Mathematics

Problem

The Maclaurin series for

\cos x

1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-\cdots

. Determine the smallest positive integer

N

such that the polynomial including terms up through

x^{2N}

approximates

\cos(0.7)

with an error less than

10^{-6}