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

Rarely Tested

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

## Formula

The value of:

$$\cos^{-1}(\cos x)$$

is the unique angle in:

$$[0,\pi]$$

having the same cosine as $$x$$.

## Usage

- Used to correctly simplify inverse cosine of cosine for arbitrary real $$x$$.

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