cosine

Etymology

It is borrowed from New Latin cosinus,^[2][3][4] a contraction of “co. sinus”, the abbreviation of complementi sinus (“the sine of the complement”).^[5][6][1] Both the Latin name and its shortened form were first used by the English mathematician Edmund Gunter,^[6][5] and the OED finds cosinus in his “Canon Triangulorum” of 1620;^[7][8] Barnhart describes the word as coined by Gunter in that year.^[8] The OED, the Shorter Oxford and Hoad instead take it as formed from English co- + sine.^[7][9][10] Sine is from Latin sinus (“fold of a garment, bend, curve, bosom”), which medieval translators of Arabic geometry used for the Arabic word for the chord of an arc, confusing it with an Arabic word for the fold of a garment.^{[5][8][11][6]} Cotangent and cosecant are formed in the same way, also in the 17th century.^[10]

Earliest recorded meaning

The sine of the complement of a given angle: 1635, in J. Wells's Sciographia,^[7][3][8] the 1630s in Etymonline.^[5]

Semantic evolution

The word began as a name for the sine of the complementary angle, the angle that makes up ninety degrees with the given one,^[7][9][6] and Johnson (1755), quoting Harris, still defined it so, as the sine of an arc that is the complement of another to ninety degrees.^[12] Modern dictionaries define it first as a ratio in a right-angled triangle, the adjacent side divided by the hypotenuse,^[2][3][9] and then as a function of any real number, given by a series or by a point on the unit circle.^[3][13] The abbreviation cos is recorded with it,^[7][2] and the term was extended to the hyperbolic cosine.^[9]

Timeline

• 1635 – the sine of the complement of an angle.^[7][3][8] Etymonline dates it to the 1630s.^[5]

Meanings

Noun

1. In a right triangle, the ratio of the side next to an acute angle to the hypotenuse; the sine of the complement of the angle: The cosine of sixty degrees is one half.^{[2][3][13][9]}
2. The corresponding trigonometric function of any real number, defined by a series or by the horizontal coordinate of a point on the unit circle.^[3][13]

Word family

• cosine law
• inverse cosine
• versed cosine

Related words

• arccosine
• sine
• sinus
• cotangent
• cosecant
• complement

References

1. ^ a b c Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d Collins English Dictionary (2023), Glasgow: HarperCollins
3. ^ a b c d e f g Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
4. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
5. ^ a b c d e Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
6. ^ a b c d Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
7. ^ a b c d e f Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
8. ^ a b c d e Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
9. ^ a b c d e Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
10. ^ a b Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
11. ^ Ayto, John (2005), Word Origins: The Secret Histories of English Words from A to Z, 2nd ed., London: A & C Black
12. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
13. ^ a b c The American Heritage Dictionary of the English Language (1992), 3rd ed., Boston: Houghton Mifflin