Reference & Related Angles

Hey everyone this is Gian, and I'm gonna be your scribe for today. Today we started the class of by going over some of the questions that we had for home work last class. Then we started a new lesson on Reference and Related Angles.

• Reference Angles are acute angles that is less than 90 degrees. They are formed in quadrant 1 and is in between the terminal arm of the angle and the x-axis. 

• Related Angles are angles formed between the positive x-axis and the terminal arm. So that the acute angle formed between the terminal arm and the x-axis is equal to the reference angle.  

We learned how to find reference angles, and the rules to find them. First you must find the related angle. The first thing that you must determine what quadrant the terminal arm finishes in. 

• If the angle is between 0 and 90 (degrees) the terminal finishes in quadrant 1.
• If the angle is between 90 (degrees) and 180 (degrees) the terminal finishes in quadrant 2. 
•  If the angle is between 180 (degrees) and 270 (degrees) the terminal finishes in quadrant 3.
• If the angle is between 270 (degrees) and 360 (degrees) the terminal finishes in quadrant 4.  

For example: 

 So what I did here was first determine my angle which is 98 (degrees) because the angle lands on quadrant II, then I subtracted 180 (degrees) which gives me the reference angle of 98 (degrees). 

* Never forget about the cast rule, and make sure to pay attention to the signs.

Related Angle Formulas:

•  If the angle terminates in Quadrant I:  = 
•  If the angle terminates in Quadrant II:  = 180 - r
•  If the angle terminates in Quadrant III:  = 180 + r
•  If the angle terminates in Quadrant IV:  = 360 - r