Evaluate each of the following: sin^-1(sin 5π/6)

Question

Evaluate each of the following:

\(sin^{-1}(sin \frac{5\pi}6)\)

Answer 1

The value of sin sin\(\frac{5\pi}6\) is \(\frac 12\)

∴ The question becomes sin^-1\((\frac 12)\)

The range of principal value of sin^–1 is \([\frac{-\pi}2,\frac{\pi}2] \) and sin\((\frac{\pi}6)=\frac 12\)

Therefore, the value of \(sin^{-1}(sin \frac{5\pi}6)\) is \(\frac{\pi}6.\)