1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Taylor Polynomials and Numerical Analysis

  1. Jan 26, 2014 #1
    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. jcsd
  3. Jan 27, 2014 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What are you doing? We have ##|\text{error}| \leq (\pi/60)^{n+1}/(n+1)!##, and this must not exceed ##10^{-6}##.
  4. Jan 28, 2014 #3


    User Avatar
    Gold Member

    this is pretty tough to read. perhaps put it in latex and then we can check it out
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted