Sine Exponential Formulation/Real Domain

Theorem
For any real number $x \in \R$:
 * $\sin x = \dfrac {e^{i x} - e^{-i x} } {2 i}$

where:
 * $e^{i x}$ denotes the exponential function
 * $\sin x$ denotes the real sine function
 * $i$ denotes the inaginary unit.

Also presented as
This result can also be presented as:
 * $\sin x = \dfrac 1 2 i \paren {e^{-i x} - e^{i x} }$

Also see

 * Cosine Exponential Formulation
 * Tangent Exponential Formulation
 * Cotangent Exponential Formulation
 * Secant Exponential Formulation
 * Cosecant Exponential Formulation


 * Arcsine Logarithmic Formulation