mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, a function ''f'' is cofunction of a function ''g'' if ''f''(''A'') = ''g''(''B'') whenever ''A'' and ''B'' are complementary angles (pairs that sum to one right angle). This definition typically applies to

trigonometric functions In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all ...

. The prefix "co-" can be found already in Edmund Gunter's ''Canon triangulorum'' (1620). For example, sine (Latin: ''sinus'') and

cosine In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side opposite that ...

(Latin: ''cosinus'', ''sinus complementi'') are cofunctions of each other (hence the "co" in "cosine"): The same is true of secant (Latin: ''secans'') and cosecant (Latin: ''cosecans'', ''secans complementi'') as well as of tangent (Latin: ''tangens'') and

cotangent In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in a ...

(Latin: ''cotangens'', ''tangens complementi''): These equations are also known as the cofunction identities. This also holds true for the versine (versed sine, ver) and coversine (coversed sine, cvs), the vercosine (versed cosine, vcs) and covercosine (coversed cosine, cvc), the haversine (half-versed sine, hav) and hacoversine (half-coversed sine, hcv), the havercosine (half-versed cosine, hvc) and hacovercosine (half-coversed cosine, hcc), as well as the exsecant (external secant, exs) and excosecant (external cosecant, exc):

References

{{reflist, refs= {{cite book , title=Algebra and Trigonometry , author-first1=Richard , author-last1=Aufmann , author-first2=Richard , author-last2=Nation , edition=8 , publisher=

Cengage Learning Cengage Group is an American educational content, technology, and services company for higher education, K–12, professional, and library markets. It operates in more than 20 countries around the world.(June 27, 2014Global Publishing Leaders 2 ...

, year=2014 , isbn=978-128596583-3 , page=528 , url=https://books.google.com/books?id=JEDAAgAAQBAJ&pg=PA528 , access-date=2017-07-28 {{cite book , author-first=Edmund , author-last=Gunter , author-link=Edmund Gunter , title=Canon triangulorum , date=1620 {{cite web , title=A reconstruction of Gunter's Canon triangulorum (1620) , editor-first=Denis , editor-last=Roegel , type=Research report , publisher=HAL , date=2010-12-06 , id=inria-00543938 , url=https://hal.inria.fr/inria-00543938/document , access-date=2017-07-28 , url-status=live , archive-url=https://web.archive.org/web/20170728192238/https://hal.inria.fr/inria-00543938/document , archive-date=2017-07-28 {{cite web , title=5.1 The Elementary Identities , work=Precalculus , author-first=John W. , author-last=Bales , date=2012 , orig-year=2001 , url=http://jwbales.home.mindspring.com/precal/part5/part5.1.html , access-date=2017-07-30 , url-status=dead , archive-url=https://web.archive.org/web/20170730201433/http://jwbales.home.mindspring.com/precal/part5/part5.1.html , archive-date=2017-07-30 {{cite book , title=Trigonometry , volume=Part I: Plane Trigonometry , first1=Arthur Graham , last1=Hall , first2=Fred Goodrich , last2=Frink , date=January 1909 , chapter=Chapter II. The Acute Angle 0Functions of complementary angles , publisher= Henry Holt and Company , location=New York , pages=11–12 , url=https://archive.org/stream/planetrigonometr00hallrich#page/n26/mode/1up {{cite web , author-first=Eric Wolfgang , author-last=Weisstein , author-link=Eric Wolfgang Weisstein , title=Coversine , work= MathWorld , publisher= Wolfram Research, Inc. , url=http://mathworld.wolfram.com/Coversine.html , access-date=2015-11-06 , url-status=live , archive-url=https://web.archive.org/web/20051127184403/http://mathworld.wolfram.com/Coversine.html , archive-date=2005-11-27 {{cite web , author-first=Eric Wolfgang , author-last=Weisstein , author-link=Eric Wolfgang Weisstein , title=Covercosine , work= MathWorld , publisher= Wolfram Research, Inc. , url=http://mathworld.wolfram.com/Covercosine.html , access-date=2015-11-06 , url-status=live , archive-url=https://web.archive.org/web/20140328110051/http://mathworld.wolfram.com/Covercosine.html , archive-date=2014-03-28 Trigonometry

See also

References