正矢

正矢（英文：Versine、Versed sine），在三角函数之中被定義為 ${\textrm {versin}}\theta =1-\cos \theta \,$ ，值域在0～2之間。

定義

正矢	${\textrm {versin}}(\theta )=2\sin ^{2}\left({\frac {\theta }{2}}\right)=1-\cos \theta \,$
餘矢	${\textrm {coversin}}\theta ={\textrm {versin}}\left({\frac {\pi }{2}}-\theta \right)=1-\sin \theta \,$
半正矢	${\textrm {haversin}}\theta ={\frac {{\textrm {versin}}\theta }{2}}={\frac {1-\cos \theta }{2}}\,$
半餘矢	${\textrm {hacoversin}}\theta ={\frac {{\textrm {coversin}}\theta }{2}}={\frac {1-\sin \theta }{2}}\,$

角θ的所有三角函数在几何上可以依据以O點為圓心的单位圓来构造。

${\frac {d}{dx}}\mathrm {versin} (x)=\sin {x}$	$\int \mathrm {versin} (x)\,dx=x-\sin {x}+C$
${\frac {d}{dx}}\mathrm {coversin} (x)=-\cos {x}$	$\int \mathrm {coversin} (x)\,dx=x+\cos {x}+C$
${\frac {d}{dx}}\mathrm {haversin} (x)={\frac {\sin {x}}{2}}$	$\int \mathrm {haversin} (x)\,dx={\frac {x-\sin {x}}{2}}+C$
${\frac {d}{dx}}\mathrm {hacoversin} (x)={\frac {-\cos {x}}{2}}$	$\int \mathrm {hacoversin} (x)\,dx={\frac {x+\cos {x}}{2}}+C$

Boyer, Carl B. 2nd. New York: Wiley. 1991.
. 牛津英語詞典 (第三版). 牛津大學出版社. 2005-09 （英语）.
Miller, J. . [2010-04-02]. （原始内容存档于2015-09-05）.
Calvert, James B. . [2010-04-02]. （原始内容存档于2007-10-02）.
. 牛津英語詞典 (第三版). 牛津大學出版社. 2005-09 （英语）.
Cites coinage by Prof. Jas. Inman, D. D., in his Navigation and Nautical Astronomy, 3rd ed. (1835).
Nair, Bhaskaran. . Rail International. 1972, 3 (3): 159–166. ISSN 0020-8442.
埃里克·韦斯坦因. . MathWorld.
埃里克·韦斯坦因. . MathWorld.

Sagitta, Apothem, and Chord by Ed Pegg, Jr., The Wolfram Demonstrations Project.

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