Question

Please show exactly how it is in MATLAB

The cosine function can be evaluated by the following infinite series: cos ? = 1 − ?^2/ 2! + ?^4/ 4! − ?^6 /6! + ⋯ Create an M-file to compute cos(1.2345 rad) for up to and including eight terms, which is up to the term x^14/14!.

a) Your program should compute and display the values of cos ? as each term in the series is added, e.g.

cos ? = 1

cos ? = 1 − ?^2/ 2!

cos ? = 1 − ?^2 /2! + ?^4/ 4!

b) Compute and display the true relative error as a percentage ?? = true value−series approximation true value × 100%

Answer 1

ANS:

CODE:

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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