Question

35 - 40. evaluate.

1. y = sin^{-1}(\frac{\sqrt{3}}{2})

Explanation:

Step1: Recall the definition of inverse sine function

The inverse sine function \(y = \sin^{-1}(x)\) has a range \([-\frac{\pi}{2},\frac{\pi}{2}]\) and \(\sin^{-1}(\sin\theta)=\theta\) when \(\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]\). We know that \(\sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}\) and \(\frac{\pi}{3}\in[-\frac{\pi}{2},\frac{\pi}{2}]\).

Answer:

\(\frac{\pi}{3}\)