Taylor series calculation of sin(x)

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.

[mehrab aslam]

recall the taylor series expansion of sin(x)=x-x^3/3!+... for i=1 , x is not calculated

[shikha sharma]

Angle is taken in radian by MATLAB

Answer 1

[the cyclist]

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.

[Andy]

Thank you so much! It works!

[Walter Roberson]

Wajih Sohail comments to the cyclist:

Thanks it helped!

[Fritz Ulysse]

how do you do it for f(x)=e^x

[Walter Roberson]

exp(x) is sum of (x^N)/(N!) for N = 0 to infinity