Compute $\sin 330^\circ$.
To find the sine of an angle, I need to recall the definition of sine in terms of 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. I remember that $\sin 30^\circ = \frac{1}{2}$, so $\sin 330^\circ = -\frac{1}{2}$. 