cosine: meaning, definition, pronunciation and examples
LowTechnical/Formal
Quick answer
What does “cosine” mean?
A trigonometric function, defined for an acute angle in a right triangle as the ratio of the length of the adjacent side to the length of the hypotenuse.
Audio
Pronunciation
Definition
Meaning and Definition
A trigonometric function, defined for an acute angle in a right triangle as the ratio of the length of the adjacent side to the length of the hypotenuse.
A periodic mathematical function (cos) of an angle, with outputs ranging from -1 to 1, fundamental to describing oscillations, waves, and circular motion. It is the x-coordinate of a point on the unit circle corresponding to a given angle.
Dialectal Variation
British vs American Usage
Differences
No difference in meaning, usage, or pronunciation. The word is identical in both varieties.
Connotations
None beyond its technical definition.
Frequency
Equally low frequency in both varieties, appearing only in specific technical/educational contexts.
Grammar
How to Use “cosine” in a Sentence
the cosine of [angle/theta/pi/3]cos([numerical value])Vocabulary
Collocations
Usage
Meaning in Context
Business
Virtually never used. An exception might be in technical presentations for engineering or data science companies discussing algorithms.
Academic
Common in secondary and tertiary education within mathematics, physics, and engineering courses.
Everyday
Extremely rare. Would only appear in conversation when discussing specific homework or a technical problem.
Technical
Core terminology in trigonometry, calculus, signal processing, computer graphics, and physics.
Vocabulary
Synonyms of “cosine”
Neutral
Weak
Vocabulary
Antonyms of “cosine”
Watch out
Common Mistakes When Using “cosine”
- Pronouncing it as /kəʊˈziːn/ or /ˈkɒz.aɪn/.
- Confusing it with 'cosine' (an old word for cousin) which is obsolete.
- Incorrectly applying the cosine rule (law of cosines) to non-triangle problems.
- Misspelling as 'cosign' or 'co-sign'.
FAQ
Frequently Asked Questions
No, they are etymologically unrelated. 'Cosine' comes from the Latin 'complementi sinus' (sine of the complement). 'Cosy' has uncertain, possibly Scandinavian, origins.
Because their values (sine = y-coordinate, cosine = x-coordinate) are derived from the coordinates of a point moving around a unit circle.
They are the same mathematical theorem. 'Cosine rule' is the more common term in UK curricula, while 'law of cosines' is prevalent in the US.
No. It is exclusively a noun. The related verb would be 'to compute/calculate/find the cosine of'.
A trigonometric function, defined for an acute angle in a right triangle as the ratio of the length of the adjacent side to the length of the hypotenuse.
Cosine is usually technical/formal in register.
Cosine: in British English it is pronounced /ˈkəʊ.saɪn/, and in American English it is pronounced /ˈkoʊ.saɪn/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
COsine = Adjacent Over hypotenuse (CAH in SOH-CAH-TOA). 'CO' sounds like 'cozy', and you get cozy with the side Adjacent to the angle.
Conceptual Metaphor
MAPPING: The cosine maps angular position to horizontal displacement. SOURCE-PATH: Cosine describes the horizontal 'shadow' or projection of a rotating radius.
Practice
Quiz
Which of the following correctly defines the cosine of an angle in a right triangle?