Difference between revisions of "Manuals/calci/COTH"
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*This function gives the hyperbolic Cotangent of 'z'. | *This function gives the hyperbolic Cotangent of 'z'. | ||
*It's also called as Circular function. | *It's also called as Circular function. | ||
| − | *COTH is the reciprocal of TANH function. | + | *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>. | *<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> | *Also relation between Hyperbolic & Trignometric function is <math>Cot(iz)=-iCoth(z)</math> & <math>Coth(iz)=-iCot(z)</math> | ||
Revision as of 03:09, 7 November 2013
COTH(z)
- where z is any real number
Description
- This function gives the hyperbolic Cotangent of 'z'.
- It's also called as Circular function.
- COTH is the reciprocal of TANH function.i.e.COTH(z)=
- i.e or iCOT(iz).where 'i' is the imaginary unit and .
- Also relation between Hyperbolic & Trignometric function is &
i.e 
or iCOT(iz).where 'i' is the imaginary unit and 
.
& 
Examples
COTH(z)
- z is any real number.
| COTH(z) | Value |
| COTH(1) | 1.3130352854993312 |
| COTH(30) | 1 |
| COTH(-45) | -1 |