Tangent of Half Angle for Spherical Triangles/Also presented as
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Tangent of Half Angle for Spherical Triangles: Also presented as
The Tangent of Half Angle for Spherical Triangles formula is also seen presented in the following form:
| \(\ds \tan \dfrac A 2\) | \(=\) | \(\ds \dfrac r {\map \sin {s - a} }\) | ||||||||||||
| \(\ds \tan \dfrac B 2\) | \(=\) | \(\ds \dfrac r {\map \sin {s - b} }\) | ||||||||||||
| \(\ds \tan \dfrac C 2\) | \(=\) | \(\ds \dfrac r {\map \sin {s - c} }\) |
where:
| \(\ds s\) | \(=\) | \(\ds \dfrac {a + b + c} 2\) | ||||||||||||
| \(\ds r\) | \(=\) | \(\ds \sqrt {\dfrac {\map \sin {s - a} \map \sin {s - b} \map \sin {s - c} } {\sin s} }\) |
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): half-angle formulae: 3.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): half-angle formulae: 3.