xi = [ 0 1 2 3 ];
f  = [ 1 1 1 1 ];
g  = xi.^2 - 3.5;
uTrue  = cos( (pi/180)*30*xi );

dot( f, g )

a = dot( uTrue, f )/dot( f, f );
b = dot( uTrue, g )/dot( g, g );

uApprox = a * f + b * g;

figure; hold on;
plot( xi, uApprox, '-or' );
plot( xi, uTrue, '-og' );
title( 'Approximation Comparison' );