## Quick Reference

A set of functions, **sinh**, **cosh**, and **tanh**, that have similar properties to trigonometric functions but are related to the hyperbola in the manner that trigonometric functions are related to the circle. The hyperbolic sine (sinh) of the angle *x* is defined by:

sinh*x* = ½(e* ^{x}* − e

^{−}

*)*

^{x}Similarly,

cosh*x* = ½(e* ^{x}* + e

^{−}

*)*

^{x}tanh*x* = (e* ^{x}* − e

^{−}

*)/(e*

^{x}*+ e*

^{x}^{−}

*)*

^{x}Hyperbolic secant (sech), cosecant (cosech), and cotangent (coth) are the reciprocals of cosh, sinh, and tanh, respectively.

*Subjects:*
Mathematics — Chemistry.

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