trigonometric function
Let an agent explain the trigonometric functions and their relations, relay identities, values and applications from mathematical references, describe historical and rarely used functions, and distinguish trigonometric from hyperbolic and inverse functions.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define Definitions.
Definition
Definitions.
Definition
Definition.
- How are the trigonometric functions defined by triangles, the unit circle and series? definition
- Is the question about trigonometric, inverse or hyperbolic functions? boundary
Relations
Identities.
Relations
Relations.
- What are the key identities, including Pythagorean, angle sum and double angle formulas? definition
- Which entry fits trigonometric identity? action
Compute Values and computation.
Values
Special values and graphs.
Values
Values.
- What are the special values and graph features of each function? measurement
- Which references are standard? provenance
Algorithms
Computation.
Algorithms
Algorithms.
- How are trigonometric functions computed by series, CORDIC and tables? provenance
- Which entry fits CORDIC? action
Apply Applications.
Physics
Physics and engineering.
Physics
Physics.
- How are trigonometric functions used in waves, rotations, navigation and signal processing? provenance
- Which entry fits Fourier analysis? action
Historical
Historical and rare functions.
Historical
Historical.
- What were the chord, versine and haversine used for, and what is the cas function? provenance
- Which sources are cited? provenance
Context History and teaching.
History
History.
History
History.
- How did trigonometry develop from Hipparchus and Indian sine tables to Euler? provenance
- Which entry fits the history of trigonometry? action
Teaching
Teaching.
Teaching
Teaching.
- How are trigonometric functions taught, and what misconceptions arise? provenance
- Which entry fits mathematics education? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- cas function, chord function, tangent and cotangent, sine and cosine, secant and cosecant, rarely used trigonometric functions, Jyā, koti-jyā and utkrama-jyā
What it is Filled
The functions of an angle that relate the angles of a right triangle to ratios of its sides and extend through the unit circle beyond acute angles, principally sine and cosine, tangent and cotangent, secant and cosecant, with historically used functions such as the chord, versine and haversine, and the cas function of the Hartley transform; sine and cosine are defined for every real input, tangent and secant are undefined where cosine is zero, and cotangent and cosecant are undefined where sine is zero. Trigonometric functions are periodic, elementary and transcendental, and are fundamental in geometry, physics, signal processing and engineering.
Why it exists Filled
Let an agent explain the trigonometric functions and their relations, relay identities, values and applications from mathematical references, describe historical and rarely used functions, and distinguish trigonometric from hyperbolic and inverse functions.
Distinguishing features Filled
- Unit circle definition
- Periodicity
- Rich identities
- Fourier basis
What robots and AI may and may not do Filled
Must not
- Mix degrees and radians silently in a calculation.
- Return an inverse value outside its principal range without saying so.
- Present a rounded value as exact in navigation, surveying or engineering results.
- Hide a division by zero, such as tangent at a right angle, behind a large number.
Only with a human decision
- Relying on its own trigonometric calculations for structural, navigation or safety-critical work.
May
- Compute sine, cosine, tangent and related functions and state whether angles are in degrees or radians.
- Explain identities and inverse functions with their valid ranges.
Moral aspects Filled
- Angle errors in surveying, navigation and construction can cause accidents and boundary disputes.
- Students rely on worked answers; wrong ones mislead learning.
Who is affected
- Engineers and surveyors
- Students
- People relying on computed positions
Owners Filled
Steward
The public: held in common as mathematical knowledge.
Links to other meta-models Filled
parent
- Q184743 - registry parent class
- Q824282 - registry parent class
- Q864333 - registry parent class
related
- periodic function - in registry terms
- elementary function - in registry terms
- transcendental function - in registry terms
- unit circle - for all real arguments
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.trigonometric-function
- Wikidata: Q93344 (https://www.wikidata.org/wiki/Q93344)
Direct properties not applicable Not applicable
- period of sine: 2 pi radians
- principal functions: 6 count
Plane XCT: no invented physical properties.
Recognition optional Filled
- Functions of angles based on the unit circle
- Sine, cosine, tangent, cotangent, secant, cosecant and historical functions
- Hyperbolic functions use the hyperbola; inverse trigonometric functions return angles
- Wave-shaped graphs of sine and cosine and the unit circle diagram.
Capabilities and actions required Filled
- explain definitions and relations
- relay identities and values
- describe applications
- distinguish related functions
Hazards and failure modes required Filled
- Degree and radian confusion
- Notation ambiguities such as sin squared and inverse
- Domain errors for tangent and secant
Standards and interfaces required Filled
- ISO 80000-2 notation for trigonometric functions
- No regulation
Context of use required Filled
- Relating angles to lengths and modelling periodic phenomena.
- sine and cosine
- tangent and cotangent
- secant and cosecant
- historical functions such as chord, versine, haversine and exsecant
- the cas function
- inverse trigonometric functions as related
- hyperbolic analogues as related
Sources Filled
- Wikidata item Q93344: trigonometric function - identity and sense of the item
- Wikipedia: Trigonometric functions - general description of the item
Open questions
- Should sine and cosine be the primary linked entries?
- How should reference tables be linked?
- The registry entry has merged aliases naming pairs and rare functions; should they be split off?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q93344/spec.json