versed sine
Extremely Rare / ArchaicTechnical / Historical / Archaic
Definition
Meaning
A trigonometric function, defined as 1 minus the cosine of an angle (versin θ = 1 − cos θ).
A historical trigonometric function used in navigation, astronomy, and surveying, now largely obsolete in modern mathematics in favor of the cosine function.
Linguistics
Semantic Notes
The term is a contraction of 'versed sine' from the Latin 'sinus versus' (flipped sine). It was part of a family of related functions (haversine, coversine, exsecant) used for calculations before the widespread use of calculators and computers. It is functionally equivalent to 2 sin²(θ/2).
Dialectal Variation
British vs American Usage
Differences
No significant regional differences exist, as the term is uniformly archaic and technical.
Connotations
Purely historical/mathematical; evokes pre-computational mathematics, celestial navigation, and classical engineering.
Frequency
Effectively zero in contemporary usage in both varieties. May appear in historical texts or highly specialized discussions of mathematical history.
Vocabulary
Collocations
Grammar
Valency Patterns
the versed sine of [angle/numeral]to compute/find the versed sineVocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “None”
Usage
Context Usage
Business
Not used.
Academic
Only in historical studies of mathematics, astronomy, or navigation.
Everyday
Never used.
Technical
Extremely rare, only in discussions of archaic computational methods or in reproducing historical calculations.
Examples
By Part of Speech
adjective
British English
- The versed sine values were tabulated in the old nautical almanac.
- He referred to the versed sine function in his historical analysis.
American English
- The versed sine table was essential for the calculation.
- She explained the versed sine formula to the class.
Examples
By CEFR Level
- The *versed sine* is a trigonometric function you will likely never use in modern practice.
- Old navigation manuals sometimes required the calculation of the *versed sine*.
- The astronomer consulted a table of *versed sines* to complete the spherical trigonometry for the star's position.
- In deriving the haversine formula for great-circle distance, one encounters the *versed sine* as an intermediate step.
Learning
Memory Aids
Mnemonic
Think: 'VERY SINE' but 'versed' (turned). It's the sine function 'flipped' or 'versed' (turned against itself), resulting in 1 minus the cosine.
Conceptual Metaphor
MATHEMATICAL FUNCTIONS ARE TOOLS (an obsolete tool in the mathematical toolkit).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not confuse with 'синус' (sine). The Russian term is 'синус-верзус' (sinus-versus) or 'версинус' (versinus).
- Avoid a direct word-for-word translation like 'опытный синус' which would be nonsensical.
Common Mistakes
- Misspelling as 'versed sign' or 'verse sine'.
- Confusing it with the more common 'haversine' (half the versed sine).
- Using it in modern trigonometric contexts where '1 − cos θ' or direct cosine manipulation is preferred.
Practice
Quiz
What is the mathematical definition of the versed sine of angle θ?
FAQ
Frequently Asked Questions
No, it is completely obsolete in practical mathematics and engineering. The cosine function and modern computing have rendered it unnecessary.
The haversine is half the versed sine: haversin(θ) = versin(θ)/2 = (1 − cos θ)/2. The haversine was more commonly used in navigation formulas.
Only in historical mathematical texts, old navigation guides, or academic papers on the history of science and mathematics.
It ensured all values in trigonometric tables were positive for angles between 0 and 180 degrees, simplifying logarithmic calculations and avoiding negative numbers before the advent of computers.