Outline of trigonometry
{{Short description|1=Overview of and topical guide to trigonometry}}
{{Trigonometry}}
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.
{{TOC limit}}
Basics
Image:Angle Symbol.svg is U+2220|228x228px]]
- 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 ==
Scholars
History
{{main|Trigonometry#Early history of trigonometry|l1=History of trigonometry}}
Fields
- 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
- Physical science
- Probability theory
- Seismology
- Statistics
- Surveying
= Physics =
= Astronomy =
= Chemistry =
= 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 =
= Engineering =
= Analog devices =
Calculus
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)
- 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
Trigonometric identities
Solution of triangles
More advanced trigonometric concepts and methods
Numerical mathematics
- Abbe error
- Hypot
- Prosthaphaeresis
- Trigonometric interpolation
- Kunstweg, an algorithm for computing sines, introduced in the late 1500s
= 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, listing sines at increments of two arcseconds, published in the late 1500s
= Spherical trigonometry =
Mnemonics
Lists
See also
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}}