Exemple 2 p 84.sagews

var('x')

x

T1(x) = x
T3(x) = T1(x) - x^3/factorial(3)
T5(x) = T3(x) + x^5/factorial(5) 

xmin = -pi
xmax = pi
G = plot(T1(x), (x, xmin, xmax), color='blue')
G+= plot(T3(x), (x, xmin, xmax), color='orange')
G+= plot(T5(x), (x, xmin, xmax), color='red')
G+= plot(sin(x), (x, xmin, xmax), color='green')
show(G)

y = sin(12*pi/180)
y.n()

0.207911690817759

yapprox = T5(12*pi/180)
yapprox.n()

0.207911694322979

R5(x) = sin(x)-T5(x)
erreur = R5(12*pi/180)
erreur.n()

-3.50521932397065e-9