Using common special-angle values, what is $\sin (30°)$?

• A. $\frac{\sqrt{3}}{2}$
• B. $1$
• C. $\frac{\sqrt{2}}{2}$
• D. $\frac{1}{2}$

Answer: (D)

Verified step by step guidance

1. Recall the special angles commonly used in trigonometry: 0°, 30°, 45°, 60°, and 90°, and their corresponding sine values.
2. Remember that the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the hypotenuse.
3. For 30°, the special right triangle to consider is the 30°-60°-90° triangle, where the sides are in the ratio 1 : \(\sqrt{3}\) : 2.
4. Identify the side opposite the 30° angle, which is the shortest side with length 1, and the hypotenuse, which has length 2.
5. Write the sine of 30° as the ratio of the opposite side to the hypotenuse: \(\sin(30^\circ) = \frac{1}{2}\).