Definition:Hyperbolic Sine

Definition

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

$\sinh: \C \to \C$:
$\forall z \in \C: \sinh z := \dfrac {e^z - e^{-z} } 2$

Real Hyperbolic Sine

On the real numbers it is defined similarly.

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.