So for this question, I first had to find the Maclaurin polynomial of  f(x)=5\cos(0.2x) which I found to be  5[1-\frac{(0.2x^2)}{2}+\frac{(0.2x^4)}{4!}], and the second part asks:
"Find the largest integer k such that for all x for which |x|<1 the Taylor polynomial  T_{5}(x) approximates f(x) with error less than  10^{-k}.

I really don't know how to go about doing this. Do you have any suggestions?