4105.sagews

var('x')
f = sin(x)
p1 = f.taylor(x, 0, 1)
p3 = f.taylor(x, 0, 3)
p5 = f.taylor(x, 0, 5)
p5

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{120} \, x^{5} - \frac{1}{6} \, x^{3} + x

graph = plot( f, x, -pi, pi, rgbcolor='red')
graph= graph + plot( p1, x, -pi, pi, rgbcolor='orange')
graph= graph + plot( p3, x, -pi, pi, rgbcolor='green')
graph= graph + plot( p5, x, -pi, pi, rgbcolor='blue')
show(graph)