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The versine or versed sine is a trigonometric function already appearing in some of the earliest trigonometric tables. There are several related functions, most notably the coversine and haversine. The latter, half a versine, is of particular importance in the haversine formula of navigation. ==Overview== The versine〔〔〔〔〔 or versed sine〔〔〔〔〔 is a trigonometric function already appearing in some of the earliest trigonometric tables. It is written as versin(''θ''),〔〔〔 vers(''θ''),〔〔〔〔〔〔 ver(''θ'') or siv(''θ'').〔(access-date=2015-11-07--> ) (reissued by Cambridge University Press, 2009; ISBN 978-1-108-00208-0)〕〔 (See errata.)〕 In Latin, it is known as the ''sinus versus''〔〔 (flipped sine), ''versinus'', ''versus'' or the ''sagitta'' (arrow). Expressed in terms of the meanwhile more commonly used "vertical" sines (''sinus rectus'') and cosines (''cosinus rectus'') functions, the versine is equal to , or 2 sin2(''θ''/2). There are several related functions corresponding to the versine: * The versed cosine,〔〔Some English sources confuse the versed cosine with the coversed sine. Historically (f.e. in Cauchy, 1821), the ''sinus versus'' (versine) was defined as siv(''θ'') = 1-cos(''θ'') and the ''cosinus versus'' (what is now also known as coversine) as cosiv(''θ'') = 1-sin(''θ''). However, in their 2009 English translation of Cauchy's work, Bradley and Sandifer incorrectly associate the ''cosinus versus'' (and cosiv) with the ''versed cosine'' (what is now also known as vercosine) rather than the ''coversed sine''. Similarly, in their 1968/2000 work, Korn and Korn associate the covers(''θ'') function with the ''versed cosine'' instead of the ''coversed sine''.〕 or vercosine,〔〔 written vercosin(''θ''), vercos(''θ'') or vcs(''θ'')〔 * The coversed sine,〔 coversine,〔〔〔〔〔〔 cosinus versus〔〔〔 or coversinus, written coversin(''θ''),〔 covers(''θ''),〔〔〔 cosiv(''θ'')〔〔〔 or cvs(''θ'')〔〔 * The coversed cosine〔 or covercosine,〔 written covercosin(''θ'') or covercos(''θ'') or cvc(''θ'')〔 In full analogy to the above mentioned four functions another set of four "half-value" functions exists as well: * The haversed sine,〔 haversine〔〔〔〔〔〔〔 or semiversus, written haversin(''θ''), semiversin(''θ''), semiversinus(''θ''), havers(''θ''),〔 hav(''θ''),〔〔〔〔〔〔 hvs(''θ''),〔The abbreviation ''hvs'' sometimes used for the haversine function in signal processing and filtering is also sometimes used for the unrelated Heaviside step function.〕 sem(''θ'')〔 or hv(''θ''), most famous from the haversine formula used historically in navigation * The haversed cosine〔 or havercosine,〔 written havercosin(''θ''), havercos(''θ''), hac(''θ'') or hvc(''θ'')〔 * The hacoversed sine,〔 also called hacoversine〔 or cohaversine〔 and written hacoversin(''θ''), semicoversin(''θ''), hacovers(''θ''), hacov(''θ'') or hcv(''θ'')〔 * The hacoversed cosine,〔 also called hacovercosine〔 or cohavercosine〔 and written hacovercosin(''θ''), hacovercos(''θ'') or hcc(''θ'')〔 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「Versine」の詳細全文を読む スポンサード リンク
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