Answer
$\frac{12}{13}$
Work Step by Step
Assuming $\theta$ = $\cos^{-1} \frac{5}{13}$ , we get-
$\cos\theta$ = $\frac{5}{13}$
From first Pythagorean identity-
$\sin\theta$ = $\sqrt {1 - \cos^{2} \theta}$
= $\sqrt {1 - (\frac{5}{13})^{2}} $
= $\sqrt {1 - \frac{25}{169}} $
= $\sqrt { \frac{169 - 25}{169}} $
= $\sqrt { \frac{144}{169}} $ = $\frac{12}{13}$
i.e. $\sin\theta$ = $\frac{12}{13}$
i.e. $\sin(\cos^{-1}\frac{5}{13})$ = $\frac{12}{13}$
