cosecant: meaning, definition, pronunciation and examples
SpecializedTechnical / Academic / Scientific
Quick answer
What does “cosecant” mean?
A trigonometric function defined as the reciprocal of the sine function.
Audio
Pronunciation
Definition
Meaning and Definition
A trigonometric function defined as the reciprocal of the sine function.
In a right triangle, the cosecant of an angle is the ratio of the length of the hypotenuse to the length of the side opposite the angle.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage; concept is identical.
Connotations
Purely mathematical term with no cultural or emotional connotations.
Frequency
Used with identical frequency in relevant academic/professional fields.
Grammar
How to Use “cosecant” in a Sentence
The cosecant (of angle θ) is...Cosecant equals hypotenuse over opposite.Csc(θ) = 1/sin(θ).Vocabulary
Collocations
Usage
Meaning in Context
Business
Virtually never used.
Academic
Core term in trigonometry and calculus courses.
Everyday
Extremely rare outside educational contexts.
Technical
Standard term in mathematics, engineering, physics, and computer graphics.
Vocabulary
Synonyms of “cosecant”
Strong
Neutral
Vocabulary
Antonyms of “cosecant”
Watch out
Common Mistakes When Using “cosecant”
- Confusing cosecant (1/sin) with secant (1/cos).
- Pronouncing it as 'co-see-cant' instead of 'co-see-kant'.
- Forgetting it's undefined when sin(θ) = 0.
FAQ
Frequently Asked Questions
Cosecant (csc) is the reciprocal of sine (sin). So, csc(θ) = 1 / sin(θ).
It is undefined when the sine of the angle is 0, which occurs at angle measures of 0°, 180°, 360°, etc. (or 0, π, 2π... radians).
Almost never. It is a specialised term confined to technical fields like mathematics, physics, and engineering.
The standard abbreviation is 'csc', as in 'csc(45°)'.
A trigonometric function defined as the reciprocal of the sine function.
Cosecant is usually technical / academic / scientific in register.
Cosecant: in British English it is pronounced /kəʊˈsiːkənt/, and in American English it is pronounced /koʊˈsiːkənt/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
CO-secant sounds like "CO-hypotenuse" - it's the ratio where the Hypotenuse is COming first (over the opposite side).
Conceptual Metaphor
N/A. Purely abstract mathematical relationship.
Practice
Quiz
What is the definition of the cosecant of an acute angle in a right triangle?