What is angle of reference in trigonometry?

Answer 1

This is a VERY important question and I am glad you asked it. First you have to remember that in drawing angles we think of 4 quadrants. Think of the XY plane - the first quadrant is where BOTH X and Y are positive. In the 2nd quadrant the X is negative and the Y is positive. In the 3rd quadrant the X and the Y are negative. In the 4th quadrant the X is positive and the Y is negative.

Normally when we draw an angle we draw an angle less than 90 degrees. However, we can draw any angle we want from 0 to 360. However that angle can be represented by an angle less than 90 degrees in a certain quadrant.

Take an angle like 120 degrees. That angle is the same as a 60 degree angle in the 2nd quadrant. A 210 degree angle is the same as a 30 degree angle in the 3rd quadrant. A 359 degree angle is the same as a 1 degree angle in the 4th quadrant.

Those smaller angles are reference angles. This explanation would be better if I could insert graphs.

I have attached a link to a picture. Alpha is the angle and Beta is the reference angle.