A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a) and (b, 1/b) on the rectangular hyperbola xy = 1, or the corresponding region when this hyperbola is re-scaled and its orientation is altered by a rotation leaving the center at the origin, as with the unit hyperbola. A hyperbolic sector in standard position has a = 1 and b > 1.
Hyperbolic sectors are the basis for the hyperbolic functions.