Manuals/calci/COTH

COTH(x)

where x is any real number.
- COTH() returns the inverse hyperbolic tangent of a number.

Description

This function gives the hyperbolic Cotangent of 'x'.
It's also called as Circular function.
Let z is any real number.
COTH is the reciprocal of TANH function.i.e.COTH(z)= $(tanh(z))^{-1}$
$COTH(z)={\frac {Cosh(z)}{Sinh(z)}}$ i.e ${\frac {e^{z}+e^{-z}}{e^{z}-e^{-z}}}$ or iCOT(iz).where 'i' is the imaginary unit and $i={\sqrt {-1}}$ .
Also relation between Hyperbolic & Trignometric function is $Cot(iz)=-iCoth(z)$ & $Coth(iz)=-iCot(z)$