Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Sine and cosine

In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the…

Measurement, Background & Software implementations

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Sine and cosine. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Domain
real number R {\displaystyle \mathbb {R} }
Fields of application
Trigonometry, Fourier series, Mathematical analysis.
General definition
sin ⁡ ( θ ) = opposite hypotenuse cos ⁡ ( θ ) = adjacent hypotenuse {\displaystyle {\begin{aligned}&\sin(\theta )={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}\\[8pt]&\cos(…
Image
[ − 1 , 1 ] {\displaystyle [-1,1]}

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Elementary descriptions

Analytic descriptions

Complex numbers relationship

Background

Software implementations

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Sine and cosine

Nodes131
Edges130
Triples86
Avg. degree1.98
Density0.015267
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Sine and cosine

Top relations

related to history · 15
Sine and cosine → Arabic, Aryabhatiya, BCE, CE, Gupta, Hipparchus, Indian, Latin, Nicaea, Ptolemy, Roman Egypt, Sanskrit, Surya Siddhanta, The, While
related to Series and polynomials · 12
Sine and cosine → As, Both, Continuity, Fourier, Let, More, One, Such, Taking, Taylor, The, This
related to Turns based implementations · 8
Sine and cosine → For, Fortran, In, Representing, SciPy, Some, The, These
related to Polar coordinates · 5
Sine and cosine → Euler's, For, Im, Re, Sine
related to Software implementations · 5
Sine and cosine → Algorithms, IEEE, The, There, This
related to Complex exponential function definitions · 4
Sine and cosine → Alternatively, Both, Euler's, For
related to Right-angled triangle definition · 4
Sine and cosine → ABC, It, The, To
related to Special angle measures · 4
Sine and cosine → As, For, However, The
related to Complex arguments · 3
Sine and cosine → Applying, It, These
related to Unit circle definition · 3
Sine and cosine → Cartesian, The, This

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle sine sin cosine cos functions angle frac theta pi function real begin end right aligned series trigonometric hypotenuse opposite

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Sine and cosineDomainreal number R {\displaystyle \mathbb {R} }1.00infobox
Sine and cosineFields of applicationTrigonometry, Fourier series, Mathematical analysis.1.00infobox
Sine and cosineGeneral definitionsin ⁡ ( θ ) = opposite hypotenuse cos ⁡ ( θ ) = adjacent hypotenuse {\displaystyle {\begin{aligned}&\sin(\theta )={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}\\[8pt]&\cos(…1.00infobox
Sine and cosineImage[ − 1 , 1 ] {\displaystyle [-1,1]}1.00infobox
soundinstance ofallowing their extension to arbitrary positive and negative values and even to complex numbers.The sine and cosine functions are commonly used to model periodic phenomena0.80text
light wavesinstance ofallowing their extension to arbitrary positive and negative values and even to complex numbers.The sine and cosine functions are commonly used to model periodic phenomena0.80text
the positioninstance ofallowing their extension to arbitrary positive and negative values and even to complex numbers.The sine and cosine functions are commonly used to model periodic phenomena0.80text
velocity of harmonic oscillatorsinstance ofallowing their extension to arbitrary positive and negative values and even to complex numbers.The sine and cosine functions are commonly used to model periodic phenomena0.80text
sunlight intensityinstance ofallowing their extension to arbitrary positive and negative values and even to complex numbers.The sine and cosine functions are commonly used to model periodic phenomena0.80text
day lengthinstance ofallowing their extension to arbitrary positive and negative values and even to complex numbers.The sine and cosine functions are commonly used to model periodic phenomena0.80text
and average temperature variations throughout the yearinstance ofallowing their extension to arbitrary positive and negative values and even to complex numbers.The sine and cosine functions are commonly used to model periodic phenomena0.80text
degreeinstance ofThe input in this table provides various unit systems0.80text

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.