% script sin2.m
% Loss of significance example x - sin(x)
% Evaluation of x - sin(x) to lose one binary digit
% using loss of significance theorem

% We can use the loss of significance theorem to
% determine an x such that we lose at most 1
% significant binary digit. We must find an x such that
% the function 1 - sin(x)/x -1/2 is positive.
% Graph the function to do this

y = @(x) 1 - sin(x)/x - 1/2;
fplot(y, [1.8, 2.0])
grid on;

% The graph shows that x = 1.9 is a suitable value
% we need to evaluate Taylor series for x - sin(x)
% to order 21 to get required accuracy since
% 1.9^23/23! (first term omitted) is about 0.997E-16