The equation describes the relationship between 3 dihedral angles in 3D. It is expressed as: $$\alpha=f(\lambda)$$

To understand the angles, itâ€™s easiest to construct a unit sphere with North and South poles and an axis that contains both poles. If a small circle is placed on the sphere such that it passes through the North pole, then $$\alpha$$ is the slope of the tangent to a point on the small circle (relative to a line of longitude) and $$\lambda$$ is the dihedral angle between the North pole and the tangent point. In order to define a family of functions, $$\upsilon$$ is a third variable that expresses the dihedral angle between the North pole and the center of the small circle.

With no spherical excess $$\upsilon = 0$$ the equation produces a sine curve. With maximum spherical excess $$\upsilon = \frac{\pi}{2}$$ the equation produces a hyperbola.

Even though the identity can produce either a sine or a hyperbola, it doesnâ€™t seem to belong to either class of functions.