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: Calculating Forward and Backwards error of the sine function

  1. Jan 29, 2010 #1
    1. The sine function is given by the infinite series
    sin(x) = x - x3/3! + x5/5! + x7/7! + .......
    a) What are the forward and backward errors if we approximate the sine function
    by using only the first term in the series, for x = 0.1, 0.5, 1.0?
    b) Using the first two terms.

    2. Relevant equations

    Forward Error: Fhat - F
    Backward Error:xhat - x

    Fhat is the function approximation.
    Xhat is the input modification used to calculate the backward error.

    This is basically from my Numerical Methods Course.

    3. The attempt at a solution

    I don't have any problem with the Forward Error analysis.

    For part a. I simply evaluated the original sin(x) function with x = .1 and got a number. Then evaluated the approximation function Fhat = x

    [ this is the sin function expanded into the Taylor series.. but only using the first term of the series]

    and then I used the F. Error equation to get the answer...

    The problem is the backward error where I have to satisfy this equation:

    F(xhat) = Fhat(x) Basically I want a xhat that when put into the original sin function will output my approximation function.

    I can't figure this out.. at all. I mean. the only time sin(x) = x is when x = 0? or am i wrong? What am i missing here? It has to be trivial!

    I mean if my function was the exponential function then my xhat would be log(Fhat) so e^xhat outputs the Fhat function.. thats easy.. but how is that applied to the sin(x) = x condition?

  2. jcsd
  3. Jan 29, 2010 #2
    NVM. I feel so retarded.

    I figured it out. Obviously it would be the inverse Sin(x) function that would allow me to calculate the backwards error..

    SO obvious wow.
  4. Jan 30, 2010 #3
    You're probably very far from being retarded :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook