What is "hyperbolic functions"

Hyperbolic \Hy`per*bol"ic\, Hyperbolical \Hy`per*bol"ic*al\, a.

1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola.

2. (Rhet.) Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression. ``This hyperbolical epitaph.''
   --Fuller.

   Hyperbolic functions (Math.), certain functions which have relations to the hyperbola corresponding to those which sines, cosines, tangents, etc., have to the circle; and hence, called hyperbolic sines, hyperbolic cosines, etc.

   Hyperbolic logarithm. See Logarithm.

   Hyperbolic spiral (Math.), a spiral curve, the law of which is, that the distance from the pole to the generating point varies inversely as the angle swept over by the radius vector.