hyperbolicfunction

hyperbolic function n.

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:

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.

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