Question

What is the value of \( \sin 30^\circ \)?

• A. \( \frac{1}{2} \)
• B. \( \frac{\sqrt{3}}{2} \)
• C. \( 1 \)
• D. \( 0 \)

Hint:

For basic angles like \( 30^\circ, 45^\circ, \) and \( 60^\circ \), remember the standard values of sine and cosine.

Answer 1

The Correct Option is A

Step 1: Recall standard trigonometric values
For common angles, sine values are: \[ \sin 0^\circ = 0, \quad \sin 30^\circ = \frac{1}{2}, \quad \sin 45^\circ = \frac{\sqrt{2}}{2}, \quad \sin 60^\circ = \frac{\sqrt{3}}{2}, \quad \sin 90^\circ = 1 \] So, \( \sin 30^\circ = \frac{1}{2} \).

Step 2: Derive using a 30-60-90 triangle
Consider a 30-60-90 right triangle, where angles are 30°, 60°, and 90°, and sides are in the ratio 1 : \( \sqrt{3} \) : 2 (opposite 30°, opposite 60°, hypotenuse).
For angle 30°: \[ \sin 30^\circ = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1}{2} \]
Step 3: Check options
Option (1) \( \frac{1}{2} \) matches.