# Need help with Taylor Polynomial approximation

• Nov 6th 2012, 04:27 AM
kimsanders82
Need help with Taylor Polynomial approximation

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

Thanks!
• Nov 6th 2012, 05:27 AM
Prove It
Re: 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 AM
kimsanders82
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)?
• Nov 6th 2012, 03:22 PM
Prove It
Re: Need help with Taylor Polynomial approximation
Quote:

Originally Posted by kimsanders82
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 :)