What is the value of $\tan\left(\sin^{-1} \frac{5}{13}\right)$?

Explanation

1. 01

   Let $\theta = \sin^{-1} \frac{5}{13}$: opposite 5, hypotenuse 13, so adjacent $\sqrt{169 - 25} = 12$.

2. 02

   $\tan \theta = \frac{5}{12}$.