View source for Sine

{{also|Appendix:Variations of "sine"}}
==English==
{{wikipedia}}
[[Image:Sine.svg|thumb|Sine function]]

===Etymology===
Borrowed from {{bor|en|la|sinus||curve, bend; bosom}}, a translation of {{der|en|ar|جَيْب||bosom}}, a misidentification of the notation {{m|ar||جيب|tr=j-y-b}}, written without [[harakat|vowel diacritics]], standing for {{der|en|ar|جِيبَ||sine}}, in turn from {{der|en|sa|ज्या||sine, chord, bowstring}} through the similar {{der|en|sa|जीव||sine, chord, life, existence}}. {{doublet|en|sinus}}.

===Pronunciation===
* {{enPR|sīn}}, {{IPA|en|/saɪn/}}
* {{audio|en|LL-Q1860 (eng)-Vealhurl-sine.wav|a=Southern England}}
* {{audio|en|LL-Q1860 (eng)-Wodencafe-sine.wav|a=US}}
* {{homophones|en|sign|syne}}
* {{rhymes|en|aɪn|s=1}}

===Noun===
{{en-noun}}

# {{lb|en|trigonometry|mathematics}} In a [[right triangle]], the [[ratio]] of the [[length]] of the [[side]] [[opposite]] an [[angle]] to the length of the [[hypotenuse]]. {{topics|en|Trigonometric functions|Functions}}

====Usage notes====
In various branches of mathematics, the sine of an angle is determined in various ways, including the following:
* The [[y-coordinate|''y''-coordinate]] of the [[point]] on the [[unit]] [[circle]] at the given [[anticlockwise]] angle from the positive [[x-axis|''x''-axis]].
* The [[sum]] of the [[real]] or [[complex]] [[power series]]<br/><br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<math>\sum_{n=1}^\infty{{(-1)^{n-1}}\over{(2n-1)!}}x^{2n-1} = x - {1\over 6} x^3 + {1\over 120} x^5 - {1\over 5040} x^7 + ...</math><br/><br/>where ''x'' is in [[radian]]s.

====Synonyms====
* Symbol: [[sin]]

====Coordinate terms====
* {{l|en|cosine}}
* {{l|en|cosecant}}
* {{l|en|cotangent}}
* {{l|en|secant}}
* {{l|en|tangent}}
* {{l|en|trigonometry}}

====Derived terms====
{{col3|en|sine-Gordon equation
|arcsine
|cosine
|sine wave
|sinical
|sinusoid
|sinusoidal|coversed sine|Fourier sine series|hacoversed sine|haversed sine|hyperbolic sine|inverse sine|sine formula|sine law|sine ratio|sine rule|versed sine}}

