Improving Cosine Approximation Using Taylor Series in Matlab

[StaloyT]

Homework Statement

Write a user-defined function that determines cos(x) using Taylor Series expansion
Stop adding terms when estimated error, E<=.000001

Homework Equations

sum S_n = S_n-1 + a_n
E = | (S_n - S_n-1)/S_n-1 |

The Attempt at a Solution

function y = cosTaylor(x)
Sn=1;
Snm1=0;
n=2;
xr=x*pi/180;
E=1;
while E >= .000001
an=(-1)^n*xr^(2*n)/(factorial(2*n));
Snm1=Sn;
Sn=Snm1+an;
n=n+1;
E=abs((Sn-Snm1)/Snm1);
end


This gives values too large compared to what they should be.
I really don't understand why this doesn't work.
Any help is appreciated.
Thanks in advance!

 

[CEL]

Why did you start n as 2? It should be 1, since in your formula for an you use 2*n.
Starting with n = 2, your first term is added to 1, making the cosine greater than unity. The following terms have absolute values smaller than the first, so you will have always too large results.