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Math Help - sinx and cosx Taylor Formula

  1. #1
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    sinx and cosx Taylor Formula

    Find the Taylor's formula for the given function f at a=0. Find both the Taylor polynomial of the indicated degree n and the remainder term

    f(x)=sinx n=4
    f(x)=cosx n=4

    I thought the Taylor formula and the remainder term for f(x)=cosx n=4, was
    1 - ((x^2)/2!) + ((x^4)/4!) - ((x^6)/6!) + ((x^8)/8!) - ((sinz)(x^5))/5!

    However, the book tells me that the answer is 1 - ((x^2)/2!) + ((x^4)/4!) - ((sinz)(x^5))/5! . What am I doing wrong here and how should i solve f(x)=sinx n=4?
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  2. #2
    MHF Contributor chisigma's Avatar
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    The Taylor expansions of f(x)=\cos x around x=0 is...

     \cos x = a_{0} + a_{1}\cdot x + a_{2} \cdot x^{2} + a_{3}\cdot x^{3} + a_{4}\cdot x^{4} + R_{4} (x) =

    = 1 + 0\cdot x - \frac{x^{2}}{2} + 0\cdot x^{3} + \frac{x^{4}}{24} - \frac{\sin \theta}{120} \cdot x^{5} (1)

    ... so that your book is wright!... don't forget that for the function \cos x is a_{1} = a_{3} = 0 ...

    Kind regards

    \chi \sigma
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