Definition:Real Hyperbolic Tangent/Definition 2

Definition
The real hyperbolic tangent function is defined on the real numbers as:


 * $\tanh: \R \to \R$:


 * $\forall x \in \R: \tanh x := \dfrac {\sinh x} {\cosh x}$

where:
 * $\sinh$ is the real hyperbolic sine
 * $\cosh$ is the real hyperbolic cosine

Also see

 * Equivalence of Definitions of Real Hyperbolic Tangent


 * Definition:Real Hyperbolic Sine
 * Definition:Real Hyperbolic Cosine
 * Definition:Real Hyperbolic Cotangent
 * Definition:Real Hyperbolic Secant
 * Definition:Real Hyperbolic Cosecant