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 ( 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..
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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..
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(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.
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