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? Thanks!