sine

Etymology

It is borrowed from Latin sinus (“a bend, curve, fold of a garment, bosom”).^{[2][3][4][5][6]} The mathematical use goes back to the medieval Latin translations of Arabic geometry: about 1150 Gherardo of Cremona used the word to render Arabic جيب (jība, “chord of an arc, sine”), which he confused with the Arabic word for a bosom or the fold of a garment.^[3][7][4][8] The two Arabic words were written alike without vowels.^[9] The Arabic term for the sine came from Sanskrit ज्या (jyā, “bowstring, chord”),^[3][4] through the similar जीव (jīva).^[10][9][4] The Latin noun is also the source of sinus and sinuous.^[8][11]

Earliest recorded meaning

In trigonometry: 1593, in Thomas Fale's Horologiographia, the Art of Dialling.^{[2][3][4][10]}

Semantic evolution

Ayto points out that the English debt to Arabic here is only one of meaning, not of form.^[8] The sine was originally a length, the straight line drawn from one end of an arc perpendicular to the radius through the other end.^[2] Johnson (1755) defined it in this way, as half the chord of twice the arc.^[2][12] From 1728 it was spoken of as the sine of an angle,^[2] and it became a ratio: in a right-angled triangle, the opposite side divided by the hypotenuse.^[13][4] The word was also used once, in 1605, for a gulf or bay, like Latin sinus.^[2][5] The sine wave of engineering is recorded from 1915.^[3]

Timeline

• 1593 – a trigonometric function, originally a length measured in a circle.^[2][10]
• 1605 – a gulf or bay (obsolete, rare).^[2]
• 1728 – the sine of an angle.^[2]
• 1915 – sine wave.^[3]

Meanings

Noun

1. A trigonometric function of an angle: in a right triangle, the ratio of the side opposite the angle to the hypotenuse; abbreviated sin.^[13][10][4]
2. In a circle centred on the origin of a coordinate system, the ratio of the y-coordinate of a point on the circle to the radius.^[13][10]

Word family

• arcsine
• cosine
• sinusoid
• sinusoidal
• sine curve
• sine wave

Related words

• sinus
• sinuous
• sinusitis
• insinuate
• tangent
• secant

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d e f Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ a b c d e f g Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
5. ^ a b Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
6. ^ Hoad, T. F., ed. (1986), The Concise Oxford Dictionary of English Etymology, Oxford: Clarendon Press
7. ^ Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
8. ^ a b c Ayto, John (2005), Word Origins: The Secret Histories of English Words from A to Z, 2nd ed., London: A & C Black
9. ^ a b Random House Webster's Unabridged Dictionary (1999), 2nd ed., New York: Random House
10. ^ a b c d e Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
11. ^ Partridge, Eric (1966), Origins: A Short Etymological Dictionary of Modern English, 4th ed., London: Routledge & Kegan Paul
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 Collins English Dictionary (2023), Glasgow: HarperCollins