using the first two terms of the Maclaurin series for y=cos(x) yields to within 0.001 over the interval |x| < k when k=
(A) 0.032
(B) 0.394
(C) 0.786
(D) 0.788
(E) 1.570
The series for cosine is alternating, so the error is less than the next term (the third one) in magnitude, so you can have $\displaystyle {x^4\over4!} \leq 0.001$.
As an afterthought, this is a dumb multiple choice question. Why not just always pick the smallest number?