Taylor series calculation of sin(x)

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Andy
Andy 2014-4-5
评论： shikha sharma 2021-8-26
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.
  2 个评论
mehrab aslam
mehrab aslam 2019-10-21
recall the taylor series expansion of sin(x)=x-x^3/3!+... for i=1 , x is not calculated

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the cyclist
the cyclist 2014-4-5
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.
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Walter Roberson
Walter Roberson 2016-11-7
exp(x) is sum of (x^N)/(N!) for N = 0 to infinity

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