sin-series.sagews

x = var('x')
f(x) = 1/(1+exp(-x))
plot(f, -6, 6) + plot(f.diff(x), -6, 6, color='red')

%time
n = var('n')
cos_ser = sum((-1)^n * (x^(2*n+1) / factorial(2*n+1)), n, 0, 52)
s = str(cos_ser)
print s[:40], "…[%d chars]…" % len(s), s[-40:]
R = RealField(106)  # coercing float to higher precision
plot(lambda x : cos_ser(x=R(x)), (x, 30, 40))

1/10813967582402909005041013058003296497 …[4469 chars]… 9 - 1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x

CPU time: 0.98 s, Wall time: 0.68 s