### Instruction: Compute $\cos 240^\circ$.### Response: I know that cosine is related to the x-coordinate of a point on the unit circle, so I want to find the point that corresponds to an angle of $240^\circ$.
One way to do that is to use the fact that $240^\circ$ is equal to $180^\circ + 60^\circ$, and I can use the angle addition formula for cosine: $\cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$.
I also know the values of cosine and sine for $180^\circ$ and $60^\circ$: $\cos 180^\circ = -1$, $\sin 180^\circ = 0$, $\cos 60^\circ = \frac{1}{2}$, and $\sin 60^\circ = \frac{\sqrt{3}}{2}$.
Plugging these values into the formula, I get $\cos 240^\circ = \cos(180^\circ + 60^\circ) = (-1)(\frac{1}{2}) - (0)(\frac{\sqrt{3}}{2}) = -\frac{1}{2}$.