The Maclaurin series expansion for the cosine function up to

The Maclaurin series expansion for the cosine function up to some number of terms is given by

cos(x) = 1 x 2 2! + x 4 4! x 6 6! + x 8 8! · · · , x n n! ,

where x is the angle in radians and n! denotes the factorial of n. For example, the cosine approximations for one, three, and five terms are as follows:

cos(x) = 1

cos(x) = 1 x 2 2! + x 4 4!

cos(x) = 1 x 2 2! + x 4 4! x 6 6! + x 8 8!

Write a function cosineApprox that takes scalar input arguments x and the number of terms t, and returns the approximate value of cos(x). So, the function will be invoked as follows:

approx = cosineApprox(x, t);

Use a for loop in your code to calculate the cosine approximation up to the specified number of terms. Use the built-in MATLAB function factorial when computing the series expansion. Assume that x is in radians. Examples of correct function behavior for various values of x and t follow:

>> x = 2*pi/3;

>> actual = cos(x)

actual = -0.5000

>> approx = cosineApprox(x, 2)

approx = -1.1932

>> approx = cosineApprox(x, 5)

approx = -0.4996

>> approx = cosineApprox(x, 10)

approx = -0.5000

Solution

% matlab code to approximate cosine value using maclaurian series

function approx = cosineApprox(x,t)
approx=1;
for i=1:1:t-1
addterm = (-1)^i*(x^(2*i))/factorial(2*i);
approx = approx + addterm;
end
end

x = 2*pi/3;
actual = cos(x);
disp(\"Original value: \");
disp(actual);
t = input(\"Enter number of terms: \");
approx = cosineApprox(x,t);
disp(\"Approximate Value: \");
disp(approx);

%{
output:

Original value:   
-0.50000
Enter number of terms: 5
Approximate Value:
-0.49957

%}