Find the value of \( \sin(330^\circ) \) using the unit circle

Step 1 ：First, we convert the angle from degrees to radians. Since \(360^\circ = 2\pi \) radians, we can say that \(330^\circ = \frac{330}{360} \cdot 2\pi = \frac{11}{6}\pi \) radians.

Step 2 ：Next, we locate this angle on the unit circle. The angle \(\frac{11}{6}\pi \) radians corresponds to the point \((\sqrt{3}/2, -1/2)\) on the unit circle. The y-coordinate of this point gives us the value of \(\sin(\frac{11}{6}\pi)\).

Step 3 ：Therefore, the value of \( \sin(330^\circ) = \sin(\frac{11}{6}\pi) = -1/2 \).