trigonometric function
Low (Technical)Highly formal, technical, academic
Definition
Meaning
Any of six fundamental mathematical functions—sine, cosine, tangent, cosecant, secant, cotangent—that relate the angles of a right‑angled triangle to ratios of its sides.
Periodic functions defined on the unit circle or complex plane, essential in modeling oscillations, waves, and periodic phenomena across mathematics, physics, and engineering.
Linguistics
Semantic Notes
Always plural form 'functions' when referring to the set; singular 'function' when specifying one (e.g., 'the sine function'). Purely technical; no figurative uses.
Dialectal Variation
British vs American Usage
Differences
No lexical differences. Pronunciation may vary slightly in stress pattern.
Connotations
None; identical technical meaning.
Frequency
Equally rare outside mathematics/engineering contexts in both varieties.
Vocabulary
Collocations
Grammar
Valency Patterns
[adjective] + trigonometric functiontrigonometric function + of + [angle/variable]calculate/compute + trigonometric functionVocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “None”
Usage
Context Usage
Business
Virtually never used.
Academic
Core term in mathematics, physics, engineering, and computer graphics courses.
Everyday
Extremely rare; only when explaining technical concepts.
Technical
Fundamental in signal processing, acoustics, navigation, and any field involving waves or rotation.
Examples
By Part of Speech
verb
British English
- We must trigonometric the angle before proceeding.
- The software can trigonometric the data automatically.
American English
- You need to trigonometric the values first.
- The algorithm will trigonometric the inputs.
adverb
British English
- The values vary trigonometrically over time.
- The signal is modulated trigonometrically.
American English
- The function behaves trigonometrically.
- The relationship is expressed trigonometrically.
adjective
British English
- The trigonometric analysis yielded precise results.
- A trigonometric approach simplified the problem.
American English
- We applied a trigonometric method to the wave data.
- The trigonometric solution was more elegant.
Examples
By CEFR Level
- Trigonometric functions are maths for triangles.
- Sine and cosine are the most common trigonometric functions.
- Engineers use trigonometric functions to calculate forces in structures.
- The Fourier series decomposes periodic signals into sums of trigonometric functions.
Learning
Memory Aids
Mnemonic
SOH‑CAH‑TOA: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
Conceptual Metaphor
ANGLES ARE RATIOS; PERIODICITY IS CIRCULAR MOTION.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid direct calque 'тригонометрическая функциональность'. Use 'тригонометрическая функция'.
- Do not confuse 'function' (функция) with 'functional' (функционал).
Common Mistakes
- Misspelling as 'trigonometrical function' (archaic).
- Using singular 'trigonometric function' to refer to the whole set.
- Confusing with hyperbolic functions.
Practice
Quiz
Which of the following is NOT a trigonometric function?
FAQ
Frequently Asked Questions
Six: sine, cosine, tangent, cosecant, secant, cotangent.
Originally defined for right triangles, they are extended via the unit circle to all real numbers and complex domains.
Modeling periodic phenomena such as sound waves, light waves, alternating current, and oscillatory motion.
Trigonometric functions relate to circles and periodic motion; hyperbolic functions relate to hyperbolas and are not periodic.