Find $T_{5}(x)$, the degree $5$ Taylor polynomial of the function $f(x)= \cos(x)$ at $a = 0$.

$T_{5}(x) =$

Find all values of $x$ for which this approximation is within $0.003076$ of the right answer. Assume for simplicity that we limit ourselves to $|x| \leq 1$.

$|x| \leq$