Find the principal values of `sin^(-1)(- 1/2)`

Explanation

To find the principal values of \( \sin^{-1}(-\frac{1}{2}) \), we can follow these steps:

### Step 1: Set up the equation
Let \( y = \sin^{-1}(-\frac{1}{2}) \). This implies that \( \sin(y) = -\frac{1}{2} \).

### Step 2: Identify the angle whose sine is \(-\frac{1}{2}\)
We know that \( \sin(30^\circ) = \frac{1}{2} \). Therefore, we can express \(-\frac{1}{2}\) as:
\[
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