For the rotation 424, degrees424 ∘ , 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 a given angle, you can use the following steps:

1. Coterminal angles are angles that share the same terminal side. They can be found by adding or subtracting multiples of 360 degrees (or 2π in radian measure).

2. Given the angle of 424 degrees, we subtract 360 degrees to find a coterminal angle within the desired range.

424 degrees - 360 degrees = 64 degrees

So, the coterminal angle between 0 and 360 degrees is 64 degrees.

3. To find the quadrant of the angle, we know that:
   • Quadrant I: 0 to 90 degrees
   • Quadrant II: 90 to 180 degrees
   • Quadrant III: 180 to 270 degrees
   • Quadrant IV: 270 to 360 degrees

Since 64 degrees falls between 0 and 90 degrees, it is in Quadrant I.

4. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since the angle is in Quadrant I, the reference angle is the angle itself, which is 64 degrees.