spherical trigonometry

In the following we deduce the cosine law for a spherical trihedron.

Let 𝐞𝟏,𝐞𝟐,πžπŸ‘ be the vertex unitary vectors as shown in the figure.

FigureΒ 1: Spherical Trihedron used to deduce trigonometric relations

The cosine of the angle Ξ± formed by the plane defined by 𝐞𝟏,𝐞𝟐 and the plane defined by 𝐞𝟏,πžπŸ‘ is:


Now, using the cyclic property of the triple vector product and Lagrange’s formula (http://planetmath.org/TripleCrossProduct), we can write:



Title spherical trigonometryMathworldPlanetmath
Canonical name SphericalTrigonometry
Date of creation 2013-03-22 17:08:13
Last modified on 2013-03-22 17:08:13
Owner fernsanz (8869)
Last modified by fernsanz (8869)
Numerical id 12
Author fernsanz (8869)
Entry type Topic
Classification msc 51M04
Related topic AreaOfASphericalTriangle