# Taylor Polynomials and Numerical Analysis

1. Jan 26, 2014

### mynorka

1. The problem statement, all variables and given/known data
Use a Taylor Polynomial about pi/4 to approximate cos(42){degrees} to an accuracy of 10^-6.

*To get an accuracy of 10^-6, use the error term to determine an nth Taylor Polynomial to use.

2. Relevant equations
x = 45 or pi/4, x0 = 42 or 7pi/30

cos(x) = Pn(x) + Rn(x)

Polynomial Term - Pn(x) = ∑f^(k)(x-x0)^k/(k)!

Error Term - Rn(x) = f^(n+1)(ζ(x))(x-x0)^(n+1)/(n+1)!

3. The attempt at a solution
(pi/60)^n/(n+1)! < ((-60/pi)*10^-6)/pi

^I get stuck at this part. I'm supposed to solve for n, but the left-hand side of this inequality confuses me.

2. Jan 27, 2014

### Ray Vickson

What are you doing? We have $|\text{error}| \leq (\pi/60)^{n+1}/(n+1)!$, and this must not exceed $10^{-6}$.

3. Jan 28, 2014

### joshmccraney

this is pretty tough to read. perhaps put it in latex and then we can check it out