Answer
We fill in the blank with $\cos$.
Work Step by Step
$$\sin\frac{2\pi}{3}=A\Big(-\frac{\pi}{6}\Big)\hspace{1cm}(1)$$
We notice that $$\frac{2\pi}{3}+\Big(-\frac{\pi}{6}\Big)=\frac{4\pi-\pi}{6}=\frac{3\pi}{6}=\frac{\pi}{2}$$
That means we can rewrite $(1)$ as
$$\sin\frac{2\pi}{3}=A\Big(\frac{\pi}{2}-\frac{2\pi}{3}\Big)$$
Now from the Cofunction Identity:
$$\sin\theta=\cos(\frac{\pi}{2}-\theta)$$
So $$A=\cos$$
In other words, we fill in the blank with $\cos$.
