Spherical Trigonometry - Identities

Identities

Spherical triangles satisfy a spherical law of cosines

The identity may be derived by considering the triangles formed by the tangent lines to the spherical triangle subtending angle C and using the plane law of cosines. Moreover, it reduces to the plane law in the small area limit.

A variation on the law of cosines, the second spherical law of cosines, (also called the cosine rule for angles ) states:

They also satisfy an analogue of the law of sines

Spherical triangles satisfy the half-side formula :

where .