Reference Angle
Pronunciation: /ˈrɛf.rəns ˈæŋ.gəl/ Explain
A reference angle is an angle between
0°
and 90° formed between the terminal
ray
of an angle and xaxis. Rule: When the ray is in the:
 Quadrant 1 The reference angle is the same as the angle, as the
angle is between 0° 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. 
References
 McAdams, David E.. All Math Words Dictionary, reference angle. 2nd Classroom edition 201501084799968. 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. http://www.allmathwords.org/en/r/referenceangle.html.
Image Credits
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.)