### Instruction: Compute $\cos 60^\circ$.### Response: I know that $\cos 60^\circ$ is related to the 30-60-90 triangle, which has special side ratios.
If I draw a 30-60-90 triangle, I can label the sides as $1$, $\sqrt{3}$, and $2$, where $1$ is opposite the 30 degree angle, $\sqrt{3}$ is opposite the 60 degree angle, and $2$ is the hypotenuse.
To find $\cos 60^\circ$, I need to use the adjacent side over the hypotenuse, which in this case is $1/2$.
So $\cos 60^\circ = 1/2$.