The point $\left(p, \frac{\pi}{3}\right)$ lies on the curve $y = \sin^{-1} x$. Which point is its mirror image in the line $y = x$, on the curve $y = \sin x$, $-\frac{\pi}{2} \le x \le \frac{\pi}{2}$?

Explanation

1. 01

   $\sin^{-1} p = \frac{\pi}{3}$ gives $p = \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$.

2. 02

   Reflecting in $y = x$ swaps the coordinates: $\left(\frac{\pi}{3}, \frac{\sqrt{3}}{2}\right)$, and indeed $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$.