Difference between revisions of "Tangent formula"
From Encyclopedia of Mathematics
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A formula establishing the dependence between the lengths of two sides of a plane triangle and the tangents of the halved sum and the halved difference of the opposite angles. The tangent formula has the form | A formula establishing the dependence between the lengths of two sides of a plane triangle and the tangents of the halved sum and the halved difference of the opposite angles. The tangent formula has the form | ||
| − | + | $$\frac{a-b}{a+b}=\frac{\tan\frac 12(A-B)}{\tan\frac 12(A+B)}.$$ | |
Sometimes the tangent formula is called the Regiomontanus formula, after the scholar who established this formula in the second half of the 15th century. | Sometimes the tangent formula is called the Regiomontanus formula, after the scholar who established this formula in the second half of the 15th century. | ||
Revision as of 12:15, 9 April 2014
A formula establishing the dependence between the lengths of two sides of a plane triangle and the tangents of the halved sum and the halved difference of the opposite angles. The tangent formula has the form
$$\frac{a-b}{a+b}=\frac{\tan\frac 12(A-B)}{\tan\frac 12(A+B)}.$$
Sometimes the tangent formula is called the Regiomontanus formula, after the scholar who established this formula in the second half of the 15th century.
Comments
References
| [a1] | M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French) |
| [a2] | E.W. Hobson, "Plane trigonometry" , Cambridge Univ. Press (1925) pp. 158 |
How to Cite This Entry:
Tangent formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tangent_formula&oldid=15709
Tangent formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tangent_formula&oldid=15709
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article