Definition:Real Hyperbolic Cotangent/Definition 2

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


 * $\coth: \R_{\ne 0} \to \R$:


 * $\forall x \in \R_{\ne 0}: \coth x := \dfrac {\cosh x} {\sinh x}$

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

It is noted that at $x = 0$ we have that $\sinh x = 0$, and so $\coth x$ is not defined at that point.

Also see

 * Equivalence of Definitions of Real Hyperbolic Cotangent


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