View source for tangent

==English==
{{wikipedia}}
[[Image:Tangent to a curve.svg|thumb|A straight line tangent to a curve]]
[[Image:Tan.svg|thumb|Tangent function of unit circle]]

===Etymology===
{{root|en|ine-pro|*teh₂g-|id=touch}}
Borrowed from {{bor|en|la|tangentem}}, the accusative of {{m|la|tangēns||touching}} (in the phrase {{m|la|[[līnea]] [[tangēns]]|t=a touching line}}), the [[Appendix:Glossary#present participle|present participle]] of the verb {{m|la|tangō||touch|pos=verb}}, from {{der|en|itc-pro|*tangō}}, from {{der|en|ine-pro|*teh₂g-||to touch|id=touch}}.

Cognate with {{cog|ang|þaccian||to touch lightly, pat, stroke}}. More at {{l|en|thack}}, {{l|en|thwack}}.

===Pronunciation===
* {{enPR|tăn'jənt}}, {{IPA|en|/ˈtæn.d͡ʒənt/}}
* {{audio|en|LL-Q1860 (eng)-Vealhurl-tangent.wav|a=Southern England}}
* {{rhymes|en|ænd͡ʒənt|s=2}}

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

# {{lb|en|differential geometry}} A {{l|en|straight}} {{l|en|line}} {{l|en|touching}} a {{l|en|curve}} at a single {{l|en|point}} without {{l|en|crossing}} it there.
#* {{quote-journal|en|year=1951|month=May|title=British Railways Standard Coaches|journal=Railway Magazine|page=327|text=One feature of the body, which is constructed of pressed-steel members, is the contour of the sides. They are in the form of a continuous radius from the bottom side to the cant rail, and to enable flat glass windows to be fitted the side panels are pressed around the window opening, forming a '''tangent''' to the curved bodyside.}}
#: {{syn|en|tangent line}}
# {{lb|en|math}} A {{l|en|function}} of an {{l|en|angle}} that gives the ratio of the {{l|en|sine}} to the {{l|en|cosine}}, in either the {{l|en|real}} or {{l|en|complex}} {{l|en|number|numbers}}. Symbols: {{m|mul|tan}}, {{m|mul|tg}}.
# A {{l|en|topic}} nearly [[unrelated]] to the main topic, but having a point in {{l|en|common}} with it.
#: ''I believe we went off onto a '''tangent''' when we started talking about monkeys on unicycles at his retirement party.''
#* {{quote-book|en|year=1928|author=Lawrence R. Bourne
|title=Well Tackled!
|chapter=1|url=http://openlibrary.org/works/OL5387037W
|passage=“Uncle Barnaby was always father and mother to me,” Benson broke in; then after a pause his mind flew off at a '''tangent'''. “Is old Hannah all right—in the will, I mean?”}}
#* '''2009''': [http://www.hecklerspray.com/author/stuart-heritage Stuart Heritage], ''[http://www.hecklerspray.com/ Hecklerspray]'', Friday the 22<sup>nd</sup> of May in 2009 at 1 o’clock p.m., “[http://www.hecklerspray.com/jon-kate-latest-people-you-dont-know-do-crap-you-dont-care-about/200934378.php Jon & Kate Latest: People You Don’t Know Do Crap You Don’t Care About]”
#*: ''Jon & Kate Plus 8'' is a show based on two facts: '''(1)''' Jon and Kate Gosselin have eight children, and '''(2)''' the word ‘Kate’ rhymes with the word ‘eight’. One suspects that if Kate were ever to have another child, a shady network executive would urge her to put it in a binbag with a brick and drop it down a well. But this is just a horrifying '''tangent'''.
# {{lb|en|art}} A [[visual]] interaction between two or more [[line]]s or [[edge]]s that creates a [[perceive]]d [[relationship]] between them, often in a way that the [[artist]] did not [[intend]].
# {{lb|en|music}} A small metal [[blade]] in a [[clavichord]] that strikes the [[string]]s to produce sound.

====Derived terms====
{{col-auto|en|arctangent|cotangent|hyperbolic tangent| fly off at a tangent|go off at a tangent|go off on a tangent|inverse tangent|tangent bundle|tangent plane|tangent space|inflectional tangent}}

