Step 1: Recall standard trigonometric values
For common angles, the sine values are: \[ \sin 0^\circ = 0, \quad \sin 30^\circ = \frac{1}{2}, \quad \sin 45^\circ = \frac{\sqrt{2}}{2}, \quad \sin 60^\circ = \frac{\sqrt{3}}{2}, \quad \sin 90^\circ = 1 \] Therefore, \( \sin 30^\circ = \frac{1}{2} \).
Step 2: Derive using a 30-60-90 triangle
Consider a 30-60-90 right triangle. The sides are in the ratio 1 : \( \sqrt{3} \) : 2, corresponding to the sides opposite the 30°, 60°, and 90° angles, respectively.
For the 30° angle: \[ \sin 30^\circ = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1}{2} \]
Step 3: Check options
Option (1) \( \frac{1}{2} \) is a match.