arc secant: meaning, definition, pronunciation and examples
C2 (Highly technical)Exclusively formal and academic, limited to mathematics, physics, and engineering contexts.
Quick answer
What does “arc secant” mean?
The inverse function of the secant (in trigonometry). For a given value x, it returns the angle whose secant is x.
Audio
Pronunciation
Definition
Meaning and Definition
The inverse function of the secant (in trigonometry). For a given value x, it returns the angle whose secant is x.
A mathematical function, typically written as arcsec(x) or sec⁻¹(x), defined for |x| ≥ 1. It returns the principal value of the angle, usually in the range [0, π] excluding π/2. It is one of the inverse trigonometric functions used extensively in calculus and engineering.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or notational differences. Both regions use 'arc secant' or 'inverse secant'. Notation may vary slightly in textbooks (arcsec vs sec⁻¹).
Connotations
Purely technical, no differential connotations.
Frequency
Extremely low frequency in general language; identical frequency in technical domains.
Grammar
How to Use “arc secant” in a Sentence
arcsec(x)the arc secant of a numberfind the arc secantarcsec is defined forVocabulary
Collocations
Examples
Examples of “arc secant” in a Sentence
adjective
British English
- The arc secant function is continuous on that interval.
- We need the arc secant values for the table.
American English
- The arc secant value is undefined there.
- The arc secant function is monotonic on that branch.
Usage
Meaning in Context
Business
Not used.
Academic
Primary context. Used in advanced mathematics, physics, and engineering courses and publications.
Everyday
Virtually never used.
Technical
Core term in pure and applied mathematics, calculus, computer algebra systems, and scientific computing.
Vocabulary
Synonyms of “arc secant”
Vocabulary
Antonyms of “arc secant”
Watch out
Common Mistakes When Using “arc secant”
- Confusing 'arc secant' (sec⁻¹x) with '(sec x)⁻¹' (which equals cos x).
- Mistaking its domain: it is defined for |x| ≥ 1, not all real numbers.
- Forgetting the principal value range [0, π] excluding π/2.
FAQ
Frequently Asked Questions
No, this is a common error. 'Arc secant' (sec⁻¹x) is the inverse function. '1 / secant' ( (sec x)⁻¹ ) is the reciprocal, which equals the cosine function.
It is defined for all real numbers x where |x| ≥ 1. In interval notation: (-∞, -1] ∪ [1, ∞).
It is essential for solving trigonometric equations where the secant of an angle is known and the angle itself is sought. It also appears in solutions to integrals in calculus.
The two most common notations are arcsec(x) and sec⁻¹(x). The latter must be carefully distinguished from exponent notation; the '-1' here denotes the inverse, not the reciprocal.
The inverse function of the secant (in trigonometry). For a given value x, it returns the angle whose secant is x.
Arc secant is usually exclusively formal and academic, limited to mathematics, physics, and engineering contexts. in register.
Arc secant: in British English it is pronounced /ˌɑːk ˈsiːkənt/, and in American English it is pronounced /ˌɑːrk ˈsiːkənt/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “none”
Learning
Memory Aids
Mnemonic
'Arc' tells you to go back to the angle. Think: 'Secant gives me a ratio from an angle; arc secant gives me the angle from a ratio.'
Conceptual Metaphor
UNDOING AN OPERATION / REVERSING A PROCESS (like asking, 'What angle would produce this secant value?').
Practice
Quiz
What is the principal value range for the arc secant function?