Solve `sinx >-1/2or` find the domain of `f(x)=1/(sqrt(1+2sinx))`

Explanation

To solve the inequality \( \sin x > -\frac{1}{2} \) and find the domain of the function \( f(x) = \frac{1}{\sqrt{1 + 2\sin x}} \), we can follow these steps:

### Step 1: Solve the Inequality \( \sin x > -\frac{1}{2} \)

1. **Identify the critical points**: The sine function equals \(-\frac{1}{2}\) at specific angles. We know that:
\[ \sin x = -\frac{1}{2} \quad \text{at} \quad x = -\frac{\pi}{6} + 2n\pi \quad \text{and} \quad x = \frac{7\pi}{6} + 2n\pi \quad \text{for} \quad n \in \mathbb{Z} \]
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