Arcsine Logarithmic Formulation

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


 * $\arcsin x = \dfrac 1 i \map \ln {i x + \sqrt {1 - x^2} }$

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

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

Also see

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