Half-side formula
Spherical triangle
In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles.[1]
Formulas
The half-side formulas are[2]
![{\displaystyle {\begin{aligned}\tan \left({\frac {a}{2}}\right)&=R\cos(S-A)\\[8pt]\tan \left({\frac {b}{2}}\right)&=R\cos(S-B)\\[8pt]\tan \left({\frac {c}{2}}\right)&=R\cos(S-C)\end{aligned}}}](../I/m/275514517e95b80a438b2d908bd6078a38495b58.svg)
where
- a, b, c are the lengths of the sides respectively opposite angles A, B, C,
- is half the sum of the angles, and
The three formulas are really the same formula, with the names of the variables permuted.
See also
References
- ↑ Bronshtein, I. N.; Semendyayev, K. A.; Musiol, Gerhard; Mühlig, Heiner (2007), Handbook of Mathematics, Springer, p. 165, ISBN 9783540721222
- ↑ Nelson, David (2008), The Penguin Dictionary of Mathematics (4th ed.), Penguin UK, p. 529, ISBN 9780141920870.
This article is issued from Wikipedia - version of the 10/30/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.