noun

*x,*to the hyperbola in a manner analogous to the relationship of the trigonometric functions to a circle, including:

**a.**The hyperbolic sine, defined by the equation sinh

*x*=

^{1}

_{2}(

*e*−

^{x}*e*

^{−}

*).*

^{x}**b.**The hyperbolic cosine, defined by the equation cosh

*x*=

^{1}

_{2}(

*e*+

^{x}*e*

^{−}

*).*

^{x}**c.**The hyperbolic tangent, defined by the equation tanh

*x*= sinh

*x*/cosh

*x.*

**d.**The hyperbolic cotangent, defined by the equation coth

*x*= cosh

*x*/sinh

*x.*

**e.**The hyperbolic secant, defined by the equation sech

*x*= 1/cosh

*x.*

**f.**The hyperbolic cosecant, defined by the equation csch

*x*= 1/sinh

*x.*