Cofunction

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Trigonometric function paired with another

title: "Cofunction" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["trigonometry"] description: "Trigonometric function paired with another" topic_path: "general/trigonometry" source: "https://en.wikipedia.org/wiki/Cofunction" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Trigonometric function paired with another ::

::figure[src="https://upload.wikimedia.org/wikipedia/commons/7/71/Sine_cosine_one_period.svg" caption="[[Sine]] and [[cosine]] are each other's cofunctions."] ::

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). This definition typically applies to trigonometric functions. The prefix "co-" can be found already in Edmund Gunter's Canon triangulorum (1620).

IdentitiesFor example, sine (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 (Latin: cosecans, secans complementi) as well as of tangent (Latin: tangens) and cotangent (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

References

  1. (2014). "Algebra and Trigonometry". [[Cengage Learning]].
  2. (1620). "Canon triangulorum".
  3. (2010-12-06). "A reconstruction of Gunter's Canon triangulorum (1620)". HAL.
  4. (2012). "5.1 The Elementary Identities". Precalculus.
  5. (January 1909). "Trigonometry". [[Henry Holt and Company]].
  6. "Coversine". [[Wolfram Research, Inc.]].
  7. "Covercosine". [[Wolfram Research, Inc.]].

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trigonometry