Answer
$ \frac{\sqrt {9-x^2}}{3}$
Work Step by Step
Step 1. Let $u=cos^{-1}(\frac{x}{3})$; we have $cos(u)=\frac{x}{3}$
Step 2. As $x\gt0$ and $\frac{x}{3}$ is in the domain, we know $u$ is in quadrant I and $sin(u)\gt0$
Step 3. We have
$sin(u)=\sqrt {1-cos^2(u)}=\sqrt {1-\frac{x^2}{9}}=\frac{\sqrt {9-x^2}}{3}$
Step 4. Thus we have
$sin(cos^{-1}(\frac{x}{3}))= \frac{\sqrt {9-x^2}}{3}$
