# Thread: Need help with Taylor Polynomial approximation

1. ## Need help with Taylor Polynomial approximation

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

Thanks!

2. ## 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).

3. ## 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)?

4. ## Re: Need help with Taylor Polynomial approximation

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