anonymous
  • anonymous
Taylor series for sinx centered at (pi)/3?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
that is a longish calculation, I can help if you tell me where you are stuck
anonymous
  • 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)
anonymous
  • anonymous
was on a test earlier, i just havent gotten it out of my brain

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anonymous
  • anonymous
but i just couldnt figure a way to put those values into the series at all
anonymous
  • 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
anonymous
  • anonymous
and the summation is missing
anonymous
  • 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
anonymous
  • anonymous
and i dnt think she wasaccepting that, otherwise *spoiler* everyone would see that loophole and pass =P
anonymous
  • anonymous
:) yeah I dont think that is fine.
anonymous
  • anonymous
exactly haha
anonymous
  • anonymous
wait a sec I get a pen and a paper and figure it out
anonymous
  • anonymous
ok, thanks. its just been bugging me like crazy
anonymous
  • anonymous
\[\sqrt{3}/2 \sum_{0}^{\infty}((-1)^{2n}/(2n!))*(x-\pi/3)^{2n}\] + \[1/2 \sum_{1}^{\infty}((-1)^{2n}/(2n+1!))*(x-\pi/3)^{2n+1}\]
anonymous
  • anonymous
I had two beers tonight so I might done some mistakes, but I guess it is correct. Ask if something isnt clear
anonymous
  • anonymous
@_@ my teacher is a troll lol. Gah she even said she expected nobody to solve it. Now I see why
anonymous
  • anonymous
and i do have one quick question
anonymous
  • anonymous
is this at high school?
anonymous
  • anonymous
if im not mistaken, wouldnt the (-1)^2n leave every term as positive?
anonymous
  • anonymous
an ye
anonymous
  • anonymous
high school
anonymous
  • anonymous
yes it would my bad, it should be just n for both
anonymous
  • anonymous
kinda wish the problems were harder in general so im used to them
anonymous
  • anonymous
buuuuuuut they have to bring iit down a bit, i guess, and im lazy -_-
anonymous
  • anonymous
I did not do this at high school, but I will have an exam about this in 3 weeks
anonymous
  • anonymous
an ok, thhanks a lot =D big help
anonymous
  • anonymous
my exam on ap calc ab/bc is next week. got some sample questions, not too bad
anonymous
  • anonymous
If you are interested in these series check the Fourier series, or ask your teacher about it. I think they are beautiful. :-)
anonymous
  • anonymous
will do, cuz i love all these dif things
anonymous
  • anonymous
just to joke around in class, ill put -e^(pi*i) in front of my answers =P
anonymous
  • 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
anonymous
  • anonymous
o, ok... that sounds like it could be awesome
anonymous
  • anonymous
one of my fav equation is e^ipi+1=0
anonymous
  • anonymous
has all the important bits of maths in it
anonymous
  • anonymous
like we were explained how taylors were often used in calculator scripts to calculate until a given tolerance was reached
anonymous
  • anonymous
are you living in the US?
anonymous
  • 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
anonymous
  • anonymous
an ye
anonymous
  • anonymous
when I graduate I might go there to teach :-)
anonymous
  • anonymous
o cool. where r u studying?
anonymous
  • anonymous
York university (UK)
anonymous
  • anonymous
o cool
anonymous
  • anonymous
math major or another?
anonymous
  • 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
anonymous
  • anonymous
teacher did that with me and i basically figured out a whole chapter on my own. i was like =DDDDDDD best teacher ever
anonymous
  • 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
anonymous
  • anonymous
thx for the advice, I will keep in mind. Yes maths major
anonymous
  • anonymous
o cool. one other question: what is non-euclidian geometry good for/ if u kno? sounds... i dnt even
anonymous
  • anonymous
well I know what it is, but I dont know why is it good :) it has interesting properties that is for sure
anonymous
  • anonymous
like parallel lines? mind=blown when i found out they intersected
anonymous
  • anonymous
if there is a given line and a point, how many parallel lines can you make from that point?
anonymous
  • anonymous
:DD nice one
anonymous
  • anonymous
it can be 0/1/2
anonymous
  • 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
anonymous
  • anonymous
knowing my desired field, im probbly gonna be using some of this
anonymous
  • anonymous
they are in 3d
anonymous
  • anonymous
(physics, dream=job in researchin stuff then teachin at a university)
anonymous
  • anonymous
if the plane is a sphere or a ellipsoid
anonymous
  • anonymous
my dad is a physics teacher, but I prefer maths
anonymous
  • 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
anonymous
  • anonymous
but I might take some astrophysics next year
anonymous
  • 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
anonymous
  • anonymous
them together=braingasm
anonymous
  • anonymous
dont ask a lot about these planes because I never learnt about them, just read a few things
anonymous
  • anonymous
nice nice :) I love mechanics
anonymous
  • anonymous
ah ok. well, i think its enough to keep me thinkin bout it. might look it up myself soon
anonymous
  • anonymous
some1 gave me a medal and became my fan, but dont know why :D
anonymous
  • anonymous
o nice haha. i may, but just cuz this is the most interesting convo ive had on here =P
anonymous
  • anonymous
now I know why, I helped with graphing a line
anonymous
  • anonymous
matrices are also a really interesting topic for me. There are bits that are boring but others are really funky
anonymous
  • 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
anonymous
  • 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
anonymous
  • anonymous
well, ive gotta go finish up some homework. been great talkng, take care =D

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