### Instruction: Compute $\cos 300^\circ$.### Response: I know that the cosine function is periodic with period $360^\circ$, so $\cos 300^\circ$ is the same as $\cos (300 - 360)^\circ = \cos (-60)^\circ$.
I also know that the cosine function is an even function, which means that $\cos (-x) = \cos x$ for any $x$.
Therefore, $\cos 300^\circ = \cos (-60)^\circ = \cos 60^\circ$.
Now I need to recall the value of $\cos 60^\circ$.
I remember that there is a special right triangle with angles $30^\circ, 60^\circ, 90^\circ$ and side lengths in the ratio $1:\sqrt{3}:2$.
If I draw this triangle and label the sides and angles, I can see that $\cos 60^\circ$ is the ratio of the adjacent side to the hypotenuse, which is $\frac{1}{2}$.