function [ fcos ] = cosine( x, n )
%Cosine Provides the cosine (cos x) of the input
%   cosine(x) takes a matrices of values (in radians) and outputs a
%   matrices containing an approximate cosine of each value in the matrix.
%
%   cosine(x) takes a matrices 'x' and returns the cosines. Tbe default
%   number of values in the series is 10.
%   cosine(x) takes a matrices 'x' and 'n', the number of values in the
%   series, and returns a matrices of the cosines of 'x'.
if (nargin < 2)  ||  isempty(n)
        n = 10;
end
validateattributes(x, {'numeric'}, {'finite', 'real', 'finite'});
validateattributes(n, {'numeric'}, {'integer', 'scalar', 'finite', 'positive'});
[columns, rows] = size(x);
fcos = zeros(columns,rows);
for i = 1:numel(x)
    fcos(i) = (sum(((-1).^(0:n)).*(x(i).^(2*(0:n)))./(factorial(2*(0:n)))));
end
if numel(fcos)~=numel(x)
    error('cosine:inputoutputmismatch','The output matrix is smaller than the input matrix')
end