Question

The value of $\cos \left({\sin }^{-1}\left(\frac{2}{3}\right)\right)$ is equal to :

• A. $\frac{\sqrt{3}}{5}$
• B. $\frac{5}{3}$
• C. $\frac{5}{\sqrt{3}}$
• D. $\sqrt{\frac{5}{3}}$
• E. $\frac{\sqrt{5}}{3}$

Answer 1

The correct option is E $\frac{\sqrt{5}}{3}$

The value of $\cos \left({\sin }^{-1}\left(\frac{2}{3}\right)\right)$ is

$=\cos \left({\cos }^{-1}\sqrt{1-{(1-\frac{2}{3})}^2}\right)$

$=\cos \left({\cos }^{-1}\left(\sqrt{1-\frac{4}{9}}\right)\right)$

$=\cos \left({\cos }^{-1}\left(\frac{\sqrt{5}}{3}\right)\right)$

$=\frac{\sqrt{5}}{3}$