gistfile1.matlab

## Author: Andrew Brown
## Created: 2014-02-11
## Estimates cos using a Maclaurin series

function void = cosapprox (xrad, acceptable_error)
  # Get true cos(xrad) value for error analysis
  true_value = cos(xrad);

  # Estimate value with Maclaurin series
  term_index = 1;
  approx = 1;

  tic
  while true
    true_error   = abs(true_value - approx);
    approx_error = abs(true_error / true_value);

    if approx_error <= acceptable_error
      break
    end

    approx += ((-1)^term_index)*(xrad^(2 * term_index) / factorial(2 * term_index));
    term_index++;
  end
  toc

  fprintf('cos(%f) approximated to be %f\n', xrad, approx)
  fprintf('true error: %f\n', true_error)
  fprintf('approximate error: %f\n', approx_error)

endfunction

octave:50> cosapprox(1.0471975512, 0.00005)
Elapsed time is 0.0010159 seconds.
cos(1.047198) approximated to be 0.500000
true error: 0.000000
approximate error: 0.000001