What is the value of $\cos\left(\sin^{-1} \frac{3}{5}\right)$?

Explanation

1. 01

   Let $\theta = \sin^{-1} \frac{3}{5}$, so $\sin \theta = \frac{3}{5}$ with $\theta$ in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, where $\cos \theta \ge 0$.

2. 02

   $\cos \theta = \sqrt{1 - \frac{9}{25}} = \frac{4}{5}$.