Approximating the sine function with polynomials.

> f1:=sin(x);

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!;

g1 := x

g2 := x-1/6*x^3

g3 := x-1/6*x^3+1/120*x^5

g4 := x-1/6*x^3+1/120*x^5-1/5040*x^7

g5 := x-1/6*x^3+1/120*x^5-1/5040*x^7+1/362880*x^9

g6 := x-1/6*x^3+1/120*x^5-1/5040*x^7+1/362880*x^9-1...

> plot({f1,g1,g2,g3,g4,g5,g6},x=-2*Pi..2*Pi,y=-5..5,scaling=constrained);

[Maple Plot]

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