Answer
$cos~ (arcsin\frac{2}{3}) = \frac{\sqrt{5}}{3}$
Work Step by Step
Let $\theta = arcsin\frac{2}{3}$
$sin~\theta = \frac{2}{3} = \frac{opp}{hyp}$
The adjacent side is $\sqrt{3^2-2^2} = \sqrt{5}$
We can find $cos~\theta$:
$cos~\theta = \frac{\sqrt{5}}{3}$
Therefore, $cos~ (arcsin\frac{2}{3}) = \frac{\sqrt{5}}{3}$
