# taylor series

• Apr 27th 2009, 10:04 PM
buttonbear
taylor series
calculate sin(6) using a taylor series centered around 2pi. be accurate w/in .001.

so.. i know what the taylor series is for sin x.. i'm actually just confused about how you can calculate something if there's no finite n value.. it doesn't say calculate sin x from n=1 to 6, it says sin 6...can someone clear this up for me? =S
• Apr 28th 2009, 03:02 AM
HallsofIvy
Quote:

Originally Posted by buttonbear
calculate sin(6) using a taylor series centered around 2pi. be accurate w/in .001.

so.. i know what the taylor series is for sin x.. i'm actually just confused about how you can calculate something if there's no finite n value.. it doesn't say calculate sin x from n=1 to 6, it says sin 6...can someone clear this up for me? =S

The Taylor's series for function f about x= a is $\displaystyle \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x- a)^n$. What you need is "Lagrange's error estimate". If you Taylor's polynomial of degree N (dropping all terms with n> N) then the error is less than or equal to $\displaystyle \frac{M_{N+1}}{(N+1)!}|x-a|^{N+1}$ where $\displaystyle M_{N+1}$ is an upper bound on the N+1 derivative of f between a and x. You need to determine N so that error estimate is less than 0.001 and sum for n= 1 to N.