====Related terms====
{{col3|en|sinus|sinuous|sinusitis|insinuate}}

====Translations====
{{trans-top|trigonometric function}}
* Afrikaans: {{t|af|sinus}}, {{t|af|sinusse}}
* Albanian: {{t+|sq|sinus|m}}
* Arabic: {{t+|ar|جَيْب|m}}
* Armenian: {{t+|hy|սինուս}}
* Azerbaijani: {{t+|az|sinus}}
* Basque: {{t|eu|sinu}}
* Bulgarian: {{t+|bg|синус|m}}
* Burmese: {{t+|my|ဆိုင်း}}
* Catalan: {{t+|ca|sinus|m}}
* Cebuano: {{t|ceb|lidpa}}
* Chinese:
*: Cantonese: {{t|yue|正弦|tr=zing3 jin4}}
*: Mandarin: {{t+|cmn|正弦|tr=zhèngxián}}
* Czech: {{t+|cs|sinus|m}}
* Danish: {{t|da|sinus}}
* Dutch: {{t+|nl|sinus|m}}
* Esperanto: {{t|eo|sinuso}}
* Finnish: {{t+|fi|sini}}
* French: {{t+|fr|sinus|m}}
* Galician: {{t|gl|seno|m}}
* Georgian: {{t-needed|ka}}
* German: {{t+|de|Sinus|m}}
* Greek: {{t+|el|ημίτονο|n}}
* Gujarati: {{t|gu|જ્યા|f}}
* Hebrew: {{t+|he|סינוס|m|tr=sinus}}
* Hindi: {{t+|hi|ज्या|f}}
* Hungarian: {{t+|hu|szinusz}}
* Icelandic: {{t|is|sínus|m}}
* Ido: {{t+|io|sinuso}}
* Indonesian: {{t+|id|sinus}}
* Irish: {{t|ga|síneas|m}}
* Italian: {{t+|it|seno|m}}
* Japanese: {{t+|ja|サイン|tr=sain}}, {{t+|ja|正弦|tr=seigen}}
* Khmer: {{t|km|ស៊ីនុស}}
* Korean: {{t+|ko|사인}}, {{t|ko|정현}}
* Macedonian: {{t|mk|синус|m}}
* Malay: {{t|ms|sinus}}
* Manx: {{t|gv|sheenys|m}}
* Norwegian: {{t+|no|sinus|m}}
* Ottoman Turkish: {{t|ota|جیب|tr=ceb}}
* Persian: {{t+|fa|جیب|tr=jayb, jeyb}}, {{t+|fa|سینوس|tr=sinus}}
* Polish: {{t+|pl|sinus|m}}
* Portuguese: {{t+|pt|seno|m}}
* Romanian: {{t+|ro|sinus|n}}
* Russian: {{t+|ru|си́нус|m}}
* Serbo-Croatian: {{t+|sh|sinus}}
* Slovak: {{t|sk|sínus|m}}
* Slovene: {{t+|sl|sinus|m}}
* Spanish: {{t+|es|seno|m}}
* Swedish: {{t+|sv|sinus}}
* Tagalog: {{t|tl|sinway}}
* Tamil: {{t|ta|செவ்வளை}}
* Thai: {{t+|th|ไซน์}}
* Ukrainian: {{t+|uk|си́нус|m}}
* Vietnamese: {{t+|vi|sin}}
{{trans-bottom}}

====See also====
{{col2|en|title=etymologically unrelated multiword terms containing "sine"|adjournment sine die|Latino sine Flexione|nulla poena sine lege|nulla pœna sine lege|sine qua non|sine quâ non|zoster sine herpete}}

===Anagrams===
* {{anagrams|en|a=eins|EINs|NIEs|Nies|sein|sien|snie}}

==Ainu==
{{cardinalbox|ain|0|1|2||tu|ord=sine ikinne}}

===Pronunciation===
* {{IPA|ain|/ɕìꜛné/}}

===Numeral===
{{ain-numeral|l|シネ}}

# [[one]]

==Bikol Central==

===Etymology===
{{bor+|bcl|es|cine}}, from a {{clipping|es|{{der|bcl|es|cinema}}|nocap=1|nocat=1}}, a reduction of {{der|bcl|es|cinematógrafo}}, from {{der|bcl|fr|cinématographe}}.

===Pronunciation===
* {{hyph|bcl|si|ne}}
* {{bcl-IPA}}

===Noun===
{{head|bcl|noun|head=síne}}

# [[cinema]]
# [[movie]], [[show]]
#: {{syn|bcl|pelikula|pasali}}

====Derived terms====
{{col3|bcl|magsine|sinehon|pasine|sinehan}}

==Cebuano==

===Etymology===
{{bor+|ceb|es|cine}}, from {{clipping|es|{{der|ceb|es|cinema}}|nocat=1}}, a reduction of {{der|ceb|es|cinematógrafo}}, from {{der|ceb|fr|cinématographe}}.

