Solution
= Solution
Put $h=x-\pi/3$. The values $f(\pi/3)=1/2$, $f'(\pi/3)=-\sqrt3/2$, and $f''(\pi/3)=-1/2$ give the <Taylor expansion>
$$
\boxed{\cos x=\frac12-\frac{\sqrt3}{2}\left(x-\frac\pi3\right)
-\frac14\left(x-\frac\pi3\right)^2+O((x-\pi/3)^3)}.
$$
The <factorial> in the quadratic term accounts for its coefficient $-1/4$.