View source for Outline of trigonometry

<!--... Attention:  THIS IS AN OUTLINE

        part of the set of 830+ outlines listed at
             [[Wikipedia:Contents/Outlines]].

                 Wikipedia outlines are
              a special type of list article.
              They make up one of Wikipedia's
                content navigation systems

             See [[Wikipedia: Outlines]] and 
    [[Wikipedia:WikiProject Outlines]] for more details.
                   Further improvements
              to this outline are on the way
...-->
{{Short description|1=Overview of and topical guide to trigonometry}}
{{Trigonometry}}

The following [[Outline (list)|outline]] is provided as an overview of and topical guide to trigonometry:

'''[[Trigonometry]]''' &ndash; branch of [[mathematics]] that studies the relationships between the sides and the angles in [[triangle]]s. Trigonometry defines the [[trigonometric functions]], which describe those relationships and have applicability to cyclical phenomena, such as [[wave]]s.

{{TOC limit<!--|limit=2-->}}

== Basics ==
[[Image:Angle Symbol.svg|thumb|right|∠, the angle symbol in [[Unicode]] is [[List of XML and HTML character entity references|U+2220]]|228x228px]]
* [[Geometry]] &ndash; mathematics concerned with questions of shape, size, the relative position of figures, and the properties of space. Geometry is used extensively in trigonometry.
* [[Angle]] &ndash; the 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 a plane, but this plane does not have to be a Euclidean plane.
* [[Ratio]] &ndash; a ratio indicates how many times one number contains another

== Content of trigonometry == 
* [[Trigonometry]]
* [[Trigonometric functions]]
* [[Trigonometric identities]]
* [[Euler's formula]]

== Scholars ==

* [[Archimedes]]
* [[Aristarchus of Samos|Aristarchus]]
* [[Aryabhata]]
* [[Bhaskara I]]
* [[Claudius Ptolemy]]
* [[Euclid]]
* [[Hipparchus]]
* [[Madhava of Sangamagrama]]
* [[Ptolemy]]
* [[Pythagoras]]
* [[Regiomontanus]]

== History ==
{{main|Trigonometry#Early history of trigonometry|l1=History of trigonometry}}

* [[Aristarchus's inequality]]
* [[Bhaskara I's sine approximation formula]]
* [[Greek astronomy]] 
* [[Indian astronomy]]
* [[Jyā, koti-jyā and utkrama-jyā]]
* [[Madhava's sine table]]
* [[Ptolemy's table of chords]]
* [[Rule of marteloio]]
* [[Āryabhaṭa's sine table]]

== Fields ==

[[Uses of trigonometry]]
* [[Acoustics]]
* [[Architecture]]
* [[Astronomy]]
* [[Biology]]
* [[Cartography]]
* [[Chemistry]]
* [[Civil engineering]]
* [[Computer graphics]]
* [[Cryptography]]
* [[Crystallography]]
* [[Economics]]
* [[Electrical engineering]]
* [[Electronics]]
* [[Game development]]
* [[Geodesy]]
* [[Mechanical engineering]]
* [[Medical imaging]]
* [[Meteorology]]
* [[Music theory]]
* [[Number theory]]
* [[Oceanography]]
* [[Optics]]
* [[Pharmacy]]
* [[Phonetics]]
* [[Outline of physical science|Physical science]]
* [[Probability theory]]
* [[Seismology]]
* [[Statistics]]
* [[Surveying]]

=== Physics ===

* [[Abbe sine condition]]
* [[Greninger chart]]
* [[Phasor]]
* [[Snell's law]]

=== Astronomy ===

* [[Equant]]
* [[Parallax]]
* [[Dialing scales]]

=== Chemistry ===

* [[Greninger chart]]

=== Geography, geodesy, and land surveying ===

* [[Hansen's problem]]
* [[Snellius–Pothenot problem]]
* [[Great-circle distance]] – how to find that distance if one knows the [[latitude]] and [[longitude]].
* [[Resection (orientation)]]
* [[Vincenty's formulae]]
* [[Geographic distance]]
* [[Triangulation in three dimensions]]

=== Navigation ===

* [[Haversine formula]]
* [[Rule of marteloio]]

=== Engineering ===

* [[Belt problem]]
* [[Phase response]]
* [[Phasor]]
* [[Rake (angle)]]

=== Analog devices ===

* [[Dialing scales]]
* [[Gunter's quadrant]]
* [[Gunter's scale]]
* [[Protractor]]
* [[Scale of chords]]

== Calculus ==

* [[Inverse trigonometric functions]]
* [[List of integrals of trigonometric functions]]
* [[List of integrals of inverse trigonometric functions]]
* [[Regiomontanus' angle maximization problem]]
* [[Tangent half-angle substitution]]
* [[Trigonometric integral]]
* [[Trigonometric substitution]]
* Applications 
** [[Fourier transform]]
** [[Wave equation]]

== Other areas of mathematics ==

* For examples of trigonometric functions as [[generating functions]] in [[combinatorics]], see [[Alternating permutation]].
* [[Dirichlet kernel]]
* [[Euler's formula]]
* [[Exact trigonometric values]]
* [[Exponential sum]]
* [[Trigonometric integral]]
* [[Trigonometric polynomial]]
* [[Trigonometric series]]

