Pronunciation: /ˈtæn.dʒənt/ Explain

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For what angle is the tangent zero?
Manipulative 1 - Tangent Created with GeoGebra.

Tangent is defined to be equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle of a right triangle. Given a tangent value, the arctangent gives the angle that gives that tangent value.

tangent=opposite/adjacent; tangent=1/cotangent; y=tan^(-1)(x) if and only if x=tan(y)
Figure 1: Tangent equations.


  1. Hutton, Charles. A Course in Mathematics, Volume II. 4th edition. pg 2. www.archive.org. G. & J. Robinson. 1804. Last Accessed 12/16/2018. http://www.archive.org/stream/courseofmathemat02huttrich#page/2/mode/1up/search/cosecant. Buy the book

More Information

  • McAdams, David E.. Cotangent. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/c/cotangent.html.
  • McAdams, David E.. Arctangent. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem, LLC. 12/16/2018. http://www.allmathword.org/en/a/arctangent.html.

Cite this article as:

McAdams, David E. Tangent. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/t/tangent.html.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/16/2018: Added definition of cotangent. (McAdams, David E.)
12/13/2018: Removed broken links, updated license, implemented new markup. Changed geogebra to new format. (McAdams, David E.)
12/31/2008: Added equations. (McAdams, David E.)
10/30/2008: Changed title to Tangent. (McAdams, David E.)
4/30/2008: Initial version. (McAdams, David E.)

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