====Related terms====
* {{l|en|tangential}}

====Translations====
{{trans-top|in geometry}}
* Arabic: {{t|ar|مُمَاسّ|m}}
* Armenian: {{t+|hy|շոշափող}}
* Belarusian: {{t|be|даты́чная|f}}
* Bulgarian: {{t+|bg|допира́телна|f}}
* Catalan: {{t|ca|tangent|f}}
* Chinese:
*: Mandarin: {{t+|cmn|切線|tr=qiēxiàn}}
* Czech: {{t|cs|tečna|f}}
* Danish: {{t|da|tangent|c}}
* Dutch: {{t+|nl|raaklijn|f}}
* Esperanto: {{t|eo|tanĝanto}}
* Finnish: {{t+|fi|tangentti}}, {{t+|fi|sivuaja}}
* French: {{t+|fr|tangente|f}}
* Galician: {{t+|gl|tanxente|f}}
* Georgian: {{t-needed|ka}}
* German: {{t+|de|Tangente|f}}
* Greek: {{t+|el|εφαπτομένη|f}}
* Hindi: {{t+|hi|स्पर्शरेखा}}
* Hungarian: {{t+|hu|érintő}}
* Icelandic: {{t+|is|snertill|m}}
* Japanese: {{t+|ja|接線|tr=せっせん, sessen}}
* Korean: {{t|ko|접선}}
* Manx: {{t|gv|tanjent|m}}
* Maori: {{t|mi|pātapa}}
* Norwegian:
*: Bokmål: {{t+|nb|tangent|m}}
*: Nynorsk: {{t|nn|tangent|m}}
* Persian: {{t+|fa|مماس|tr=momâss}}
* Polish: {{t+|pl|styczna|f}}
* Portuguese: {{t+|pt|tangente|f}}
* Romanian: {{t+|ro|tangentă|f}}
* Russian: {{t+|ru|каса́тельная|f}}
* Slovak: {{t|sk|dotyčnica|f}}
* Spanish: {{t+|es|tangente|f}}
* Swedish: {{t+|sv|tangent|c}}
* Tagalog: {{t|tl|dikit}}
* Telugu: {{t|te|తిర్యగ్రేఖ}}
* Thai: {{t|th|เส้นสัมผัส}}
* Turkish: {{t+|tr|teğet}}
* Ukrainian: {{t|uk|доти́чна|f}}
* Vietnamese: {{t+|vi|tiếp tuyến}}
{{trans-bottom}}

{{trans-top|in trigonometry}}
* Afrikaans: {{t|af|tangens}}, {{t|af|tangense|p}}, {{t|af|raaklyn}}, {{t|af|raaklyne|p}}
* Arabic: {{t|ar|ظِلّ الزَّاوِيَة|m}}
* Armenian: {{t+|hy|տանգենս}}
* Belarusian: {{t|be|та́нгенс|m}}
* Bulgarian: {{t|bg|та́нгенс|m}}
* Burmese: {{t|my|တန်းဂျင့်}}
* Catalan: {{t|ca|tangent|f}}
* Cebuano: {{t|ceb|liras}}
* Chinese:
*: Mandarin: {{t+|cmn|正切|tr=zhèngqiē}}
* Czech: {{t+|cs|tangens|m}}
* Danish: {{t|da|tangens|c}}
* Dutch: {{t+|nl|tangens|m}}
* Esperanto: {{t|eo|tangento}}
* Finnish: {{t+|fi|tangentti}}
* French: {{t+|fr|tangente|f}}
* German: {{t+|de|Tangens|m}}
* Greek: {{t+|el|εφαπτομένη|f}}
* Hebrew: {{t+|he|טנגנס|m|tr=tangens}}
* Hungarian: {{t+|hu|tangens}}
* Icelandic: {{t|is|tangens|m}}
* Italian: {{t+|it|tangente|f}}
* Japanese: {{t+|ja|タンジェント|tr=tanjento}}, {{t+|ja|正接|tr=せいせつ, seisetsu}}
* Khmer: {{t|km|តង់សង់}}
* Korean: {{t|ko|탄젠트}}
* Manx: {{t|gv|tanjent|m}}
* Maori: {{t|mi|pātapa}}
* Norwegian:
*: Bokmål: {{t|nb|tangens|m}}
*: Nynorsk: {{t|nn|tangens|m}}
* Polish: {{t+|pl|tangens|m}}
* Portuguese: {{t+|pt|tangente|f}}
* Romanian: {{t+|ro|tangentă|f}}
* Russian: {{t+|ru|та́нгенс|m}}
* Spanish: {{t+|es|tangente|f}}
* Swedish: {{t+|sv|tangens|c}}
* Tagalog: {{t|tl|tanway}}
* Thai: {{t|th|แทนเจนต์}}
* Turkish: {{t+|tr|tanjant}}
* Ukrainian: {{t+|uk|та́нгенс|m}}
* Vietnamese: {{t+|vi|tang}}
{{trans-bottom}}

