>	taylor(sin(x),x=0,6);

>	T5:=x->1*x-1/6*x^3+1/120*x^5;

>	plot({sin(x),T5(x)},x=0..7.5,y=-10..10,thickness=2);

>	taylor(sin(x),x=0,10);

>	T10:=x->1*x-1/6*x^3+1/120*x^5-1/5040*x^7+1/362880*x^9;

>	plot({sin(x),T10(x)},x=0..7.5,y=-10..10,thickness=2);

>	taylor(sin(x),x=0,16);

>	T15:=x->1*x-1/6*x^3+1/120*x^5-1/5040*x^7+1/362880*x^9-1/39916800*x^11+1/6227020800*x^13-1/1307674368000*x^15;

>	plot({sin(x),T15(x)},x=-3..7.5,y=-3..3,thickness=2);

>	evalf(sin(6));

>	evalf(T15(6));

>	evalf(sin(6)-T15(6));

>	evalf(T15(6-2*Pi));

>	evalf(sin(6)-T15(6-2*Pi));

>	evalf(T5(6-2*Pi));

>	evalf(sin(6)-T5(6-2*Pi));

>	T3:=x->1*x-1/6*x^3;

>	evalf(T3(6-2*Pi));

>	evalf(sin(6)-T3(6-2*Pi));

>	evalf(T3(6-2*3.14159));

>	evalf(sin(6)-T3(6-2*3.14159));

>	plot({sin(x),T3(x),T5(x),T10(x),T15(x)},x=-8..8,y=-10..10,thickness=2);

>	evalf[2009](sin(6));

>

>