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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Law of cotangents ： ウィキペディア英語版 Law of cotangents In trigonometry, the law of cotangents〔The Universal Encyclopaedia of Mathematics, Pan Reference Books, 1976, page 530. English version George Allen and Unwin, 1964. Translated from the German version Meyers Rechenduden, 1960.〕 is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. Just as three quantities whose equality is expressed by the law of sines are equal to the diameter of the circumscribed circle of the triangle (or to its reciprocal, depending on how the law is expressed), so also the law of cotangents relates the radius of the inscribed circle of a triangle (the inradius) to its sides and angles. ==Statement== Using the usual notations for a triangle (see the figure at the upper right), where $a,\; b,\; c$ are the lengths of the three sides, $A,\; B,\; C$ are the vertices opposite those three respective sides, $\backslash alpha\backslash ,$, $\backslash beta\backslash ,$, $\backslash gamma\backslash ,$ are the corresponding angles at those vertices, $s$ is the semi-perimeter, that is, $s\; =\; (a+b+c)/2$, and $r$ is the radius of the inscribed circle, the law of cotangents states that :$\backslash frac\; =\; \backslash frac\; =\; \backslash frac\; =\; \backslash frac\backslash ,$ and furthermore that the inradius is given by :$r\; =\; \backslash sqrt\}\backslash ,.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Law of cotangents」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.