{ Reference and Coterminal Angles By Henry Burke

 These are two or more angles in standard position with the same terminal side. Standard position is where the vertex is at the origin and the initial side along the positive X-axis. These angles are found by taking the measure of the angle, and adding multiples of 360 degrees. Every angle has infinite coterminal angles. What are coterminal angles?

Coterminal angles example Image source:

This is the acute angle formed by the terminal side of the given angle and the X-axis. This is only if the angle is not one of the four quadrantal angles (90, 180, 270, 360). If the angle is greater than 360, or less than 0, the reference angle can be found by using a coterminal angle. What is a reference angle?

Reference angle example Image source: /reference.gif /reference.gif

 Quadrant 1= Actual  Quadrant 2= 180-angle  Quadrant 3= Angle-180  Quadrant 4= 360-angle Reference Angle Formulas

 Q: If the angle measure is 50 degrees in standard position, find one coterminal angle.  A: = 410 degrees Example 1

 Q: If the angle measure is 110 degrees in standard position, find the reference angle.  A: = 70 degrees Example 2

 Q: If the angle measure is -120 degrees, find the reference and one coterminal angle.  A: = 240 degrees (coterminal) = 60 degrees (reference) Example 3

 Q: If the angle measure is 279 degrees, find the reference and two coterminal angles.  A: = 81 degrees (reference) = 639 degrees (coterminal) 279+(360(2))= 999 degrees (coterminal) Example 4

If the angle measure is degrees, find the reference and two coterminal angles! Final Problem