### Instruction: Compute $\cos 330^\circ$.### Response: I know that $\cos 330^\circ$ is the same as $\cos (-30^\circ)$, since rotating 330 degrees counter-clockwise is the same as rotating 30 degrees clockwise.
I also know that $\cos (-\theta) = \cos \theta$ for any angle $\theta$, since cosine is an even function.
So I can simplify $\cos 330^\circ$ to $\cos 30^\circ$.
Now I recall that $\cos 30^\circ$ is one of the special angles that has a nice expression in terms of radicals.
I can use the 30-60-90 right triangle to find it.
In such a triangle, the hypotenuse is 2, the shorter leg is 1, and the longer leg is $\sqrt{3}$.
The angle opposite the shorter leg is 30 degrees, so $\cos 30^\circ$ is the ratio of the adjacent side to the hypotenuse.
That means $\cos 30^\circ = \frac{\sqrt{3}}{2}$.