Difference between revisions of "Manuals/calci/COTH"
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*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. | ||
| − | *<math>COTH(z)=\frac{Cosh(z)}{Sinh(z)}</math> i.e <math>\frac {e^z+e^{-z}} {e^z-e^{-z}}</math> or | + | *<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 | + | *Also relation between Hyperbolic & Trignometric function is <math>Cot(iz)=-iCoth(z)</math> & <math>Coth(iz)=-iCot(z)</math> |
| − | |||
== Examples == | == Examples == | ||
Revision as of 06:27, 5 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.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle COTH(z)=\frac{Cosh(z)}{Sinh(z)}} i.e or ICOT(iz).where 'I' is the imaginary unit and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i=\sqrt{-1}} .
- Also relation between Hyperbolic & Trignometric function is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Cot(iz)=-iCoth(z)} & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Coth(iz)=-iCot(z)}
or ICOT(iz).where 'I' is the imaginary unit and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i=\sqrt{-1}}
.Examples
COTH(z)
- z is any real number.
| COTH(z) | Value(Radian) |
| COTH(1) | 1.3130352854993312 |
| COTH(30) | 1 |
| COTH(-45) | -1 |