Pronunciation: /ˈju.nɪt ˈsɜr.kəl/ Explain
A unit circle is a
of exactly 1.
The unit circle is used to define the sine and cosine functions.
Figure 1: Unit Circle
Relationship Between Unit Circle and Trigonometric Functions
In right triangle trigonometry,
is defined as opposite/hypotenuse, and
is defined as adjacent/hypotenuse. Looking at the unit circle, the radius is the
hypotenuse of a right triangle. The red leg of the right triangle (see manipulative 1)
is the adjacent leg. So the cosine is equal to adjacent/hypotenuse. But, in
the unit circle, the hypotenuse is always 1. So the cosine is always equal to
the length of the adjacent leg of the right triangle. By a similar argument, the
sine is always equal to the length of the blue leg, the opposite leg.
Circle Trigonometric Identities
- McAdams, David E.. All Math Words Dictionary, unit circle. 2nd Classroom edition 20150108-4799968. pg 186. Life is a Story Problem LLC. January 8, 2015. Buy the book
- unit circle. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 12/17/2018. http://www.merriam-webster.com/dictionary/unit circle. Buy the book
- McAdams, David E.. Circle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/c/circle.html.
Cite this article as:
McAdams, David E. Unit Circle. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/u/unitcircle.html.
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/17/2018: Removed broken links, updated license, implemented new markup, implemented new GeoGebra applications. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
1/9/2010: Added "References". (McAdams, David E.)
11/27/2008: Added circle trigonometric identities. (McAdams, David E.)
9/15/2008: Expanded 'More Information'. (McAdams, David E.)
6/15/2008: Added manipulative for relationship between trigonometric functions and the unit circle. ( (McAdams, David E.)
3/11/2008: Changed See Also to match current standards. (McAdams, David E.)
8/18/2007: Initial version. (McAdams, David E.)