Hyperbolic-function meaning
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 ( ex − e− 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 ( ex − e&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..