For the Maclaurin series sinx=x−3!x3+5!x5−7!x7+⋯, let Pn(x) denote the polynomial obtained by keeping all terms up to and including x2n+1. What is the smallest integer n for which ∣sinx−Pn(x)∣<10−5 for every x in [−1,1]?
a) n=2
b) n=5
c) n=3
d) n=4