Let $T_{k}(x)$ be the degree $k$ Taylor polynomial of the function $f(x) = \sin(x)$ at $a = 0$. Suppose you approximate $f(x)$ by $T_{k}(x)$. If $|x| \leq 1$, how many terms are needed (that is, what is $k$) to obtain an error less than $\frac{1}{6}$ ?

Hint: use the alternating series approximation.

Answer: