Arcsine Logarithmic Formulation

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


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

where $\arcsin x$ is the arcsine and $i^2 = -1$.

Proof
Assume $ y \in \R $, $ -\dfrac \pi 2 \le y \le \dfrac \pi 2 $.

Also see

 * Arccosine Logarithmic Formulation
 * Arctangent Logarithmic Formulation
 * Arccotangent Logarithmic Formulation
 * Arcsecant Logarithmic Formulation
 * Arccosecant Logarithmic Formulation