Taylor polynomials practice question 9

The centre is $\dfrac{\pi}{6}$, not 0. At which point must each derivative be evaluated, and in powers of what is the polynomial written?

About $x = a$, $T_{2}(x) = f(a) + f'(a)(x - a) + \dfrac{f''(a)}{2!}(x - a)^{2}$. Here $a = \dfrac{\pi}{6}$.

$f'(x) = \cos x$ and $f''(x) = -\sin x$. At $\dfrac{\pi}{6}$, $\sin\dfrac{\pi}{6} = \dfrac{1}{2}$ and $\cos\dfrac{\pi}{6} = \dfrac{\sqrt{3}}{2}$.