9.2  Reference Angles

Reference Angles and Coterminal Angles

Reference Angles

    A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis.

   Looking at the diagram at the right.    

  The reference angle and quadrants

                 Q1 is the angle itself

                 Q2 is found by subtracting the given angle from π (or 180°)

                 Q3 is found by subtracting π (or 180°) from the angle.

                 Q4 is found by subtracting the given angle from 2π (or 360°)

Coterminal Angles

Coterminal Angles are angles that share the same initial side and terminal sides.

Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.  

Coterminal Angles Examples

Find one positive coterminal angle to 110 degrees.

110 + 360 = 470 degrees

Find one negative coterminal angle to 150 degrees.

150 - 360 = -210 degrees

Find one positive and one negative angle that is

coterminal to pi/6 radians.

pi/6 + 2pi = 13pi/6  (positive)

pi/6 - 2pi = -11pi/6  (negative)

If there are more than one complete revolution, 4pi or 720 degrees

will be added/subtracted to each angle.