Cotangent: meaning, definitions and examples

๐Ÿ“
Add to dictionary

cotangent

 

[ kษ™สŠหˆtรฆnสคษ™nt ]

Noun
Context #1 | Noun

trigonometry

Cotangent is a trigonometric function defined as the ratio of the length of the adjacent side to the length of the opposite side of a right triangle. It is also the reciprocal of the tangent function. In mathematical terms, if ฮธ is an angle in a right triangle, then cot(ฮธ) = adjacent/opposite. Cotangent is commonly used in various applications in science and engineering, especially in fields dealing with oscillations, waves, and periodic functions.

Synonyms

cotan, cotg.

Examples of usage

  • The cotangent of 45 degrees equals 1.
  • In calculus, cotangent functions are used to solve integrals involving trigonometric identities.
  • To find the angle in a right triangle, you can use the cotangent function.
  • The identity cot(ฮธ) = 1/tan(ฮธ) helps in simplifying trigonometric equations.

Translations

Translations of the word "cotangent" in other languages:

๐Ÿ‡ต๐Ÿ‡น cotangente

๐Ÿ‡ฎ๐Ÿ‡ณ เค•เฅ‹เคŸเฅ‡เค‚เคœเฅ‡เค‚เคŸ

๐Ÿ‡ฉ๐Ÿ‡ช Kotangens

๐Ÿ‡ฎ๐Ÿ‡ฉ kotangen

๐Ÿ‡บ๐Ÿ‡ฆ ะบะพั‚ะฐะฝะณะตะฝั

๐Ÿ‡ต๐Ÿ‡ฑ kotangens

๐Ÿ‡ฏ๐Ÿ‡ต ใ‚ณใ‚ฟใƒณใ‚ธใ‚งใƒณใƒˆ

๐Ÿ‡ซ๐Ÿ‡ท cotangente

๐Ÿ‡ช๐Ÿ‡ธ cotangente

๐Ÿ‡น๐Ÿ‡ท kotanjant

๐Ÿ‡ฐ๐Ÿ‡ท ์ฝ”ํƒ„์  ํŠธ

๐Ÿ‡ธ๐Ÿ‡ฆ ู‚ุงุทุน ุงู„ุฒุงูˆูŠุฉ

๐Ÿ‡จ๐Ÿ‡ฟ kotangens

๐Ÿ‡ธ๐Ÿ‡ฐ kotangens

๐Ÿ‡จ๐Ÿ‡ณ ไฝ™ๅˆ‡

๐Ÿ‡ธ๐Ÿ‡ฎ kotangens

๐Ÿ‡ฎ๐Ÿ‡ธ kotangens

๐Ÿ‡ฐ๐Ÿ‡ฟ ะบะพั‚ะฐะฝะณะตะฝั

๐Ÿ‡ฌ๐Ÿ‡ช แƒ™แƒแƒขแƒแƒœแƒ’แƒ”แƒœแƒขแƒ˜

๐Ÿ‡ฆ๐Ÿ‡ฟ kotanjant

๐Ÿ‡ฒ๐Ÿ‡ฝ cotangente

Etymology

The term 'cotangent' originates from the Latin prefix 'co-' meaning 'together with' and 'tangens', which means 'touching' in Latin. The word 'tangent' itself has roots in mathematics dating back to the medieval period when scholars were exploring relationships between angles and sides of triangles. The introduction of the cotangent function came as mathematicians expanded their work with trigonometric ratios. Cotangent, being the reciprocal of tangent, began to gain prominence alongside other trigonometric functions as a necessary tool in geometry, astronomy, and later in calculus. Its formal acceptance into mathematical literature occurred during the Renaissance era when the study of angles and their relationships became crucial in understanding motion and harmonics. Over time, cotangent has been incorporated into various mathematical disciplines, solidifying its role in the foundational knowledge of trigonometry.