== Geometric foundations ==

* [[Altern base]]
* [[Angle]]
** [[Plane angle]]
** [[Solid angle]]
** [[Spherical angle]]
** [[Right angle]]
* [[Angle excess]]
* [[Angular distance]]
* [[Angular unit]]
** [[Degree (angle)]]
** [[Gon (angle)]] (aka Grad, Gradian)
** [[Radian]]
** [[Turn (angle)]]
* [[Brocard points]]
* [[Chord (geometry)]]
* [[Circle]] (also see [[List of circle topics]])
** [[Unit circle]]
* [[Hypotenuse]]
* [[Opposites post]]
* [[pi|{{pi}}]] (pi)
* [[Ptolemy's theorem]]
* [[Pythagorean theorem]]
* [[Regiomontanus' angle maximization problem]]
* [[Thales' theorem]]
* [[Trigonometric function]]
* [[Trigonometry of a tetrahedron]]
* [[Triangle]] (also see [[List of triangle topics]])

== Trigonometric functions ==

* [[Sine]], [[Cosine]], [[Tangent (trigonometric function)]], [[Cotangent]], [[Secant (trigonometric function)]], [[Cosecant]] – see [[Trigonometric function]]
* <!--intentionally lower-case initial "a"-->[[atan2]]<!--intentionally lower-case initial "a"-->
* <nowiki>c</nowiki>is&mdash;see [[Euler's formula]]
* [[Cofunction]]
* [[Exsecant]]
* [[Gudermannian function]]
* [[Inverse trigonometric functions]]
* [[Jyā, koti-jyā and utkrama-jyā]]
* [[Versine]]

== Trigonometric identities ==

[[Trigonometric identity]] ([[List of trigonometric identities|list]])
* [[De Moivre's formula]]
* [[Euler's formula]]
* [[Hermite's cotangent identity]]
* [[Lagrange's trigonometric identities]]
* [[Morrie's law]]
* [[Proofs of trigonometric identities]]
* [[Pythagorean trigonometric identity]]
* [[Tangent half-angle formula]]

== Solution of triangles ==

[[Solution of triangles]]
* [[Law of sines]]
* [[Law of cosines]]
* [[Law of tangents]]
* [[Law of cotangents]]
* [[Mollweide's formula]]

== More advanced trigonometric concepts and methods ==

* [[Chebyshev polynomials]]
* [[Conway triangle notation]]
* [[Exact trigonometric constants]]
* [[Generalized trigonometry]]
* [[Gudermannian function]]
* [[Lissajous curve]]
* [[Polar sine]]
* [[Rational trigonometry]]
* [[Spread polynomials]]

== Numerical mathematics ==

* [[Abbe error]]
* [[Hypot]]
* [[Prosthaphaeresis]]
* [[Trigonometric interpolation]]
* [[Kunstweg]], an algorithm for computing sines, introduced in the late 1500s

=== Trigonometric tables ===

[[Trigonometric tables]]
* [[Generating trigonometric tables]]
* [[Āryabhaṭa's sine table]]
* [[Bhaskara I's sine approximation formula]]
* [[Madhava's sine table]]
* [[Ptolemy's table of chords]], written in the second century A.D.
* [[Rule of marteloio]]
* [[Canon Sinuum (Bürgi)|Canon Sinuum]], listing sines at increments of two arcseconds, published in the late 1500s

=== Spherical trigonometry ===

[[Spherical trigonometry]]
* [[Half-side formula]]
* [[Haversine formula]]

== Mnemonics ==

[[mnemonics in trigonometry]]
*[[All Students Take Calculus]]

== Lists ==

* [[List of integrals of trigonometric functions]]
* [[List of integrals of inverse trigonometric functions]]
* [[List of trigonometric identities]]
* [[Table of mathematical symbols]]

==See also==

* [[Algebra]]
* [[Hyperbolic function]]
* [[List of exponential topics]]
* [[Outline of geometry]]
* [[Precalculus]]
* [[Spherical geometry]]
* [[Table of mathematical symbols]]

== External links ==

{{Wikibooks|Trigonometry}}

* [https://web.archive.org/web/20060924185418/http://www.ping.be/~ping1339/gonio.htm An introduction to trigonometry]
* [https://web.archive.org/web/20070930031406/http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=212&bodyId=81 Benjamin Banneker's Trigonometry Puzzle] at [http://mathdl.maa.org/convergence/1/ Convergence]
* [http://www.clarku.edu/~djoyce/trig/ Dave's short trig course]
* [https://web.archive.org/web/20060414195120/http://www.pupress.princeton.edu/books/maor/ Trigonometric Delights], by [[Eli Maor]], Princeton University Press, 1998.  Ebook version, in PDF format, full text presented.
* [https://web.archive.org/web/20071104225720/http://baqaqi.chi.il.us/buecher/mathematics/trigonometry/index.html Trigonometry] by Alfred Monroe Kenyon and Louis Ingold, The Macmillan Company, 1914. In images, full text presented.
* [http://catcode.com/trig/index.html Trigonometry FAQ]
* [http://www.mathwords.com/index_trig.htm Trigonometry on Mathwords.com] index of trigonometry entries on Mathwords.com
* [http://www.plainmath.net/index.php?page=trig Trigonometry on PlainMath.net] Trigonometry Articles from PlainMath.Net

{{outline footer}}

[[Category:Outlines of mathematics and logic|Trigonometry]]
[[Category:Outlines|Trigonometry]]
[[Category:Trigonometry| 1]]
[[Category:Mathematics-related lists|Trigonometry]]