How To Compute The Reference Angles In Radians

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HomeAcademics & The Arts ArticlesMath ArticlesTrigonometry ArticlesHow to Compute the Reference Angles in RadiansByMary Jane Sterling Updated2016-03-26 10:57:14From the bookTrigonometry For DummiesShare

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Solving for the reference angle in radians is much easier than trying to determine a trig function for the original angle. To compute the measure (in radians) of the reference angle for any given angle theta, use the rules in the following table.

Finding Reference Angles in Radians

Quadrant	Measure of Angle Theta	Measure of Reference Angle
I	0 to π/2	è
II	π/2 to π	ð – è
III	π to 3π/2	è – ð
IV	3π/2 to 2π	2ð – è

To find the reference angle for

1. Determine the quadrant in which the terminal side lies.

   An angle measuring

   

   has its terminal side in QII, which you know because

   

   is slightly less than 1, making the angle slightly less than π.

2. Do the operation indicated for that quadrant.

   Subtract

   

   from π. When you do so, you get

   

   so the reference angle is

   

About This Article

This article is from the book: 

Trigonometry For Dummies

About the book author:

Mary Jane Sterling (Peoria, Illinois) is the author of Algebra I For Dummies, Algebra Workbook For Dummies, Algebra II For Dummies, Algebra II Workbook For Dummies, and many other For Dummies books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics.

This article can be found in the category: 

Trigonometry

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