MATLAB: Taylor series calculation of sin(x)

for loopsinxtaylor series

hello! The problem I am having trouble with is this:
Calculate g(x) = sin(x) using the Taylor series expansion for a given value of x. Solve for g(pi/3) using 5, 10, 20 and 100 terms in the Taylor series (use a loop)
So I tried the following in the script editor:
 clear
 clc
 n = input('Enter number of iiterations (n): ' );
 x = pi/3;
 y = zeros(1,n);
 for i = 1:n
   y(i) = (-1)^i*x^(2*i+1)/factorial(2*i+1); 
 end
 SINx = sum(y);
however when i run the script, the value of SINx that I get isn't what sin(pi/3) is supposed to be and I just can't figure out why.

Best Answer

With that series, you need to sum starting from 0, not 1:
 for i = 0:n
   y(i+1) = (-1)^i*x^(2*i+1)/factorial(2*i+1); 
 end
Notice that I offset your indexing into the y variable, so that the i=0 term is the first one in the vector.
Related Question