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To solve this problem, let's address each angle one by one:

### Method:
1. **Identify the coterminal angle**: A coterminal angle can be found by adding or subtracting \( 360^\circ \) until the angle falls within \( 0^\circ \) to \( 360^\circ \). For negative angles, keep adding \( 360^\circ \) until it is positive.
2. **Determine the quadrant**:
   - **Quadrant I**: \( 0^\circ \) to \( 90^\circ \)
   - **Quadrant II**: \( 90^\circ \) to \( 180^\circ \)
   - **Quadrant III**: \( 180^\circ \) to \( 270^\circ \)
   - **Quadrant IV**: \( 270^\circ \) to \( 360^\circ \)

Now, let's analyze each angle.

### Solutions:
1. **\( 960^\circ \)**
   - Coterminal: \( 960 - 2 \cdot 360 = 240^\circ \)
   - Quadrant: III

2. **\( -1085^\circ \)**
   - Coterminal: Keep adding \( 360 \) until positive.
     \( -1085 + 3 \cdot 360 = 95^\circ \)
   - Quadrant: II

3. **\( 2000^\circ \)**
   - Coterminal: \( 2000 - 5 \cdot 360 = 200^\circ \)
   - Quadrant: III

4. **\( -790^\circ \)**
   - Coterminal: \( -790 + 3 \cdot 360 = 290^\circ \)
   - Quadrant: IV

5. **\( 8800^\circ \)**
   - Coterminal: \( 8800 - 24 \cdot 360 = 160^\circ \)
   - Quadrant: II

6. **\( -12000^\circ \)**
   - Coterminal: \( -12000 + 34 \cdot 360 = 120^\circ \)
   - Quadrant: II

7. **\( 1220^\circ \)**
   - Coterminal: \( 1220 - 3 \cdot 360 = 140^\circ \)
   - Quadrant: II

8. **\( -400^\circ \)**
   - Coterminal: \( -400 + 2 \cdot 360 = 320^\circ \)
   - Quadrant: IV

9. **\( 29700^\circ \)**
   - Coterminal: \( 29700 - 82 \cdot 360 = 180^\circ \)
   - Quadrant: On the negative x-axis

10. **\( 2000^\circ \)**
    - Coterminal: \( 2000 - 5 \cdot 360 = 200^\circ \)
    - Quadrant: III

### Summary:

| Angle        | Coterminal Angle | Quadrant/Axis          |
|--------------|------------------|------------------------|
| \( 960^\circ \)    | \( 240^\circ \)      | III                    |
| \( -1085^\circ \)  | \( 95^\circ \)       | II                     |
| \( 2000^\circ \)   | \( 200^\circ \)      | III                    |
| \( -790^\circ \)   | \( 290^\circ \)      | IV                     |
| \( 8800^\circ \)   | \( 160^\circ \)      | II                     |
| \( -12000^\circ \) | \( 120^\circ \)      | II                     |
| \( 1220^\circ \)   | \( 140^\circ \)      | II                     |
| \( -400^\circ \)   | \( 320^\circ \)      | IV                     |
| \( 29700^\circ \)  | \( 180^\circ \)      | Negative x-axis       |
| \( 2000^\circ \)   | \( 200^\circ \)      | III                    |

Would you like me to clarify any part of this explanation? 

### Additional Questions:
1. How do we find coterminal angles for negative values?
2. Why is it important to understand quadrants when dealing with trigonometric functions?
3. Can an angle be both positive and in the fourth quadrant?
4. What is the significance of angles on axes (like \(180^\circ\) or \(360^\circ\)) in trigonometry?
5. How can we determine the reference angle from a coterminal angle?

### Tip:
When working with large angles, try reducing the angle modulo \(360^\circ\) directly to quickly find the coterminal angle.

Given the following angles in standard position, identify each of the following: (a) Quadrant or Axis where its terminal side lies, (b) Smallest positive coterminal angle.

Find the quadrant or axis and the smallest positive coterminal angle for angles like 960°, -1085°, 2000°, and more. This step-by-step guide explains how to reduce angles and determine their position in the unit circle.

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