### Instruction: Compute $\cos 150^\circ$.### Response: Hey, I know a quick trick for this one.
Really, what is it?
We know that $\cos(90^\circ + \theta) = -\sin \theta$.
That's true, but what does that have to do with the problem?
We can write $150^\circ$ as $90^\circ + 60^\circ$.
Ok, so $\cos 150^\circ = \cos (90^\circ + 60^\circ)$.
So using the identity, we know that $\cos 150^\circ = -\sin 60^\circ$.
Ok, and we know that $\sin 60^\circ = \sqrt{3}/2$.