    oh yeah, LOL. My dearest apologies ^_^

  127. anonymous
    • 5 years ago
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    anyhow, I'm off to bed now, good night :) don't let me catch you cursing or overreacting next time =P

  128. anonymous
    • 5 years ago
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    lol, OK, bye

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