# 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

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.

### 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.)