Taylor series for sinx centered at (pi)/3?

- anonymous

Taylor series for sinx centered at (pi)/3?

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- katieb

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- anonymous

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

- 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

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

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- anonymous

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

- 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

and the summation is missing

- 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

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

- anonymous

:) yeah I dont think that is fine.

- anonymous

exactly haha

- anonymous

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

- anonymous

ok, thanks. its just been bugging me like crazy

- 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

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

- anonymous

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

- anonymous

and i do have one quick question

- anonymous

is this at high school?

- anonymous

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

- anonymous

an ye

- anonymous

high school

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

an ok, thhanks a lot =D big help

- anonymous

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

- anonymous

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

- anonymous

will do, cuz i love all these dif things

- anonymous

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

- 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

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

- anonymous

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

- anonymous

has all the important bits of maths in it

- anonymous

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

- anonymous

are you living in the US?

- 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

an ye

- anonymous

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

- anonymous

o cool. where r u studying?

- anonymous

York university (UK)

- anonymous

o cool

- anonymous

math major or another?

- 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

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

- 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

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

:DD nice one

- anonymous

it can be 0/1/2

- 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

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

- anonymous

they are in 3d

- anonymous

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

- anonymous

if the plane is a sphere or a ellipsoid

- anonymous

my dad is a physics teacher, but I prefer maths

- 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

but I might take some astrophysics next year

- 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

them together=braingasm

- anonymous

dont ask a lot about these planes because I never learnt about them, just read a few things

- anonymous

nice nice :) I love mechanics

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

now I know why, I helped with graphing a line

- anonymous

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

- 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

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

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

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