### Instruction: Compute $\sin 225^\circ$.### Response: To find $\sin 225^\circ$, I can use the trigonometric identity $\sin (180^\circ + \theta) = -\sin \theta$.
This means that $\sin 225^\circ = -\sin (225^\circ - 180^\circ) = -\sin 45^\circ$.
Now, I recall that $\sin 45^\circ = \frac{\sqrt{2}}{2}$, so $\sin 225^\circ = -\frac{\sqrt{2}}{2}$.