Question

The principal value of \(\sin^{-1}(\frac{1}{2})\) is :

• A. \(-\frac{\pi}{6}\)
• B. \(\frac{\pi}{6}\)
• C. \(\frac{\pi}{3}\)
• D. \(-\frac{\pi}{3}\)

Answer 1

The Correct Option is A

The principal value of \(\sin^{-1}(\frac{1}{2})\) is determined by finding the angle \(\theta\) such that:

• \(-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}\)
• \(\sin(\theta) = \frac{1}{2}\)

Recall that \(\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}\).

Since \(\frac{\pi}{6}\) satisfies the condition \(-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}\) and corresponds to the sine function result \(\frac{1}{2}\), it follows that:

The principal value of \(\sin^{-1}(\frac{1}{2})\) is indeed \(\frac{\pi}{6}\).

Therefore, the correct answer is:

\(\frac{\pi}{6}\)