Hyperbolic Sine in terms of Sine

Theorem
Let $z \in \C$ be a complex number.

Then:


 * $i \sinh x = \sin \paren {i x}$

where:
 * $\sin$ denotes the complex sine
 * $\sinh$ denotes the hyperbolic sine
 * $i$ is the imaginary unit: $i^2 = -1$.

Also see

 * Hyperbolic Cosine in terms of Cosine
 * Tangent of Imaginary Number
 * Cotangent of Imaginary Number
 * Secant of Imaginary Number
 * Cosecant of Imaginary Number