Difference between revisions of "Manuals/calci/SECH"
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* SECH is the reciprocal of COSH function. | * SECH is the reciprocal of COSH function. | ||
* SECH(z)=<math>cosh (z)^{-1}</math> i.e, <math>\frac{ 2} {e^z+e^{-z}} </math> or SEC(iz). where 'i' is the imaginary unit and <math>i=\sqrt{-1}</math> | * SECH(z)=<math>cosh (z)^{-1}</math> i.e, <math>\frac{ 2} {e^z+e^{-z}} </math> or SEC(iz). where 'i' is the imaginary unit and <math>i=\sqrt{-1}</math> | ||
| − | * Also relation between Hyperbolic & | + | * Also relation between Hyperbolic & Trigonometric function is <math>Sec(iz) = Sech(z)</math> & <math>Sec(iz) = Sec(z)</math> |
| + | *SECH(-z) = SECH(z) | ||
== Examples == | == Examples == | ||
Revision as of 06:05, 5 November 2013
SECH(z)
- where z is any real number
Description
- This function gives the hyperbolic Secant of 'z',
- It is also called as Circular function.
- SECH is the reciprocal of COSH function.
- SECH(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 cosh (z)^{-1}} i.e, 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 \frac{ 2} {e^z+e^{-z}} } or SEC(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 & Trigonometric 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 Sec(iz) = Sech(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 Sec(iz) = Sec(z)}
- SECH(-z) = SECH(z)
Examples
SECH(z)
- z is any real number.
| SECH(z) | Value(Radian) |
| SECH(0) | 1 |
| SECH(10) | 0.00009079985933781728 |
| SECH(7) | SECH(7)=0.001823762414 |