Principal-Value Rule for $$\sin^{-1}(\sin x)$$

Principal-Value Rule for $$\sin^{-1}(\sin x)$$

## Formula

For:

$$x\in\left[\frac{(2n-1)\pi}{2},\frac{(2n+1)\pi}{2}\right]$$

the value of $$\sin^{-1}(\sin x)$$ is obtained by reflecting $$x$$ into:

$$\left[-\frac\pi2,\frac\pi2\right]$$

## Usage

- Used for general inverse-sine equations involving angles outside the principal range.