Outline Of Trigonometry

Short description: Overview of and topical guide to 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.

Basics

∠, 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

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) (aka 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

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

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

External links

An introduction to trigonometry
Benjamin Banneker's Trigonometry Puzzle at Convergence
Dave's short trig course
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 Trigonometry Articles from PlainMath.Net

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