Editing Spherical trigonometry (section)

===Notation===
[[File:Spherical trigonometry basic triangle.svg|thumb|right|200px|The basic triangle on a unit sphere.]]
*Both vertices and angles at the vertices of a triangle are denoted by the same upper case letters {{mvar|A}}, {{mvar|B}}, and {{mvar|C}}.
*Sides are denoted by lower-case letters: {{mvar|a}}, {{mvar|b}}, and {{mvar|c}}. The sphere has a radius of 1, and so the side lengths and lower case angles are equivalent (see [[arc length]]). 
*The ''angle'' {{mvar|A}} (respectively, {{mvar|B}} and {{mvar|C}}) may be regarded either as the [[dihedral angle]] between the two planes that intersect the sphere at the ''[[vertex (geometry)|vertex]]'' {{mvar|A}}, or, equivalently, as the angle between the [[tangent]]s of the great circle arcs where they meet at the vertex.
*Angles are expressed in [[radian]]s. The angles of ''proper'' spherical triangles are (by convention) less than {{pi}}, so that <math display=block>
\pi < A + B + C < 3\pi
</math>(Todhunter,<ref name=todhunter/> Art.22,32). 
In particular, the sum of the angles of a spherical triangle is strictly greater than the sum of the angles of a triangle defined on the Euclidean plane, which is always exactly {{pi}} radians.
*Sides are also expressed in radians. A side (regarded as a great circle arc) is measured by the angle that it subtends at the centre. On the unit sphere, this radian measure is numerically equal to the arc length. By convention, the sides of ''proper'' spherical triangles are less than {{pi}}, so that <math display=block>0 < a + b + c < 2\pi
</math>(Todhunter,<ref name=todhunter/> Art.22,32).
*The sphere's radius is taken as unity. For specific practical problems on a sphere of radius {{mvar|R}} the measured lengths of the sides must be divided by {{mvar|R}} before using the identities given below. Likewise, after a calculation on the unit sphere the sides {{mvar|a}}, {{mvar|b}}, and {{mvar|c}} must be multiplied by&nbsp;{{mvar|R}}.