Arccosine Logarithmic Formulation

Theorem
For any real number $x: -1 \le x \le 1$:


 * $ \displaystyle \arccos x = -i \ln \left({i \sqrt{1-x^2} + x}\right) $

where $\arccos x$ is the arccosine and $i^2 = -1$.

Proof
Assume $ y \in \R $, $ 0 \le y \le \pi $.

Also see

 * Arcsine Logarithmic Formulation
 * Arctangent Logarithmic Formulation
 * Arccotangent Logarithmic Formulation
 * Arcsecant Logarithmic Formulation
 * Arccosecant Logarithmic Formulation