Question

find the exact value of $sin 330^circ$ in simplest form with a rational denominator.

Explanation:

Step1: Identify reference angle

$330^\circ = 360^\circ - 30^\circ$, so reference angle is $30^\circ$.

Step2: Determine sign of sine

$330^\circ$ is in Quadrant IV, where sine is negative.

Step3: Compute exact value

$\sin 330^\circ = -\sin 30^\circ = -\frac{1}{2}$

Answer:

$-\frac{1}{2}$