Final answer:
To find the reference angle for 1,406 degrees, subtract the nearest multiple of 360 degrees without going over 1,406. The reference angle is positive and measures the smallest angle between the terminal side and the x-axis.
Step-by-step explanation:
To find the reference angle for 1,406 degrees, we need to subtract the nearest multiple of 360 degrees without going over 1,406. In this case, 1,406 - 1,440 = -34 degrees is the equivalent angle in the first rotation. Since reference angles are always positive and measure the smallest angle between the terminal side and the x-axis, we take the absolute value of -34, which is 34 degrees.