Difference between revisions of "Manuals/calci/COTH"

Revision as of 03:05, 7 November 2013

COTH(z)

This function gives the hyperbolic Cotangent of 'z'.
It's also called as Circular function.
COTH is the reciprocal of TANH function.
$COTH(z)={\frac {Cosh(z)}{Sinh(z)}}$ 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 $Cot(iz)=-iCoth(z)$ & $Coth(iz)=-iCot(z)$

COTH(z)

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 *It's also called as Circular function.
 *COTH is the reciprocal of TANH function.
-*<math>COTH(z)=\frac{Cosh(z)}{Sinh(z)}</math>  i.e <math>\frac {e^z+e^{-z}} {e^z-e^{-z}}</math> or ICOT(iz).where 'I' is the imaginary unit and <math>i=\sqrt{-1}</math>.
+*<math>COTH(z)=\frac{Cosh(z)}{Sinh(z)}</math>  i.e <math>\frac {e^z+e^{-z}} {e^z-e^{-z}}</math> or iCOT(iz).where 'i' is the imaginary unit and <math>i=\sqrt{-1}</math>.
 *Also relation between Hyperbolic & Trignometric function is <math>Cot(iz)=-iCoth(z)</math> & <math>Coth(iz)=-iCot(z)</math>