For the rotation minus, start fraction, 40, pi, divided by, 13, end fraction− 13 40π ​ , find the coterminal angle from 0, is less than or equal to, theta, is less than, 2, pi0≤θ<2π, the quadrant, and the reference angle.

The question seems to be asking for the coterminal angle, the quadrant, and the reference angle for the given rotation of -40π/13. Here's how you can find these:

1. Coterminal Angle: Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. To find the coterminal angle between 0 and 2π for -40π/13, you can add multiples of 2π until you get an angle in this range.

-40π/13 + 2πn = θ, where n is an integer, and 0 ≤ θ < 2π

Choosing n=4 gives us a coterminal angle of 8π/13.

2. Quadrant: The quadrant can be determined by the coterminal angle. Since 8π/13 is greater than π/2 but less than π, the angle is in the second quadrant.

3. Reference Angle: The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. For an angle in the second quadrant, the reference angle is π - the angle. So, the reference angle is π - 8π/13 = 5π/13.