#sin(a_*x_):= if(a<0,-sin(-a*x) );
sin(-x_):= -sin(x);
sin(0.5pi+x_):= cos(x);
sin(-0.5*pi+x_):= -cos(x);
sin(0.5pi-x_):= cos(x);
sin(asin(x_)):=x;
sin(2pi+x_):=sin(x);
sin(-2pi+x_):=sin(x);
sin(pi+x_):= -sin(x);
sin(-pi+x_):= -sin(x);

sin(pi) := 0;
sin(2pi):=0;
sin(3pi):=0;
sin(0.25*pi):=sqrt(2)/2;
sin(0.5*pi):=1;
sin(1.5*pi):=-1;
sin(-2pi):=0;
sin(-3pi):=0;
sin(-0.5*pi):=1;
sin(-1.5*pi):=-1;

sin(1,0):=1;
sin(2,0):=0;