Evaluate the following inverse trigonometric expression:
`sin^(-1)("sin"(7pi)/6)`

Explanation

To evaluate the expression \( \sin^{-1}(\sin(7\pi/6)) \), we will follow these steps:

### Step 1: Evaluate \( \sin(7\pi/6) \)
The angle \( 7\pi/6 \) can be rewritten as:
\[ 7\pi/6 = \pi + \pi/6 \]
This means that \( 7\pi/6 \) is in the third quadrant, where sine is negative.

### Step 2: Find the reference angle
The reference angle for \( 7\pi/6 \) is \( \pi/6 \). Therefore, we have:
\[ \sin(7\pi/6) = -\sin(\pi/6) \]

### Step 3: Calculate \( \sin(\pi/6) \)
From trigonometric values, we know:
\[ \sin(\pi/6) = \frac{1}{2} \]
Thus,
\[ \sin(7\pi/6) = -\frac{1}{2} \]

### Step 4: Substitute back into the inverse sine function
Now, we substitute this value back into the inverse sine function:
\[ \sin^{-1}(\sin(7\pi/6)) = \sin^{-1}\left(-\frac{1}{2}\right) \]

### Step 5: Determine the angle for \( \sin^{-1}(-\frac{1}{2}) \)
The value \( \sin^{-1}(-\frac{1}{2}) \) corresponds to the angle in the range of \( -\frac{\pi}{2} \) to \( \frac{\pi}{2} \) where sine is negative. The angle that satisfies this is:
\[ -\frac{\pi}{6} \]

### Final Result
Therefore, the final result is:
\[ \sin^{-1}(\sin(7\pi/6)) = -\frac{\pi}{6} \]