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Math Help - taylor series

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by buttonbear View Post
    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 \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 \frac{M_{N+1}}{(N+1)!}|x-a|^{N+1} where 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.
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