===Pronunciation===
* {{hyph|ceb|si|ne}}

===Noun===
{{ceb-noun}}

# [[film]]; [[movie]]
# {{lb|ceb|dated}} [[cinema]]; [[movie theater]]

====Quotations====
* {{seeCites|ceb}}

====Derived terms====
{{col3|ceb|sinehan}}

{{C|ceb|Film|Cinematography|Buildings}}

==Danish==

===Pronunciation===
* {{IPA|da|/siːnə/|[ˈsiːnə]|[ˌsiːnə]}}

===Pronoun===
{{head|da|pronoun}}

# {{plural of|da|sin}}

====See also====
{{Danish personal pronouns}}

==Finnish==
{{wikipedia|lang=fi}}

===Etymology===
{{suffix|fi|sini|e|id1=blue}}

===Pronunciation===
{{fi-p|*}}

===Noun===
{{fi-noun}}

# [[bluing]] {{gl|blue pigment used for coloring clothes when washing}}
# [[blueprint]] {{gl|paper-based reproduction usually of a technical drawing}}

====Declension====
{{fi-decl-hame|sin|||ä}}

===Anagrams===
* {{anagrams|fi|a=eins|-isen|ensi|ensi-|ines|sein}}

==Irish==

===Pronunciation===
* {{IPA|ga|/ˈʃɪnʲə/|ref={{R:ga:SjPh|57}}|a=Munster,Connacht}}
* {{IPA|ga|/ˈʃɪn̠ʲə/|ref1={{R:ga:Quiggin|90}}|a=Ulster}}
* {{hmp|ga|sinne|qq1=Ulster}}

===Etymology 1===
From {{inh|ga|sga|sine}}, {{m|sga|siniu}}, comparative form of {{m|sga|sen||old}}.<ref>{{R:DIL|37576|head=1 sine}}</ref>

====Adjective====
{{head|ga|comparative adjective}}

# {{infl of|ga|sean||comd}}: [[older]]

===Etymology 2===
From {{inh|ga|sga|sine||teat, dug, pap}}, from {{inh|ga|cel-pro|*sɸenyos}}, from {{der|ga|ine-pro|*pstḗn}}. Cognate with {{cog|non|speni||teat}}, {{cog|en|spean||teat (of a cow)}}.<ref>{{R:DIL|37578|head=3 sine}}</ref>

====Noun====
{{ga-noun|f|~|siní}}

# [[nipple]]

=====Declension=====
{{ga-decl-f4|si|ne|ní}}

=====Derived terms=====
* {{l|ga|sine siain||uvula}}

===Mutation===
{{ga-mut}}

===References===
{{reflist|size=smaller}}

===Further reading===
* {{R:ga:ODonaill}}

{{topics|ga|Body parts}}

==Latin==

===Pronunciation===
* {{la-IPA}}

===Etymology 1===
The function of this preposition was previously done with the use of ''sē, sēd'' (see {{m|la|sē-}}, {{m|la|sed}}), from {{der|la|ine-pro|*swé||self}}, thus meaning "by itself", "without". Some still refer the ''si-'' in ''sine'' to this root, others refer it to {{der|la|ine-pro|*só||this}}, whence {{m|la|si||if}}. And as sometimes ''nesi'' was also written, with ''-ne'' being {{m|la|nē||not}}, ''sine'' might literally mean "not this". Compare with {{m|la|nisi}}.

Yet others refer ''sine'' to {{der|la|ine-pro|*sénHi|*sen(H)i|for oneself, without}}, itself possibly related to {{m|ine-pro|*swé}} or more likely a locative of {{m|ine-pro|*senH-}}.<ref>{{R:itc:EDL|page=565|head=sine}}</ref><ref>{{R:txb:Adams|head=snai|pages=779–781}}</ref> Thus cognate with {{cog|grc|ᾰ̓́νευ}}, {{m|grc|ἄτερ||without}}, {{cog|sa|सनुतर्|t=away, off}}, {{cog|ang|sundor}}; compare especially {{cog|txb|snai}} and {{cog|sga|sain||separated, different}} ({{cog|cel-pro|*sanis}}), which may reflect the original PIE adverb.

