Question

Evaluate:
$\sin \left({\cos }^{-1}\frac{4}{5}\right).$

• A. $\frac{4}{5}$
• B. $\frac{3}{4}$
• C. $\frac{3}{5}$
• D. Can't be determined.

Answer 1

The correct option is C $\frac{3}{5}$

$\mathrm{Let}{\cos }^{-1}\frac{4}{5}=\theta .\mathrm{Then},$
$\cos \theta =\frac{4}{5}$
$\Rightarrow \sin \theta =\frac{3}{5}(\because \cos \theta >0\Rightarrow \theta >0)$
$\therefore \sin \left({\cos }^{-1}\frac{4}{5}\right)=\sin \theta =\frac{3}{5}$