function s = nTermSine1(x,n)
% nTermSine1  Evaluate the n-term series approximation to sin(x)
%             Simplest approach: evaluate each term from scratch
%
% Synopsis:  s = nTermSine1(x,n)
%
% Input: x = argument of sine(x)
%        n = number of terms in the series
%
% Output: s = approximation to sin(x) with n terms of the series

term = x;
s = term;   %  Initialize the sum and the sign of the term
sgn = 1;
fprintf('\n    i   sign    k        term             s\n');
fprintf(' %4d  %4d  %4d  %18.13f  %8.5f\n',1,sgn,1,term,s);
for i=2:n
  sgn = -sgn;          %  switch sign of term
  k = 2*i - 1;
  term = sgn*(x^k)/factorial(k);
  s = s + term;
  fprintf(' %4d  %4d  %4d  %18.13f  %8.5f\n',i,sgn,k,term,s)
end