MATH122
Reference angles

The reference angle A' of a given angle is the acute angle between the terminal side of A and the x-axis—always the x-axis; not the y-axis.

Use a sketch to help decide which angle to use and the order of the subtraction to find it.

Note that the reference angle A' does not have a direction; it is always considered as an acute angle (between 0 ° and 90 °); all its trig function values are positive.

Example: Find the reference angle for each of the following angles.

Angle

Arithmetic to find reference angle

Reference angle

150 °

180 ° -150 °

30 °

375 °

375 ° -360 °

15 °

-125 °

180 ° +(-125 ° )

55 °

Problems: Find the reference angle in degree measure.

  1. 160°
  2. 340°
  3. 200°
  4. -160°
  5. 92°
  6. 279°
  7. 218°

Answers:

  1. 20°
  2. 20°
  3. 20°
  4. 20°
  5. 88°
  6. 81°
  7. 38°