arc cosine: meaning, definition, pronunciation and examples
Very Low (Technical)Technical/Scientific
Quick answer
What does “arc cosine” mean?
The inverse function of the cosine.
Audio
Pronunciation
Definition
Meaning and Definition
The inverse function of the cosine; the angle whose cosine is a given number.
A trigonometric function, also denoted as arccos or cos⁻¹, which returns the principal value of the angle (typically in radians or degrees) corresponding to a given cosine value between -1 and 1.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or spelling differences. Both regions use the term identically.
Connotations
Purely mathematical, with no cultural connotations.
Frequency
Used with equal, low frequency in specialized technical contexts in both regions.
Grammar
How to Use “arc cosine” in a Sentence
arc cosine of [number]arccos([number])Vocabulary
Collocations
Examples
Examples of “arc cosine” in a Sentence
verb
British English
- We need to arc cosine this result to find the phase angle.
- You cannot directly arc cosine a value greater than one.
American English
- The subroutine arccosines the input to return an angle.
- You'll need to arc-cosine that value in the next step.
adverb
British English
- The angle was calculated arc-cosine-wise.
American English
- The function processed the data arc-cosine.
adjective
British English
- The arc cosine function is monotonic.
- Use the arc cosine key on your calculator.
American English
- The arccos value is expressed in radians.
- Check the arc-cosine result for quadrant correctness.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Used in mathematics, physics, engineering, and computer science courses and literature.
Everyday
Not used.
Technical
Core term in trigonometry, calculus, signal processing, and geometry.
Vocabulary
Synonyms of “arc cosine”
Vocabulary
Antonyms of “arc cosine”
Watch out
Common Mistakes When Using “arc cosine”
- Confusing arccos(x) with 1/cos(x) (which is secant).
- Forgetting the restricted range of the output angle.
- Pronouncing it as 'arc co-sign'.
FAQ
Frequently Asked Questions
Yes, 'arccos' is the standard abbreviation for 'arc cosine', just as 'cos' is for 'cosine'.
No, the input to the arc cosine function must be between -1 and 1 inclusive. The output is an angle.
It returns an angle. The units (radians or degrees) depend on the context or calculator setting. In pure mathematics, radians are standard.
Arc cosine (arccos x) is the inverse function of cosine. Secant (sec x) is the reciprocal function (1/cos x). They are completely different operations.
The inverse function of the cosine.
Arc cosine is usually technical/scientific in register.
Arc cosine: in British English it is pronounced /ˌɑːk ˈkəʊ.saɪn/, and in American English it is pronounced /ˌɑːrk ˈkoʊ.saɪn/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “None”
Learning
Memory Aids
Mnemonic
Arc Cosine is like asking the question: "What ANGLE (the arc) has this COSINE value?" It's the 'angle-finder' for cosine.
Conceptual Metaphor
A reverse lookup or an 'undo' button for the cosine function.
Practice
Quiz
What is the value of arccos(1)?