Arcsine Logarithmic Formulation

Theorem
For any real number $x$ s.t. $-1 \le x \le 1$,


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

where $\sin^{-1} x$ is the arcsine and $i^2 = -1$.