cosine

English

Cosine function

Etymology

co- +‎ sine, short for complementi sinus in Latin, meaning “sine of the complement”. Doublet of cosinus.

Pronunciation

• (UK) IPA^(key): /ˈkəʊ.saɪn/
• (US) IPA^(key): /ˈkoʊ.saɪn/

  • Audio (US):

    (file)

• (General Australian) IPA^(key): /ˈkəʉ.sɑɪn/
• Rhymes: -əʊsaɪn, -oʊsaɪn
• Homophone: cosign

Noun

cosine (plural cosines)

1. (trigonometry) In a right triangle, the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse. Symbol: cos

Usage notes

In various branches of mathematics, the cosine of an angle is determined in various ways, including the following:

• The x-coordinate of the point on the unit circle at the given anticlockwise angle from the x-axis.
• The sum of the real or complex power series
  
       $\sum _{n=0}^{\infty }{\frac {(-1)^{n}x^{2n}}{(2n)!}}=1-{x^{2} \over 2}+{x^{4} \over 24}-{x^{6} \over 720}+{x^{8} \over 40320}-\cdots$
  
  where x is in radians.

Derived terms

• cosine formula
• cosine law
• cosine rule
• coversed cosine
• Fourier cosine series
• hyperbolic cosine
• inverse cosine
• Lambert's cosine law
• versed cosine

 

Related terms

• arccosine
• sine

Translations

trigonometric function

• Arabic: جَيْب تَمَام m (jayb tamām)
• Armenian: կոսինուս (hy) (kosinus)
• Basque: kosinu
• Bulgarian: ко́синус m (kósinus)
• Burmese: ကိုဆိုင်း (kuihcuing:)
• Catalan: cosinus m
• Cebuano: kalidpa
• Chinese:

  Mandarin: 餘弦／余弦 (zh) (yúxián)

• Czech: kosinus (cs) m
• Dutch: cosinus (nl) m
• Esperanto: kosinuso
• Finnish: kosini (fi)
• French: cosinus (fr) m
• Georgian: კოსინუსი (ḳosinusi)
• German: Kosinus (de) m
• Greek: συνημίτονο (el) n (synimítono)
• Hebrew: קוסינוס (he) m (cosinus)
• Hungarian: koszinusz (hu)
• Icelandic: kósínus m
• Irish: comhshíneas m
• Italian: coseno (it) m
• Japanese: コサイン (ja) (kosain), 余弦 (ja) (よげん, yogen)
• Khmer: កូស៊ីនុស (kousiinuh)
• Korean: 코사인 (kosain), 여현 (yeohyeon)
• Macedonian: косинус m (kosinus)
• Malay: kosinus (ms)
• Manx: co-heenys m
• Maori: whenu
• Norwegian:

  Bokmål: cosinus (no) m

  Nynorsk: cosinus m

• Polish: cosinus (pl) m, kosinus (pl)
• Portuguese: co-seno (pt) m
• Romanian: cosinus (ro) n
• Russian: ко́синус (ru) m (kósinus)
• Serbo-Croatian:

  Cyrillic: ко̀синус m

  Roman: kòsinus (sh) m

• Sicilian: cusinu m
• Slovak: kosínus m
• Slovene: kòsínus (sl) m
• Spanish: coseno m
• Swedish: cosinus (sv) c
• Tagalog: kasinway
• Tamil: துணைசெவ்வளை (tuṇaicevvaḷai)
• Thai: โคไซน์ (th) (koo-saai)
• Ukrainian: ко́синус (uk) m (kósynus)
• Vietnamese: côsin

See also

• power series
• secant
• tangent
• trigonometry

 

Anagrams

• Enciso, Inscoe, Senoic, coines, conies, oscine

Italian

Noun

cosine f

1. plural of cosina

Anagrams

• cenosi, coseni, inceso, nescio, osceni

Old French

Noun

cosine oblique singular, f (oblique plural cosines, nominative singular cosine, nominative plural cosines)

1. (female) cousin

Declension

• see cosin

Descendants

• French: cousine