4.4 Reference Angles

What is a Reference Angle? 

 - If an angle is in standard position, the reference angle is the acute angle formed by the terminal side of the original angle and the horizontal axis.
- In other words, the reference angle is the other half of the whole or the quadrant.
Examples:

How do you find a Reference Angle?

- You can find the value of an angle from the reference angle, and vice-versa.
- Depending on if the angle is in radians or degrees, you can find the reference angle by subtracting the horizontal axis value (in degrees or radians) from or vice-versa.
-In Quadrant I, the angle is it's own reference angle.
Examples:

  1. = 300° 

Reference Angle= 360° - 300° = 60°

You subtract  from 360° because 360° is the closest x-axis to .

 2. =


The closest x-axis to is the radian value of . Therefore, you have to subtract from because it is in Quadrant III. 

 3.
First, you have to find a co-terminal angle so it is easier to find the reference angle.



Now that you concluded is co-terminal to , you can subtract 150 from 180.


You subtract from 180 degrees because it is the closest x-axis to your co-terminal angle. 


Sources/For More Help:
-Our textbook
-http://www.mathwarehouse.com/trigonometry/reference-angle/finding-reference-angle.php
-http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceAngles.htm
-http://www.mathopenref.com/reference-angle.html
-http://www.youtube.com/watch?v=3RD-zJUj5Bo&noredirect=1