write the taylor series expansion for cos(x) in matlab

To write Taylor series expansion for cos(x) in MATLAB, we need to first define the x values and the number of terms in the expansion. The general formula for the Taylor series expansion of cos(x) is:

cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...

Here is the MATLAB code for calculating the Taylor series expansion of cos(x):

main.m
x = 0.5; % Value of x for cos(x)
n = 10; % Number of terms to include in the expansion
result = 0; % Initialize the result to zero

for i=0:n
    result = result + ((-1)^i*x^(2*i))/factorial(2*i);
end

disp(result); % Display the result
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In this code, we first define the value of x as 0.5 and the number of terms in the expansion as 10. We then initialize the result to zero and use a for loop to calculate each term in the expansion, summing them up in the result variable. We use the built-in MATLAB function factorial to calculate the factorials in each term.

When we run this code, it will output the value of the Taylor series expansion of cos(0.5) up to the 10th term. The more terms we include, the more accurate the result will be.