The cosine function can be evaluated by the following infinite series: cos x = 1

Question

The cosine function can be evaluated by the following infinite series: cos x = 1- x^2/2! + x^4/4! - x^6/6! +... Write an M-file to implement this formula so that it computes and prints out the values of cos x as each term in the series is added. Employ the library function for the cosine in your Matlab to determine the true value. In other words, compute and print in sequence the values for cos x = 1; cos x = 1- x^2/2!; up to the order term n of your choosing. For each of the preceding, cos x = 1 x^2/2! + x^4/4! compute and display percent relative error as % error = (true-series approximation)/true times 100%. Have the program print out the series approximation and the error at each step.

Explanation / Answer

clc;
clear all;
close all;
n=input(' Enter the number of terms u want in expantion ');
% % let x= pi/6
x=pi/3;
sum=0;
for k=0:n
sum=sum+(-1)^k*x^(2*k)/factorial(2*k);
cosx=sum;
cosx
p_err=abs(cos(x)-cosx)/cosx*100
  
end

output:

Enter the number of terms u want in expantion 3

cosx =

1

p_err =

50.0000

cosx =

0.4517

p_err =

10.6957

cosx =

0.5018

p_err =

0.3580

cosx =

0.5000

p_err =

0.0071

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