# Hyperbolic-function definition

hīpər-bŏlĭk
Any of a set of six functions related, for a real or complex variable x, to the hyperbola in a manner analogous to the relationship of the trigonometric functions to a circle, including:
• The hyperbolic sine, defined by the equation sinh x =12 ( exe x ).
• The hyperbolic cosine, defined by the equation cosh x =12 ( ex + e x ).
• The hyperbolic tangent, defined by the equation tanh x = sinh x /cosh x.
• The hyperbolic cotangent, defined by the equation coth x = cosh x /sinh x.
• The hyperbolic secant, defined by the equation sech x = 1/cosh x.
• The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.
noun
Any of a set of six functions related, for a real or complex variable x, to the hyperbola in a manner analogous to the relationship of the trigonometric functions to a circle, including:
• The hyperbolic sine, defined by the equation sinh x =1 /2 ( exe&spminus;x ).
• The hyperbolic cosine, defined by the equation cosh x =1 /2 ( ex + e&spminus;x ).
• The hyperbolic tangent, defined by the equation tanh x = sinh x /cosh x.
• The hyperbolic cotangent, defined by the equation coth x = cosh x /sinh x.
• The hyperbolic secant, defined by the equation sech x = 1/cosh x.
• The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.
(mathematics) A function that is derived from some arithmetic operations on the exponential function with base e and the inverse function, and was named after the corresponding similar trigonometric function.
noun