Inverse Sine of a Cosine

Inverse Sine of a Cosine

## Formula

For:

$$x\in[0,\pi]$$

$$\sin^{-1}(\cos x)=\frac\pi2-x$$

when:

$$x\in\left[0,\frac\pi2\right]$$

and:

$$\sin^{-1}(\cos x)=x-\frac\pi2$$

when:

$$x\in\left[\frac\pi2,\pi\right]$$

## Usage

- Used to simplify inverse sine applied to cosine while respecting the principal range.