Difference between revisions of "Hyperbolic trigonometric functions"

Revision as of 09:15, November 16, 2008

The hyperbolic trigonometric functions are analogs of the standard trigonometric functions using a hyperbola as the defining conic section rather than a circle. They are defined as:

Hyperbolic sine: $sinh(x)={\frac {e^{x}-e^{-x}}{2}}$
Hyperbolic cosine: $cosh(x)={\frac {e^{x}+e^{-x}}{2}}$
Hyperbolic tangent: $tanh(x)={\frac {sinh(x)}{cosh(x)}}={\frac {e^{x}-e^{-x}}{e^{x}+e^{-x}}}$
Hyperbolic cosecant: $csch(x)={\frac {1}{sinh(x)}}={\frac {2}{e^{x}-e^{-x}}}$
Hyperbolic secant: $sech(x)={\frac {1}{sinh(x)}}={\frac {2}{e^{x}+e^{-x}}}$
Hyperbolic tangent: $coth(x)={\frac {cosh(x)}{sinh(x)}}={\frac {e^{x}+e^{-x}}{e^{x}-e^{-x}}}$

Revision as of 01:03, November 16, 2008 (view source) CSGuy (talk \| contribs) (New page: The '''hyperbolic trigonometric functions''' are analogs of the standard trigonometric functions using a hyperbola rather than a circle. They are defined as: *Hyperbolic sine: <math>sinh...)		Revision as of 09:15, November 16, 2008 (view source) Foxtrot (talk \| contribs) m (undeadend) Newer edit →
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−	The '''hyperbolic trigonometric functions''' are analogs of the standard trigonometric ~~functions~~ using a hyperbola rather than a circle. They are defined as:	+	The '''hyperbolic trigonometric functions''' are analogs of the standard [[trigonometric function]]s using a [[hyperbola]] as the defining [[conic section]] rather than a [[circle]]. They are defined as:

	*Hyperbolic sine: <math>sinh(x) = \frac{e^x - e^{-x}}{2}</math>		*Hyperbolic sine: <math>sinh(x) = \frac{e^x - e^{-x}}{2}</math>