Solving Backward Interpolation Problem | Explanation and Solution

[Ahmedzica]

Hi guys,

I was solving this problem using backward interpolation
https://dl.dropboxusercontent.com/u/49829206/1.PNG

and I got this solution

https://dl.dropboxusercontent.com/u/49829206/3.PNG

but What I don't get is that how come is the the forth difference is constant while it not in real because forth difference of sin(x) will be either cos(x) or sin(x)

Edit: images replaced with links, please don't post images wider than about 800 pixels.

 

[mfb]

The 4th difference is neither a cos nor a sin, but the 4th difference is small if you restrict the analysis to the range 25° to 45°. Therefore, the assumption that the 3th difference is constant gives a good approximation. This method is similar to a Taylor series.