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
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 Trigonometry Trigonometric functions Trigonometric identities Euler's formula
Scholars Archimedes Aristarchus Aryabhata Bhaskara I Claudius Ptolemy Euclid Hipparchus Madhava of Sangamagrama Ptolemy Pythagoras Regiomontanus
History
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 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) (a.k.a. Grad, Gradian) Radian Turn (angle) Brocard points Chord (geometry) Circle (also see List of circle topics) Unit circle Hypotenuse Opposites post π (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 atan2 cis—see Euler's formula Cofunction Exsecant Gudermannian function Inverse trigonometric functions Jyā, koti-jyā and utkrama-jyā Versine
Trigonometric identities Trigonometric identity (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, 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
An introduction to trigonometry Benjamin Banneker's Trigonometry Puzzle at Convergence Dave's short trig course Archived 2008-06-15 at the Wayback Machine Trigonometric Delights, by Eli Maor, Princeton University Press, 1998. Ebook version, in PDF format, full text presented. Trigonometry by Alfred Monroe Kenyon and Louis Ingold, The Macmillan Company, 1914. In images, full text presented. Trigonometry FAQ Trigonometry on Mathwords.com index of trigonometry entries on Mathwords.com Trigonometry on PlainMath.net Archived 2007-10-27 at the Wayback Machine Trigonometry Articles from PlainMath.Net