The Law of Cosines in Spherical Trigonometry


Let A,B,C be the vertex angles of a spherical triangle on the unit sphere, and a,b,c the lengths of the opposite sides, measured by the angles they subtend at the center.

SPHERICAL LAW OF COSINES:

cosa = cosb cosc + sinb sinc cosA.

(There is also the

SPHERICAL LAW OF SINES:

sina / sinA = sinb / sinB = sinc / sinC.)


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