Reference and Related Angles

Good Evening Everyone, its Karen

In the beginning of class, Mr. P mentioned about the Principia Mathematica outline will be due on October 25, Monday. So don't forget to talk to your group mates about your topic within this week! before the long weekend. Today we talked about the Reference and Related Angle.

Reference Angle - is the acute angle (angle less than 90° formed in Quadrant 1 , between the terminal arm of the angle and the x-axis.

Related Angle- is an angle formed between the positive x-axis and the terminal arm such that the acute angle formed between the terminal arm and the nearer x-axis is equal to the reference angle.

To find the related angle the first thing that you must determine is what Quadrant the terminal arm of an angle finishes in.

- If the angle is between 0° and 90° the terminal arm finishes in Quadrant 1.

- If the angle 90° and 180° the terminal arm finishes in Quadrant 2.
- If the angle 180° and 270° the terminal arm finishes in Quadrant 3

- If the angle 270° and 360° the terminal arm finishes in Quadrant 4


To find the related angle use the following formulas
- If the angle terminates in Quadrant 1: Θ=Θ-Θ

- If the angle terminates in Quadrant 2: Θ=180° - Θ

- If the angle terminates in Quadrant 3: Θ=180°+Θ
- If the angle terminates in Quadrant 4: Θ=360°-Θ

Example 1: a) 98°

In this example the angle terminates in Quadrant 2: which means that we have to use the formula
Ɵ = 180 - Ɵ.

For homework, Reference and Related Angles worksheets. Also this website might help you to understand more about our topic for today, Functions of Any Angle.