## anonymous 5 years ago Taylor series for sinx centered at (pi)/3?

1. anonymous

that is a longish calculation, I can help if you tell me where you are stuck

2. anonymous

well, if i recall i got down to the expansion but the coefficients to eachterm were alternating values (i thinnk it went rt(3)/2, 1/2, (-rt(3)/2, -1/2)

3. anonymous

was on a test earlier, i just havent gotten it out of my brain

4. anonymous

but i just couldnt figure a way to put those values into the series at all

5. anonymous

yeah that is right. the formula for the taylor series is T=fn(x)/n! *(x-a)^n where fn(x) is the nth derivative

6. anonymous

and the summation is missing

7. anonymous

ye, that i know, but those values... the only way i could figure to put them into the series was leaving an f^n((pi)/3) in there

8. anonymous

and i dnt think she wasaccepting that, otherwise *spoiler* everyone would see that loophole and pass =P

9. anonymous

:) yeah I dont think that is fine.

10. anonymous

exactly haha

11. anonymous

wait a sec I get a pen and a paper and figure it out

12. anonymous

ok, thanks. its just been bugging me like crazy

13. anonymous

$\sqrt{3}/2 \sum_{0}^{\infty}((-1)^{2n}/(2n!))*(x-\pi/3)^{2n}$ + $1/2 \sum_{1}^{\infty}((-1)^{2n}/(2n+1!))*(x-\pi/3)^{2n+1}$

14. anonymous

I had two beers tonight so I might done some mistakes, but I guess it is correct. Ask if something isnt clear

15. anonymous

@_@ my teacher is a troll lol. Gah she even said she expected nobody to solve it. Now I see why

16. anonymous

and i do have one quick question

17. anonymous

is this at high school?

18. anonymous

if im not mistaken, wouldnt the (-1)^2n leave every term as positive?

19. anonymous

an ye

20. anonymous

high school

21. anonymous

yes it would my bad, it should be just n for both

22. anonymous

kinda wish the problems were harder in general so im used to them

23. anonymous

buuuuuuut they have to bring iit down a bit, i guess, and im lazy -_-

24. anonymous

I did not do this at high school, but I will have an exam about this in 3 weeks

25. anonymous

an ok, thhanks a lot =D big help

26. anonymous

my exam on ap calc ab/bc is next week. got some sample questions, not too bad

27. anonymous

If you are interested in these series check the Fourier series, or ask your teacher about it. I think they are beautiful. :-)

28. anonymous

will do, cuz i love all these dif things

29. anonymous

just to joke around in class, ill put -e^(pi*i) in front of my answers =P

30. anonymous

the taylor series only gives a good approximation about a function at a given point. The Fouries series gives for every point of the function. Also it is used a lot in life. JPEG, MP3

31. anonymous

o, ok... that sounds like it could be awesome

32. anonymous

one of my fav equation is e^ipi+1=0

33. anonymous

has all the important bits of maths in it

34. anonymous

like we were explained how taylors were often used in calculator scripts to calculate until a given tolerance was reached

35. anonymous

are you living in the US?

36. anonymous

an ye. im kind of self-discovering more and more about that neat little equation on my own. still need to find some proof of it or something so i canrelate it into everything else

37. anonymous

an ye

38. anonymous

when I graduate I might go there to teach :-)

39. anonymous

o cool. where r u studying?

40. anonymous

York university (UK)

41. anonymous

o cool

42. anonymous

math major or another?

43. anonymous

also, when u teach, please do ur students a favor. intrigue the ones that carewith stuff theyve never heard of and theyll ask about it over and over an mybe even figure it out on their own

44. anonymous

teacher did that with me and i basically figured out a whole chapter on my own. i was like =DDDDDDD best teacher ever

45. anonymous

and that was just from mentioning one sentence about it =P so either im a huge nerd and love it or i dnt even know

46. anonymous

thx for the advice, I will keep in mind. Yes maths major

47. anonymous

o cool. one other question: what is non-euclidian geometry good for/ if u kno? sounds... i dnt even

48. anonymous

well I know what it is, but I dont know why is it good :) it has interesting properties that is for sure

49. anonymous

like parallel lines? mind=blown when i found out they intersected

50. anonymous

if there is a given line and a point, how many parallel lines can you make from that point?

51. anonymous

:DD nice one

52. anonymous

it can be 0/1/2

53. anonymous

hm... ok. so.... if the definition of parallel is slightly altered... im having random thoughts atm like 4d non-flat planes an stuff. idk if those r even possible, but im tryin to think of themm

54. anonymous

knowing my desired field, im probbly gonna be using some of this

55. anonymous

they are in 3d

56. anonymous

(physics, dream=job in researchin stuff then teachin at a university)

57. anonymous

if the plane is a sphere or a ellipsoid

58. anonymous

my dad is a physics teacher, but I prefer maths

59. anonymous

ok. so spherical planes... ok, im starting to see how some of this might work. tho im probbly wrong =P just tying it to some things ive heard

60. anonymous

but I might take some astrophysics next year

61. anonymous

well, i like physics just cuz of how math-intensive it is, in addition to how some cutting edge research keeps my curiosity going constantly

62. anonymous

them together=braingasm

63. anonymous

64. anonymous

nice nice :) I love mechanics

65. anonymous

ah ok. well, i think its enough to keep me thinkin bout it. might look it up myself soon

66. anonymous

some1 gave me a medal and became my fan, but dont know why :D

67. anonymous

o nice haha. i may, but just cuz this is the most interesting convo ive had on here =P

68. anonymous

now I know why, I helped with graphing a line

69. anonymous

matrices are also a really interesting topic for me. There are bits that are boring but others are really funky

70. anonymous

o haha. i feel horrible when i try to help some ppl.... ill say something and then they wont get it cuz ill explain it before knoiwing their math level

71. anonymous

an o. i havent dealt much with matrices. tho i need to. they just havent been stressed in any of my classes for some reason

72. anonymous

well, ive gotta go finish up some homework. been great talkng, take care =D