For the rotation minus, 1006, degrees−1006 ∘ , find the coterminal angle from 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , the quadrant, and the reference angle.

To find the coterminal angle between 0 and 360 degrees for -1006 degrees, you need to add 360 degrees repeatedly until you get an angle in the desired range.

Step 1: Add 360 to -1006 -1006 + 360 = -646 degrees

Step 2: The result is still less than 0, so add 360 again -646 + 360 = -286 degrees

Step 3: The result is still less than 0, so add 360 again -286 + 360 = 74 degrees

So, the coterminal angle between 0 and 360 degrees for -1006 degrees is 74 degrees.

Next, to find the quadrant, you need to know the ranges for each quadrant:

• Quadrant I: 0 to 90 degrees
• Quadrant II: 90 to 180 degrees
• Quadrant III: 180 to 270 degrees
• Quadrant IV: 270 to 360 degrees

74 degrees falls in Quadrant I.

Finally, the reference angle for an angle in Quadrant I is just the angle itself, so the reference angle is 74 degrees.