Outline of trigonometry

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 -

  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

• 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
• Vincenty's formulae
• Geographic distance
• Triangulation in three dimensions

  Navigation

• Haversine formula
• Rule of marteloio

  Engineering

• Belt problem
• Phase response
• Phasor
• Rake

  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 constants
• Exponential sum
• Trigonometric integral
• Trigonometric number
• Trigonometric polynomial
• Trigonometric series

  Geometric foundations

• Altern base
• Angle
• * Plane angle
• * Solid angle
• * Spherical angle
• * Right angle
• Angle excess
• Angular distance
• Angular unit
• * Degree
• * Gon
• * Radian
• * Turn
• Brocard points
• Chord
• Circle
• * Unit circle
• Hypotenuse
• Opposites post
• pi|
• Ptolemy's theorem
• Pythagorean theorem
• Regiomontanus' angle maximization problem
• Thales' theorem
• Trigonometric function
• Trigonometry of a tetrahedron
• Triangle

  Trigonometric functions

• Sine, Cosine, Tangent, Cotangent, Secant, 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

• 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

• 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

• 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

• Half-side formula
• Haversine formula

  Mnemonics

• 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