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Math Help - Need help with Taylor Polynomial approximation

  1. #1
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    Need help with Taylor Polynomial approximation

    Please help with the following:

    Use a Taylor polynomial to approximate cos(0.75) with an error less than 0.001.

    Thanks!
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  2. #2
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    Re: Need help with Taylor Polynomial approximation

    You should know that \displaystyle \begin{align*} \cos{x} = \sum_{n = 0}^{\infty} \frac{(-1)^n \, x^{2n}}{(2n)!} \end{align*}. So let \displaystyle \begin{align*} x = 0.75 \end{align*} and keep adding terms until you reach your required accuracy (i.e. stop when you have enough digits repeating).
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    Re: Need help with Taylor Polynomial approximation

    so you get:

    1 - (0.75^2/2) +(0.75^4/4!) - (0.75^6/6!).....

    would the polynomial answer just be the first 3 terms (up to the 4th power)?
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    Re: Need help with Taylor Polynomial approximation

    Quote Originally Posted by kimsanders82 View Post
    so you get:

    1 - (0.75^2/2) +(0.75^4/4!) - (0.75^6/6!).....

    would the polynomial answer just be the first 3 terms (up to the 4th power)?
    Get a decimal answer each time you add a term, keep going until you have the first three decimal places matching
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