Approximating the sine function with polynomials.
> f1:=sin(x);
> g1:=x; g2:=g1-x^3/3!; g3:=g2+x^5/5!; g4:=g3-x^7/7!; g5:=g4+x^9/9!; g6:=g5-x^11/11!;
> plot({f1,g1,g2,g3,g4,g5,g6},x=-2*Pi..2*Pi,y=-5..5,scaling=constrained);
>