The ablative is from a PIE ablative of separation or a comitative-instrumental analogous to {{m|la|cum}}. Compare {{m+|sa|विना}}.

====Preposition====
{{la-prep|sine|ablative}}

# [[without]]
#: {{ux|la|Sum '''sine''' rēgnō.|t=I am '''without''' a kingdom.}}
#: {{ux|la|Mundus '''sine''' cæsaribus.|t=A world '''without''' Caesars.}}

=====Derived terms=====
{{col4|la|sine anno|sine causā|sine diē|sine nōmine|sine prōle|decessit sine prole|sum sine regno|injuria sine damno}}

=====Descendants=====
* {{desc|frp|sen}}
* {{desc|fur|cence}}
* {{desc|it|senza}}
* {{desc|roa-oca}}
** {{desc|ca|sense|sens}}
* {{desctree|fro|senz}}
* {{desctree|roa-opt|sen}}
* {{desctree|osp|sin}}
* {{desc|sc|sine}}

====References====
<references/>
* {{R:L&S}}
* {{R:ine:IEW|page=907}}

===Etymology 2===
{{nonlemma}}

====Verb====
{{head|la|verb form}}

# {{inflection of|la|sinō||2|s|pres|actv|impr}}

==Middle Dutch==

===Determiner===
{{head|dum|determiner form}}

# {{inflection of|dum|sijn||f|nom//acc|s|;|nom//acc|p}}

==Middle English==

===Noun===
{{head|enm|noun}}

# {{alt form|enm|synne}}

==Neapolitan==

===Pronunciation===
* {{IPA|nap|/ˈsinɛ/|/ˈsinɐ/}}

===Particle===
{{head|nap|particle}}

# [[yes]]

==Norwegian Bokmål==

===Etymology===
From {{inh|nb|non|sínir}}.

===Pronunciation===
* {{IPA|nb|/siːne/}}

===Determiner===
{{head|nb|determiner form|g=p}}

# {{plural of|nb|sin}}

===See also===
{{nb-pers-pron}}

===References===
* {{R:Dokumentasjonsprosjektet|sin}}

===Anagrams===
* {{anagrams|nb|isen|isne|neis|nise|sein|si-en|-isen|snei}}

==Norwegian Nynorsk==

===Etymology===
From {{inh|nn|non|sínir}}.

===Pronunciation===
* {{IPA|nn|/²siːnə/}} {{nn-pronu-note}}

===Determiner===
{{head|nn|determiner|g=p}}

# {{plural of|nn|sin}}

===References===
* {{R:The Nynorsk Dictionary|sin}}

==Old English==

===Pronunciation===
* {{ang-IPA|sīne}}

===Pronoun===
{{head|ang|pronoun form|head=sīne}}

# {{infl of|ang|sīn||acc|f|s|;|ins|m//n|s|;|nom//acc|m//f|p}}

==Old French==

===Noun===
{{fro-noun|m}}

# {{alternative form of|fro|cisne}}

===Noun===
{{fro-noun|m}}

# {{alternative form of|fro|signe}}

==Old Irish==

===Etymology===
From {{inh|sga|cel-pro|*sɸenyos}}, itself from {{der|sga|ine-pro|*pstḗn}}.

