Cofunction
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In mathematics, 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).[1] This definition typically applies to trigonometric functions.[2][3] The prefix "co-" can be found already in Edmund Gunter's Canon triangulorum (1620).[4][5]
Template:AnchorFor example, sine (Latin: sinus) and cosine (Latin: cosinus,[4][5] sinus complementi[4][5]) are cofunctions of each other (hence the "co" in "cosine"):
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The same is true of secant (Latin: secans) and cosecant (Latin: cosecans, secans complementi) as well as of tangent (Latin: tangens) and cotangent (Latin: cotangens,[4][5] tangens complementi[4][5]):
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These equations are also known as the cofunction identities.[2][3]
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):
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See also
- Hyperbolic functions
- Lemniscatic cosine
- Jacobi elliptic cosine
- Cologarithm
- Covariance
- List of trigonometric identities
References
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- ↑ 2.0 2.1 Template:Cite book
- ↑ 3.0 3.1 Template:Cite web
- ↑ 4.0 4.1 4.2 4.3 4.4 Template:Cite book
- ↑ 5.0 5.1 5.2 5.3 5.4 Template:Cite web