1. The problem asks for the value of $\sin 30^\circ$. 2. Recall the sine function in trigonometry gives the ratio of the length of the opposite side to the hypotenuse in a right triangle. 3. A key special angle is $30^\circ$, where $\sin 30^\circ = \frac{1}{2}$. 4. This is a standard value derived from the properties of a 30-60-90 triangle. 5. Therefore, the correct answer is option a: $\frac{1}{2}$.