The infinite series for $~\cos x~$ is given by
$\displaystyle\cos x=1-\frac{x^2}{2!}+\frac{{{x}^{4}}}{4!}-\frac{{{x}^{6}}}{6!}+...+\frac{{{\left( -1 \right)}^{n}}{{x}^{2n}}}{(2n)!}+...\,$
On the interval $~-1\le x\le 1\,$, what is the minimum number of terms necessary to approximate the value of $~\cos x~$ accurate to the nearest $~0.001\,$?
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