Question

What is the area of a loop of the curve \( y = \sin 30^\circ \)?

• A. \( \frac{\pi a^2}{8} \)
• B. \( \frac{\pi a^2}{24} \)
• C. \( \frac{\pi a^2}{2} \)
• D. \( \frac{\pi a^2}{3} \)

Hint:

The area of a curve can be found by integrating the equation for the curve and using the appropriate limits.

Answer 1

The Correct Option is B

Step 1: Use the Formula for Area.
The area of a loop formed by the curve \( y = \sin \theta \) can be computed using integration. The total area enclosed by the curve is \( \frac{\pi a^2}{24} \), based on the specific geometry of the curve.
Step 2: Conclusion.
The correct answer is (B), \( \frac{\pi a^2}{24} \).