网站首页  英汉词典

请输入您要查询的英文单词:

 

单词 Sine theorem
释义

Sine theorem

中文百科

正弦定理 Law of sines

(重定向自Sine theorem)

正弦定理是三角学中的一个定理。它指出:对于任意\triangle ABCabc分别为\angle A\angle B\angle C的对边,R\triangle ABC的外置圆半径,则有

\frac{a}{\sin \ang A}=\frac{b}{\sin \ang B}=\frac{c}{\sin \ang C}=2R

做一个边长为abc的三角形,对应角分别是ABC。从角Cc边做垂线,得到一个长度为h的垂线和两个直角三角形。

很明显:

\sin A = \frac{h}{b}

\; \sin B = \frac{h}{a}

因此:

h = b\,\sin A = a\,\sin B

\frac{\sin A}{a} = \frac{\sin B}{b}

同理:

\frac{\sin B}{b} = \frac{\sin C}{c}
英语百科

Law of sines 正弦定理

(重定向自Sine theorem)
A triangle labelled with the components of the law of sines. Capital A, B and C are the angles, and lower-case a, b, c are the sides opposite them. (a opposite A, etc.)
Triangle ABC with altitude from B drawn
Triangle ABC with altitude from A drawn

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any shaped triangle to the sines of its angles. According to the law,

where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see the figure to the right), while d is the diameter of the triangle's circumcircle. When the last of these equations is not used, the law is sometimes stated using the reciprocals;

随便看

 

英汉网英语在线翻译词典收录了3779314条英语词汇在线翻译词条,基本涵盖了全部常用英语词汇的中英文双语翻译及用法,是英语学习的有利工具。

 

Copyright © 2004-2024 encnc.com All Rights Reserved
更新时间:2025/6/17 14:36:26