How to find reference angles?

Hobert Dula: For many people it is easier to convert the angle to degrees, determine the reference angle in degrees, and then convert back to radians.First a few examples in degrees. The reference angle is the smallest angle back or forward to the x-axis. 70 --> 70, 170 --> 10, 220 --> 40, 300 --> 60.For an angle between 0 and 90 degrees the reference angle is equal to the angle. For an angle between 90 and 180 degrees the reference angle is equal to 180 degrees minus the angle. For an angle between 180 and 270 degrees the reference angle is equal to the angle minus 180 degrees. For an angle between 270 and 360 degrees the reference angle is equal to 360 degrees minus the angle.Now for your four examples:17pi/6 * 180/pi = 510 degrees which is coterminal with 510-360=150 degrees.The reference angle is 30 degrees. 30 * pi/180 = pi/6 in radians.-4pi/3 = -240 degrees which is coterminal with -240+360 = 120 degrees.The reference angle is 60 degrees = pi/3.-pi = -180 d! egrees is coterminal with 180 degrees. Reference angle = 0.2.3 radians * 180/pi = 131.78 degrees. The reference angle is 48.22 degrees= 48.22 * pi/180 = 0.84 radians. Notice the reference angle and the coterminal angle between 0 and 2pi of the original angle always have sum or difference 0 or pi or 2pi....Show more