===Pronunciation===
* {{IPA|sga|[ˈsʲinʲe]}}

===Noun===
{{sga-noun|m}}

# [[nipple]], [[teat]]

====Inflection====
Usual declension:
{{sga-decl-io-masc|sin}}

A variant dental-stem declension can also be found.
{{sga-decl-t&d|d|sinid|sined}}

====Descendants====
* {{desc|ga|sine}}
* {{desc|gv|sheeiney}}
* {{desc|gd|sine}}
* {{desc|mga|triphne|der=1|t=having three teats}}

===Mutation===
{{sga-mutation|s|ine}}
{{sga-mutation|sw|ine}}

===Further reading===
* {{R:DIL|37578}}

==Pali==

===Alternative forms===
{{pi-alt}}

===Verb===
{{pi-verb form}}

# {{pi-nr-inflection of|sinoti||opt|act|3s|t=to bind}}

==Polish==

===Pronunciation===
{{pl-pr}}

===Adjective===
{{head|pl|adjective form}}

# {{inflection of|pl|siny||n|nom//acc//voc|s|;|nonvirile|nom//acc//voc|p}}

==Romanian==

===Etymology===
{{inh+|ro|la|sē}}, as with {{m|ro|mine}}, {{m|ro|tine}}.

===Pronunciation===
* {{IPA|ro|/ˈsi.ne/}}
* {{rhymes|ro|ine|s=2}}

===Pronoun===
{{head|ro|pronoun|cat2=personal pronouns|stressed [[reflexive]]-[[accusative]] form of '''[[el#Romanian|el]]''', '''[[ea#Romanian|ea]]''', '''[[ei#Romanian|ei]]''', and '''[[ele#Romanian|ele]]'''}}

# {{lb|ro|direct object|preceded by preposition, such as "pe", "cu", "la", or "pentru"}} [[himself]], [[herself]], [[itself]], [[themselves]]
#: {{syn|ro|se<q:unstressed form>}}

==Scottish Gaelic==

===Pronunciation===
* {{IPA|gd|/ˈʃinə/}}

===Etymology 1===
From {{inh|gd|sga|sine|t=teat, dug, pap}}, from {{inh|gd|cel-pro|*sɸenyos}}, from {{der|gd|ine-pro|*pstḗn}}. Cognate with {{cog|non|speni|t=teat}}, {{cog|en|spean|t=teat (of a cow)}}.

====Noun====
{{gd-noun|g=f|gen=sine|pl=sinean}}

# {{lb|gd|anatomy}} [[nipple]], [[teat]]

===Etymology 2===
Borrowed from {{bor|gd|en|gin}}.

====Noun====
{{gd-noun|g=f}}

# [[gin]] {{gloss|drink}}

===Etymology 3===
From {{inh|gd|sga|sine|t=old age, seniority, antiquity}}, from {{m|gd|sen|t=old}}.

====Noun====
{{gd-noun|g=f}}

# [[oldness]]
# [[old age]]

===Etymology 4===
{{nonlemma}}

====Adjective====
{{head|gd|adjective form|cat2=comparative adjectives}}

# {{inflection of|gd|sean|t=old||comd}}

===Mutation===
{{gd-mut-cons|si|ne}}

===References===
* {{R:Dwelly}}
* {{R:DIL|37576|head=1 sine}}
* {{R:DIL|37577|head=2 sine}}
* {{R:DIL|37578|head=3 sine}}

==Serbo-Croatian==

===Noun===
{{sh-noun form}}

# {{infl of|sh|sina||gen|s|;|nom//acc//voc|p}}

==Tagalog==

===Alternative forms===
* {{alt|tl|cine}}

===Etymology===
{{bor+|tl|es|cine}}, from a {{clipping|es|cinema|nocap=1|nocat=1}}, a reduction of {{m|es|cinematógrafo}}, from {{der|tl|fr|cinématographe}}.

===Pronunciation===
{{tl-pr}}

===Noun===
{{tl-noun|b=+}}

# [[film]]; [[movie]]
#: {{syn|tl|pelikula|puting-tabing}}
# {{lb|tl|dated}} [[cinema]]; [[movie theater]]
#: {{syn|tl|sinehan}}

====Derived terms====
* {{l|tl|sinehan}}

====Related terms====
{{col3|tl|sinematograpiya|sinematograpo|sinematika}}

===Further reading===
* {{R:Pambansang Diksiyonaryo}}