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{{Short description|1=Overview of and topical guide to trigonometry}}
{{merge from|List of trigonometry topics|date=November 2011|discuss=Talk:Outline of trigonometry#Merge from List of trigonometry topics}}
{{Trigonometry}}

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


'''[[Trigonometry]]''' &ndash; a 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 waves.
'''[[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}}
{{TOC limit<!--|limit=2-->}}


== Basics ==
== Basics ==
[[Image:Angle Symbol.svg|thumb|right|∠, the angle symbol in [[Unicode]] is [[List of XML and HTML character entity references|U+2220]]|228x228px]]
[[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, relative position of figures, and the properties of space. Geometry is used extensively in trigonometry.
* [[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; 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.
* [[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;
* [[Ratio]] &ndash; a ratio indicates how many times one number contains another


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


== Scholars associated with the development of trigonometry ==
== Scholars ==


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


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


* [[Aristarchus's inequality]]
* [[History of trigonometry]]
* [[Bhaskara I's sine approximation formula]]
* [[Greek astronomy]]
* [[Greek astronomy]]
* [[Indian 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 that use trigonometry ==
== Fields ==
{{main|Uses of trigonometry}}


[[Uses of trigonometry]]
* [[Acoustics]]
* [[Acoustics]]
* [[Architecture]]
* [[Architecture]]
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* [[Surveying]]
* [[Surveying]]


=== Physics ===
== Trigonometry in calculus ==

* [[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]]
* [[Inverse trigonometric functions]]
* [[List of integrals of 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 integral]]
* [[Trigonometric substitution]]
* [[Trigonometric substitution]]
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** [[Fourier transform]]
** [[Fourier transform]]
** [[Wave equation]]
** [[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 ==
== Lists ==
{{main|List of trigonometry topics}} – an extensive list of individual Wikipedia articles


* [[List of integrals of trigonometric functions]]
* [[List of integrals of trigonometric functions]]
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* [[Algebra]]
* [[Algebra]]
* [[Hyperbolic function]]
* [[List of exponential topics]]
* [[Outline of geometry]]
* [[Outline of geometry]]
* [[Precalculus]]
* [[Precalculus]]
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== External links ==
== External links ==

{{Wikibooks|Trigonometry}}
{{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]
* [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.
* [http://www.ping.be/~ping1339/gonio.htm An introduction to trigonometry]
* [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://catcode.com/trig/index.html Trigonometry FAQ]
* [http://www.pupress.princeton.edu/books/maor/ Trigonometric Delights], by [[Eli Maor]], Princeton University Press, 1998. Ebook version, in PDF format, full text presented.
* [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://www.plainmath.net/index.php?page=trig Trigonometry on PlainMath.net] Trigonometry Articles from PlainMath.Net
* [http://www.mathwords.com/index_trig.htm Trigonometry on Mathwords.com] index of trigonometry entries on Mathwords.com
* [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
* [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]

{{outline footer}}
{{outline footer}}


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

Latest revision as of 12:17, 30 October 2023

Trigonometry
Reference
Laws and theorems
Calculus
Mathematicians

The following outline is provided as an overview of and topical guide to trigonometry:

Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves.

Basics

[edit]
∠, the angle symbol in Unicode is U+2220
  • Geometry – mathematics concerned with questions of shape, size, the relative position of figures, and the properties of space. Geometry is used extensively in trigonometry.
  • Angle – 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 – a ratio indicates how many times one number contains another

Content of trigonometry

[edit]

Scholars

[edit]

History

[edit]
Main article: History of trigonometry

Fields

[edit]

Uses of trigonometry

Physics

[edit]

Astronomy

[edit]

Chemistry

[edit]

Geography, geodesy, and land surveying

[edit]
[edit]

Engineering

[edit]

Analog devices

[edit]

Calculus

[edit]

Other areas of mathematics

[edit]

Geometric foundations

[edit]

Trigonometric functions

[edit]

Trigonometric identities

[edit]

Trigonometric identity (list)

Solution of triangles

[edit]

Solution of triangles

More advanced trigonometric concepts and methods

[edit]

Numerical mathematics

[edit]

Trigonometric tables

[edit]

Trigonometric tables

Spherical trigonometry

[edit]

Spherical trigonometry

Mnemonics

[edit]

mnemonics in trigonometry

Lists

[edit]

See also

[edit]
[edit]
Wikibooks has a book on the topic of: Trigonometry
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