Reference Angle

Pronunciation: /ˈrɛf.rəns ˈæŋ.gəl/ Explain

A reference angle is an angle between and 90° formed between the terminal ray of an angle and x-axis. Rule: When the ray is in the:

  • Quadrant 1 The reference angle is the same as the angle, as the angle is between and 90°
  • Quadrant 2 The reference angle is 180° - α. In this case the reference angle is negative.
  • Quadrant 3 The reference angle is α - 180°.
  • Quadrant 4 The reference angle is 360° - α. In this case the reference angle is negative.

Click on the blue points and drag them to change the figure.

Why are the reference angles for angles between 90° and 180° degrees negative?
Manipulative 1 - Reference Angle Created with GeoGebra.


  1. McAdams, David E.. All Math Words Dictionary, reference angle. 2nd Classroom edition 20150108-4799968. pg 153. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Reference Angle. 5/2/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

5/2/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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