In mathematics, a

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...

''f'' is cofunction of a function ''g'' if ''f''(''A'') = ''g''(''B'') whenever ''A'' and ''B'' are

complementary angles In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles ar ...

. 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 a ...

. The prefix "co-" can be found already in

Edmund Gunter Edmund Gunter (158110 December 1626), was an English clergyman, mathematician, geometer and astronomer of Welsh descent. He is best remembered for his mathematical contributions which include the invention of the Gunter's chain, the Gunter's q ...

's ''Canon triangulorum'' (1620). For example,

sine 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 that is op ...

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

cosecant 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 al ...

(Latin: ''cosecans'', ''secans complementi'') as well as of

tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More ...

(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 The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'',coversine The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'',vercosine The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'',covercosine The versine or versed sine is a trigonometric function found in some of the earliest ( Sanskrit ''Aryabhatia'',haversine The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'',hacoversine The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'',havercosine The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'',hacovercosine The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'',exsecant The exsecant (exsec, exs) and excosecant (excosec, excsc, exc) are trigonometric functions defined in terms of the secant and cosecant functions. They used to be important in fields such as surveying, railway engineering, civil engineering, astro ...

(external secant, exs) and

excosecant The exsecant (exsec, exs) and excosecant (excosec, excsc, exc) are trigonometric functions defined in terms of the secant and cosecant functions. They used to be important in fields such as surveying, railway engineering, civil engineering, as ...

(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 the higher education, K-12, professional, and library markets. It operates in more than 20 countries around the world.(Jun 27, 2014Global Publishing Leaders ...

, 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 Henry Holt and Company is an American book-publishing company based in New York City. One of the oldest publishers in the United States, it was founded in 1866 by Henry Holt and Frederick Leypoldt. Currently, the company publishes in the fields ...

, 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 ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science ...

, 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=

, 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