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In graph Frontier

Sine and cosine

In mathematics, sine and cosine are trigonometric functions of an angle.

At a glance

Type
waves
Disciplines 2
Mental models 2
Role in the graph
Cross-disciplinary bridge
reaches 5 discipline lenses

Key signals

Cross-disciplinary reach
Disciplines
2
  • Mathematics
  • Geometry
Evidence & development

Dependencies

What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.

Enables · leads to

Trigonometrydepends onSine and cosineEstablished

Open Trigonometry →

trigonometry depends on sine and cosine.

Mechanism: Trigonometry rests on sine and cosine: these functions link a triangle's angles to the ratios of its sides.

Sources:

System context

Sine and cosineis aFunctionEstablished

Open Function →

sine and cosine is a kind of function.

Mechanism: Sine and cosine are functions of an angle: they return the coordinates of a point moving around the unit circle.

Sources:

Structural role & consequence

Interpreted from the current atlas graph — what the connections mean, not just how many there are.

  • 33% of its relationships cross field boundaries, reaching 5 other disciplines — unusual in a discipline where most concepts stay within their field.

    structural · Structural graph analysis — not a claim of importance, causation or history.

  • Currently dark in the atlas: no key date stored · 3 of 3 of its relations lack claim-level evidence.

    atlas representation · Describes the current Thinking OS representation, not the state of the world.

  • Exercises 2 annotated mental models — a concept that connects several thinking patterns.

    curated · Curated annotations, not a derived measure.

  • Structural neighbourhood: 3 → 27 → 96 concepts reachable within 3 hops.

    structural · Structural reach — being reachable is not the same as being understood.

33%

cross-field
2 within-field, 1 cross-field

0 of 3 relations carry evidence · concept has a verified source

Strengths & constraints

Constraints

  • Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
  • No dated history stored — the atlas records no key date for this concept. atlas representation

Conditions

  • Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural

Dependency radial

What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.

TrigonometrySine and cosine◀ builds onenables ▶

What builds on this

1 concept build on this directly, 1 in total, across 2 disciplines.

GeometryMathematics

Structural downstream reach along dependency edges — not a claim of historical necessity.

Seen through each discipline

How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.

Mathematics

Through this lens it connects to Function and Trigonometry.

Sine and cosine through the Mathematics lens

Geometry

Through this lens it connects to Trigonometry.

Sine and cosine through the Geometry lens

Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.

This idea also appears in…

The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”

Oscillation23 disciplines · 22 concepts
Waves21 disciplines · 20 concepts

Concepts

  • ResonancePhysicsAcousticsMechanical Engineering

    shares a mental model · shares a mental model

  • WavePhysicsAcousticsOptics

    shares a mental model · shares a mental model

  • Standing wavePhysicsAcoustics

    shares a mental model · shares a mental model

  • OscillationPhysicsMechanicsBiology

    shares a mental model · crosses a discipline boundary

  • Electromagnetic radiationPhysicsElectromagnetismOptics

    shares a mental model

  • SignalInformation TheoryElectrical EngineeringNeuroscience

    shares a mental model

Mental models at work here

The scientific picture
  • Connects 3 other ideas across 2 disciplines.
  • A cross-disciplinary bridge — its connections reach into 5 other fields.
  • Most of its connections are of the “Kind & structure” kind.
  • It exercises 2 reusable thinking patterns.

Derived from the graph’s real structure — observations, not a score.

Sources