https://file.aiquickdraw.com/mathbot/file/1729256267346fm1vqmvr.jpg

Give me the solutions same with they're angle Drawing 

I have opened the image you uploaded. Let's solve the problem step by step, focusing on both identifying the quadrant or axis and determining the smallest positive coterminal angle for each given angle.

### Key concepts:
1. **Quadrants**:
   - 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 \(360^\circ\)

2. **Coterminal Angles**:
   - To find the coterminal angle, we add or subtract multiples of \(360^\circ\) until the result is between \(0^\circ\) and \(360^\circ\).

#### 1. \(960^\circ\)
   - **Coterminal Angle**: \(960^\circ - 2(360^\circ) = 240^\circ\)
   - **Quadrant**: III (since \(180^\circ < 240^\circ < 270^\circ\))

#### 2. \(-1,085^\circ\)
   - **Coterminal Angle**: \(-1,085^\circ + 3(360^\circ) = 35^\circ\)
   - **Quadrant**: I (since \(0^\circ < 35^\circ < 90^\circ\))

#### 3. \(2,000^\circ\)
   - **Coterminal Angle**: \(2,000^\circ - 5(360^\circ) = 200^\circ\)
   - **Quadrant**: III (since \(180^\circ < 200^\circ < 270^\circ\))

#### 4. \(-790^\circ\)
   - **Coterminal Angle**: \(-790^\circ + 3(360^\circ) = 290^\circ\)
   - **Quadrant**: IV (since \(270^\circ < 290^\circ < 360^\circ\))

#### 5. \(8,800^\circ\)
   - **Coterminal Angle**: \(8,800^\circ - 24(360^\circ) = 160^\circ\)
   - **Quadrant**: II (since \(90^\circ < 160^\circ < 180^\circ\))

#### 6. \(-12,000^\circ\)
   - **Coterminal Angle**: \(-12,000^\circ + 34(360^\circ) = 120^\circ\)
   - **Quadrant**: II (since \(90^\circ < 120^\circ < 180^\circ\))

#### 7. \(1,220^\circ\)
   - **Coterminal Angle**: \(1,220^\circ - 3(360^\circ) = 140^\circ\)
   - **Quadrant**: II (since \(90^\circ < 140^\circ < 180^\circ\))

#### 8. \(-400^\circ\)
   - **Coterminal Angle**: \(-400^\circ + 2(360^\circ) = 320^\circ\)
   - **Quadrant**: IV (since \(270^\circ < 320^\circ < 360^\circ\))

#### 9. \(29,700^\circ\)
   - **Coterminal Angle**: \(29,700^\circ - 82(360^\circ) = 180^\circ\)
   - **Axis**: Negative x-axis (since it's exactly \(180^\circ\))

#### 10. \(2,000^\circ\)
   - **Coterminal Angle**: \(2,000^\circ - 5(360^\circ) = 200^\circ\)
   - **Quadrant**: III (same as question 3)

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### Drawing Explanation:

For each angle, I'll now describe its position visually:

1. **960°**: The terminal side is 240° in Quadrant III.
2. **-1085°**: The terminal side is 35° in Quadrant I.
3. **2000°**: The terminal side is 200° in Quadrant III.
4. **-790°**: The terminal side is 290° in Quadrant IV.
5. **8800°**: The terminal side is 160° in Quadrant II.
6. **-12000°**: The terminal side is 120° in Quadrant II.
7. **1220°**: The terminal side is 140° in Quadrant II.
8. **-400°**: The terminal side is 320° in Quadrant IV.
9. **29700°**: The terminal side lies exactly on the negative x-axis at 180°.
10. **2000°**: The terminal side is again 200° in Quadrant III.

Do you have any questions about these steps, or would you like me to provide further details?

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### Five Follow-up Questions:
1. How can you find the coterminal angle of a negative angle?
2. What is the relationship between an angle and its quadrant?
3. Can an angle have more than one coterminal angle?
4. What happens when an angle lands exactly on an axis?
5. How would you calculate coterminal angles for angles beyond \(360^\circ\)?

### Tip: 
When working with coterminal angles, remember that any angle plus or minus multiples of \(360^\circ\) will always land in the same position on the unit circle.

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

Learn how to identify the quadrant or axis of a given angle and find its smallest positive coterminal angle. This problem explains coterminal angles using the formula θ ± 360°n and classifies angles by their quadrant, perfect for students in Grades 10-12.

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