{{trans-top|nearly unrelated topic}}
* Catalan: {{t|ca|tangent|f}}
* Danish: {{t|da|sidespor|n}}
* Esperanto: {{t|eo|parentezaĵo}}
* Finnish: {{t|fi|sivuraide}}, {{t|fi|harhapolku}}
* German: {{t+|de|Nebensache|f}}
* Polish: {{t|pl|punkt wspólny|m}}
* Russian: {{t|ru|смежная тема|f}}
{{trans-bottom}}

{{trans-top|(art) visual interaction between lines}}
{{trans-bottom}}

{{checktrans-top}}
* Italian: {{t+check|it|tangente|f}} (1)
{{trans-bottom}}

===Adjective===
{{en-adj|-}}

# {{lb|en|geometry}} Touching a curve at a single point but not crossing it at that point.
# Of a topic, only loosely related to a main topic.
# {{lb|en|railroading|of track}} Straight; not horizontally curved.
#: {{ux|en|The collision occurred on a two-mile stretch of '''tangent''' track.}}

====Derived terms====
* {{l|en|tangently}}

===See also===
* {{l|en|cosine}}
* {{l|en|non sequitur}}
* {{l|en|sine}}
* {{l|en|trigonometry}}

{{C|en|Trigonometry|Trigonometric functions|Shapes|Curves}}

==Catalan==

===Etymology===
{{bor+|ca|la|tangēns|tangentem}}.

===Pronunciation===
* {{ca-IPA}}

===Noun===
{{ca-noun|f}}

# {{lb|ca|trigonometry}} {{l|en|tangent}}

====Derived terms====
* {{l|ca|cotangent}}

===Further reading===
* {{R:ca:IEC2}}

==Danish==

===Etymology===
Ultimately from {{der|da|la|tangēns}}; cf. German {{m|de|Tangente}}.

===Noun===
{{da-noun|en|er}}

# {{lb|da|geometry}} {{l|en|tangent}}
#: {{ux|da|Differentialregning kan fortolkes som forsøget på at bestemme en '''tangents''' hældning.|Differential calculus may be interpreted as the attempt to determine the slope of a '''tangent'''.}}
# [[piano key]]

====Declension====
{{da-noun-infl|en|er}}

====Related terms====
* {{l|da|tangens}}
* {{l|da|tangerende}}
* {{l|da|tangere}}

===References===
* {{R:Den Danske Ordbog}}

==French==

===Etymology===
{{bor+|fr|la|tangēns|tangentem}}.

===Pronunciation===
* {{fr-IPA}}
* {{audio|fr|LL-Q150 (fra)-Lyokoï-tangent.wav}}

===Adjective===
{{fr-adj}}

# {{lb|fr|mathematics}} [[tangential]]
# [[borderline]]

===Further reading===
* {{R:fr:TLFi}}

==Latin==

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

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

# {{inflection of|la|tangō||3|p|futr|actv|indc}}

==Norwegian Bokmål==
{{wikipedia|lang=no}}

===Etymology===
From {{der|nb|de|Tangente}}, {{m|de|Tangens}}, ultimately from {{der|nb|la|tangēns}}.

===Noun===
{{nb-noun-m1}}

# {{lb|nb|geometry}} {{l|en|tangent}}
# {{lb|nb|musical instruments}} [[key]] (e.g., on a piano)

===References===
* {{R:The Bokmål Dictionary}}

==Norwegian Nynorsk==
{{wikipedia|lang=nn}}

===Etymology===
From {{der|nn|de|Tangente}}, {{m|de|Tangens}}, ultimately from {{der|nn|la|tangēns}}.

===Noun===
{{nn-noun-m1}}

# {{lb|nn|geometry}} {{l|en|tangent}}
# {{lb|nn|musical instruments}} [[key]] (e.g., on a piano)

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

==Romanian==

===Etymology===
{{bor+|ro|fr|tangent}}, {{bor|ro|la|tangens|tangēns, tangentem}}.

===Adjective===
{{ro-adj}}

# {{l|en|tangent}}

====Declension====
{{ro-decl-adj}}

==Swedish==
{{wikipedia|lang=sv}}

===Etymology===
Ultimately from {{der|sv|la|tangēns}}; cf. German {{m|de|Tangente}}.

===Noun===
{{sv-noun|c}}

# a [[key]] (on a typewriter, computer keyboard, piano, or the like)
# {{lb|sv|mathematics}} a {{l|en|tangent}}
# {{lb|sv|mathematics|dated|only in the singular definite}} {{l|en|tangent}} (trigonometric function)
#: {{syn|sv|tangens|tan}}

====Declension====
{{sv-infl-noun-c-er}}

====Derived terms====
* {{l|sv|tangentbord||keyboard}}

====Related terms====
* {{l|sv|tangens}}
* {{l|sv|tangera}}

===References===
* {{R:svenska.se|so}}
* {{R:svenska.se|saol}}
* {{R:svenska.se|saob}}