One of those functions has a catenary-shaped graph, and those functions are analogues of the trigonometric functions.
On most of the Earth, the shadow of a sundial traces out a path of this shape. This shape is generated by a parametric graph with one coordinate equal to the tangent function and the other equal to the secant function. A group of functions is based on doubling the area between one of these shapes, a segment connecting this shape to the origin, and the x-axis. One of those functions has a catenary-shaped graph, and those functions are analogues of the trigonometric functions. One of these shapes is created by graphing y equals one over x. Name these conic sections with eccentricities greater than one that consist of two asymptotic branches.
On most of the Earth, the shadow of a sundial traces out a path of this shape.
hyperbolas