Difference between revisions of "Manuals/calci/COTH"
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| − | <div style="font-size:30px">'''COTH( | + | <div style="font-size:30px">'''COTH(x)'''</div><br/> |
| − | * where | + | * where x is any real number. |
| + | **COTH() returns the inverse hyperbolic tangent of a number. | ||
| + | |||
==Description== | ==Description== | ||
| − | *This function gives the hyperbolic | + | *This function gives the hyperbolic Cotangent of 'x'. |
| − | *COTH is the reciprocal of TANH function. | + | *It's also called as Circular function. |
| − | *COTH | + | *Let z is any real number. |
| − | *Also relation between | + | *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>. | |
| + | *Also relation between Hyperbolic & Trignometric function is <math>Cot(iz)=-iCoth(z)</math> & <math>Coth(iz)=-iCot(z)</math> | ||
== Examples == | == Examples == | ||
| − | '''COTH( | + | '''COTH(x)''' |
| − | *''' | + | *'''x''' is any real number. |
{|id="TABLE1" class="SpreadSheet blue" | {|id="TABLE1" class="SpreadSheet blue" | ||
|- class="even" | |- class="even" | ||
| − | |'''COTH( | + | |'''COTH(x)''' |
| − | |'''Value | + | |'''Value''' |
|- class="odd" | |- class="odd" | ||
| Line 29: | Line 32: | ||
|- class="odd" | |- class="odd" | ||
| COTH(-45) | | COTH(-45) | ||
| − | + | | -1 | |
| − | |||
|} | |} | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|EmJKuQBEdlc|280|center|Hyperbolic COT}} | ||
==See Also== | ==See Also== | ||
| Line 45: | Line 51: | ||
*[http://en.wikipedia.org/wiki/Trigonometric_functions List of Trigonometric Functions] | *[http://en.wikipedia.org/wiki/Trigonometric_functions List of Trigonometric Functions] | ||
*[http://en.wikipedia.org/wiki/Hyperbolic_function Hyperbolic Function] | *[http://en.wikipedia.org/wiki/Hyperbolic_function Hyperbolic Function] | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 17:31, 18 June 2018
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)=
- 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(x)
- x is any real number.
| COTH(x) | Value |
| COTH(1) | 1.3130352854993312 |
| COTH(30) | 1 |
| COTH(-45) | -1 |
Related Videos
See Also
References