Find the principal value of `sin^(-1)(-1/sqrt2)`.

Explanation

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

### Step-by-Step Solution

1. **Understand the Function**: The function \( \sin^{-1}(x) \) gives the angle \( y \) such that \( \sin(y) = x \). The principal value of \( \sin^{-1}(x) \) is defined in the range \( \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \).

2. **Set Up the Equation**: We want to find \( y \) such that:
\[
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