How do you find the reference angle in degrees and radians 120 degrees?

1 Answer
Feb 10, 2016

The reference angle is the angle between the terminal arm of the angle and the x axis always larger than 0 degrees and smaller than 90 degrees.

Explanation:

Since 120 degrees is in quadrant 2, the reference angle, represented by #theta#, can be found by solving the equation #120 + theta = 180#

#theta = 60#

So, the reference angle is 60 degrees. To convert this to radians, we multiply by the ratio #pi/180#.

#60 xx(pi/180)#

Before we multiply, we can have the 180 eliminate the 60 and become a 3 in the denomiator.

This leaves us with #pi/3# radians, which is our reference angle in radians.

Practice exercises:

  1. Find the reference angle, in degrees and in radians, of 40 degrees.

  2. Find the reference angle, in degrees and in radians, of 335 degrees.

Good luck!