create a script for the taylor series of cos(x) in matlab

main.m
function [y] = cos_taylor_series(x, num_terms)
% This function computes the Taylor series of cos(x)
% up to a given number of terms.
%
% Inputs:
%   x: angle (in radians) at which to evaluate the Taylor series
%   num_terms: number of terms to include in the series
%
% Output:
%   y: estimated value of cos(x) using the Taylor series

% Initialize variables
y = 0;
sign = 1;
fact = 1;

% Evaluate the Taylor series
for n = 0:num_terms-1
    term = sign * (x^(2*n)) / fact;
    y = y + term;
    sign = -sign;
    fact = fact * (2*n+1) * (2*n+2);
end

end
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In this script, cos_taylor_series(x, num_terms) is a function that takes two inputs: x is the angle (in radians) at which to evaluate the Taylor series, and num_terms is the number of terms to include in the series. The output y is the estimated value of cos(x) using the Taylor series.

The script evaluates the Taylor series using a for loop, where n is the loop index. Inside the loop, the term variable represents each term in the series, and y accumulates the sum of all the terms. The sign variable alternates between positive and negative, and fact updates as needed to compute the factorial in each term.