# Definition:Hyperbolic Sine/Real

## Definition

The real hyperbolic sine function is defined on the real numbers as:

$\sinh: \R \to \R$:
$\forall x \in \R: \sinh x := \dfrac {e^x - e^{-x} } 2$

## Also see

• Results about the hyperbolic sine function can be found here.

## Linguistic Note

The usual symbol sinh for hyperbolic sine is awkward to pronounce.

Some pedagogues say it as shine, and some as sinch.

Others prefer the mouthful which is hyperbolic sine