% -----------------------------------------------------
% forloop_cosxtaylorseries.m
% -----------------------------------------------------
% Write a program to compute the value of cos(x) using the taylor series
% expansion of the cosine function. The program should work for any value
% of x (in radians) and any number of terms in the taylor series N. Also
% compute the value of cos(x) using the cos function in MATLAB.
% -----------------------------------------------------
% Notes: This can also be done using vectors only. This is left to the
% user as a practice problem.
% -----------------------------------------------------
% Priya Thamburaj Goeser
% Original: January 10th 2011
% Modified: March 5th 2012
% Copyright (c) 2012 Priya Thamburaj Goeser.
% All Rights Reserved.
%------------------------------------------------------
clear all
clc
% Define the angle x in radians and the number of terms N
x=pi/6;
N=10;
% for loop with counter k, k starts at 0,
% has an increment of 1, ends at N.
for k=0:1:N
% Compute each term in the series,
% one at a time for each k.
% The term is computed and assigned
% to the (k+1)th position since the
% index of a vector must be positive integers only.
terms(k+1)=((-1)^k)*...
(x^(2*k))/factorial(2*k);
% The ... defines continuation of the same command line.
end;
% Compute the sum of all the terms
f_costaylorseries=sum(terms);
% Compute the value of the function cos(x) using the cos function
f_cos=cos(x);
% display both results for comparison
disp('The value of cos(x) using the cos function');
disp(f_cos);
disp('The value of cos(x) using the taylor series');
disp(f_costaylorseries);
% Quiz questions:
% What is the value of k after this program has been executed (run)?
% Re-write this program without using a loop.