Hyperbolic trigonometric functions

This article page is a stub, please help by expanding it.

The arguments of hyperbolic trigonometric functions are hyperbolic angles.

Hyperbolic sine

$\sinh(z):={\frac {e^{z}-e^{-z}}{2}}.\,$

Hyperbolic cosine

$\cosh(z):={\frac {e^{z}+e^{-z}}{2}}.\,$

Hyperbolic tangent

$\tanh(z):={\frac {\sinh(z)}{\cosh(z)}}={\frac {e^{z}-e^{-z}}{e^{z}+e^{-z}}}={\frac {e^{2z}-1}{e^{2z}+1}}.\,$

Hyperbolic cosecant

${\rm {csch}}(z):={\frac {1}{\sinh(z)}}={\frac {2}{e^{z}-e^{-z}}}.\,$

Hyperbolic secant

${\rm {sech}}(z):={\frac {1}{\cosh(z)}}={\frac {2}{e^{z}+e^{-z}}}.\,$

Hyperbolic cotangent

$\coth(z):={\frac {1}{\tanh(z)}}={\frac {\cosh(z)}{\sinh(z)}}={\frac {e^{z}+e^{-z}}{e^{z}-e^{-z}}}={\frac {e^{2z}+1}{e^{2z}-1}}.\,$

See also

• Trigonometric functions
  • Circular trigonometric functions
  • Hyperbolic trigonometric functions

• Inverse trigonometric functions
  • Inverse circular trigonometric functions
  • Inverse hyperbolic trigonometric functions

• Category:Hyperbolic function templates
  • {{sinh}}
  • {{cosh}}
  • {{tanh}}
  • {{csch}}
  • {{sech}}
  • {{coth}}
  • {{arsinh}}
  • {{arcosh}}
  • {{artanh}}
  • {{arcsch}}
  • {{arsech}}
  • {{arcoth}}

External links

• Hyperbolic function—Wikipedia.org.