Answer
$n=2$
Work Step by Step
$cos x = \Sigma^{\infty}_{n=0} (-1)^{n} \frac{x^{2n}}{(2n)!} = 1- \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} + ... $
$c=0$
$|R_{n}(x)| = \frac{(x-c)^{n+1}}{(n+1)!} max |f^{n+1}(z)|$
$|R_{1}(0.1)| = \frac{(0.1-0)^{1+1}}{(1+1)!}(1) \approx 0.005 \gt 0.001$
$|R_{2}(0.1)| = \frac{(0.1-0)^{2+1}}{(2+1)!}(1) \approx 0.000177 \lt 0.001$
2nd degree polynomial needed
$cosx \approx \frac{x^2}{2!}$
