# MATLAB Help for expansion of cos(x) using a Taylor Series

1. Feb 11, 2010

### Tuttle917

I was hoping somebody would be able to help me as I am pretty new to Matlab. I am trying to create a for-loop to describe the taylor series expansion of cos(x)= (-1)^n*x^2n/(2n)! and to see how it converges towards cos(x). Below is the code that I have used to plot the different orders of n, but I was wondering if there was a way to make this work for any value of n?

n=0;
for x = -6:0.25:6
n=n+1;
y(n)=x;
F(n)=cos(x);
F0(n)=1;
F2(n)=1-0.5*x^2;
F4(n)=1-0.5*x^2+(1/24)*x^4;
end
plot(y,F,y,F0,y,F2,y,F4)
axis([-6 6 -1.5 1.5])

I have tried

n=0;
for x=(-2:.25:2)
n=n+1;
Y(n)=x;
F(n)=cos(x);
G(n)=1+(-1)^n*x^(2*n)/prod(1:2*n);
end
plot(y,G)

but the plot for G does not come close to cos(x) as the values of n are not constant and the plot goes to zero. Any help would be greatly appreciated.

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