Answer
$$\frac{{\sqrt {9 - {x^2}} }}{3}$$
Work Step by Step
$$\eqalign{
& \cos \left( {{{\sin }^{ - 1}}\left( {\frac{x}{3}} \right)} \right) \cr
& {\text{From the triangle shown below}} \cr
& \sin \theta = \frac{x}{3} \cr
& \theta = {\sin ^{ - 1}}\left( {\frac{x}{3}} \right),{\text{ then}} \cr
& \cos \left( {{{\sin }^{ - 1}}\left( {\frac{x}{3}} \right)} \right) = \cos \theta \cr
& {\text{From the triangle we obtain }}\cos \theta \cr
& \cos \left( {{{\sin }^{ - 1}}\left( {\frac{x}{3}} \right)} \right) = \frac{{\sqrt {9 - {x^2}} }}{3} \cr} $$
