Definition of "hyperbolic function" [hyperbolic function]

• 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: (noun)
• The hyperbolic sine, defined by the equation sinh x = 1/2 (ex - e-x). (noun)
• The hyperbolic cosine, defined by the equation cosh x = 1/2 (ex + e-x). (noun)
• The hyperbolic tangent, defined by the equation tanh x = sinh x/cosh x. (noun)
• The hyperbolic cotangent, defined by the equation coth x = cosh x/sinh x. (noun)

American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.