Difference between revisions of "Manuals/calci/COTH"

Revision as of 16:30, 18 June 2018

COTH(x)

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

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 $Cot(iz)=-iCoth(z)$ & $Coth(iz)=-iCot(z)$

COTH(z)

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-<div style="font-size:30px">'''COTH(z)'''</div><br/>
+<div style="font-size:30px">'''COTH(x)'''</div><br/>
-* where z is any real number
+* where x is any real number.
+**COTH() returns the inverse hyperbolic tangent of a number.
 ==Description==
-*This function gives the hyperbolic Cotangent of 'z'.
+*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)=<math>(tanh (z))^{-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>.