Let $T_{k}(x)$: be the taylor polynomial of degree k of the function $f(x) = \sin(x)$ at $a = 0$.
Suppose you approximate $f(x)$ by $T_{k}(x)$, and if $|x| \leq 1$, how many terms do you need (that is, what is k) for you to have your error to be less than $\frac{1}{6}$ ? (Hint: use the alternating series approximation.)