Trig confusion?

Question

theta = 2 pi over 3
theta = 120 degrees
but i cant figure out how to Label the reference angle in both degrees and radians.

Answer 1

2pi/3 is 4pi/6, so that's somewhere between pi/2 (which is 3pi/6) and pi (which is 6pi/6). So it's in the second quadrant. The reference angle would therefore be pi - 2pi/3 = pi/3 raidans, or 60 degrees.

Remember that if you multiply an angle in radians by 180/pi, you get the measure in degrees.

Answer 2

360 degrees = 2pi radians so 1 radian =360/2pi degrees
and 1 degree=2pi/360 radians