function x = chebyshev3 ( n )

%*****************************************************************************80
%
%% chebyshev3() returns the Type 3 Chebyshev points.
%
%  Discussion:
%
%    Note that this point set is NOT symmetric in [-1,+1].
%    It is sometimes augmented by the value -1.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    02 March 2018
%
%  Author:
%
%    John Burkardt.
%
%  Input:
%
%    integer N, the number of points.
%
%  Output:
%
%    real X(N), the points.
%
  angle(1:n) = ( 2 * n - 2 * ( 1 : n ) + 1 ) * pi / ( 2 * n + 1 );
  x(1:n) = cos ( angle );

  return
end

