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