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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- Nov 6th 2012, 04:27 AMkimsanders82Need 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! - Nov 6th 2012, 05:27 AMProve ItRe: Need help with Taylor Polynomial approximation
You should know that $\displaystyle \displaystyle \begin{align*} \cos{x} = \sum_{n = 0}^{\infty} \frac{(-1)^n \, x^{2n}}{(2n)!} \end{align*}$. So let $\displaystyle \displaystyle \begin{align*} x = 0.75 \end{align*}$ and keep adding terms until you reach your required accuracy (i.e. stop when you have enough digits repeating).

- Nov 6th 2012, 06:20 AMkimsanders82Re: 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)? - Nov 6th 2012, 03:22 PMProve ItRe: Need help with Taylor Polynomial approximation