Solve for $x$ \[ 3 \sin ^{-1} x=\frac{\pi}{6} \]

Step 1 ：The given equation is \(3 \sin ^{-1} x=\frac{\pi}{6}\).

Step 2 ：To solve for \(x\), we need to isolate \(x\) on one side of the equation. We can do this by dividing both sides of the equation by 3, which will give us \(\sin ^{-1} x=\frac{\pi}{18}\).

Step 3 ：Then, we can take the sine of both sides to get \(x=\sin\left(\frac{\pi}{18}\right)\).

Step 4 ：After calculating, we find that \(x = 0.17364817766693033\).

Step 5 ：Final Answer: \(\boxed{0.17364817766693033}\)