Find Reference Angle
What is the reference angle to an angle in standard position?
If A is an angle in standard position, its reference angle A_{r} is the acute angle formed by the x axis and the terminal side of angle A. See figure below.
Two or more coterminal angles have the same reference angle.
Assume angle A is positive and less than 360° (2π), we have 4 possible cases:
1. If angle A is in quadrant I then the reference angle A_{ r} = A .
2. If angle A is in quadrant II then the reference angle A_{ r} = 180°  A if A is given degrees and A_{ r} = π  A if A is given in radians.
3. If angle A is in quadrant III then the reference angle A_{ r} = A  180° if A is given degrees and A_{ r} = A  π if A is given in radians.
4. If angle A is in quadrant IV then the reference angle A_{ r} = 360°  A if A is given degrees and A_{ r} = 2π  A if A is given in radians.
Example 1: Find the reference angle to angle A = 120 °.
Example 2: Find the reference to angle A =  15 π / 4.
Example 3: Find the reference angle to angle A =  30°
Exercises:Find the reference angle to angles
More references on angles.
