% Program 3.3 Building a sin calculator key, attempt #1
% Approximates sin curve with degree 3 polynomial
%     (Caution: do not use to build bridges,
%     at least until we have discussed accuracy.)
% Input:  x
% Output: approximation for sin(x)
function y=sin1(x)
% First calculate the interpolating polynomial and 
%   store coefficients
b=pi*(0:3)/6;yb=sin(b);    % b holds base points
c=newtdd(b,yb,4);
%For each input x, move x to the fundamental domain and evaluate
%      the interpolating polynomial
s=1;                       % Correct the sign of sin
x1=mod(x,2*pi);
if x1>pi
  x1 = 2*pi-x1;
  s = -1;
end
if x1 > pi/2
  x1 = pi-x1;
end
y = s*nest(3,c,x1,b);