### Instruction: Compute $\sin 330^\circ$.### Response: To find the sine of an angle, I need to recall the definition of sine in terms of the unit circle.
I can visualize a unit circle with its center at the origin and a ray that forms an angle of $330^\circ$ with the positive x-axis.
The sine of this angle is the y-coordinate of the point where the ray intersects the unit circle.
I can use the fact that the unit circle is symmetric about the x-axis to relate $\sin 330^\circ$ to $\sin 30^\circ$.
If I reflect the ray across the x-axis, I get a new ray that forms an angle of $30^\circ$ with the positive x-axis.
The y-coordinate of the intersection point is the same for both rays, except for the sign.
Therefore, $\sin 330^\circ = -\sin 30^\circ$.
I remember that $\sin 30^\circ = \frac{1}{2}$, so $\sin 330^\circ = -\frac{1}{2}$.