https://file.aiquickdraw.com/mathbot/file/1730637126889kt9piyby.jpg

To complete this table by converting between degrees and radians, we use the following relationship:

\[
\text{Radians} = \text{Degrees} \times \frac{\pi}{180^\circ}
\]

and

\[
\text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi}
\]

Let's solve each entry accordingly:

### Step-by-Step Solutions:

1. **600° to Radians:**
   \[
   600^\circ \times \frac{\pi}{180^\circ} = \frac{600 \pi}{180} = \frac{10 \pi}{3}
   \]
   So, \(600^\circ\) in radians is \(\frac{10 \pi}{3}\).

2. **Convert \( -1900^\circ \) to Radians:**
   \[
   -1900^\circ \times \frac{\pi}{180^\circ} = \frac{-1900 \pi}{180} = -\frac{95 \pi}{9}
   \]
   So, \(-1900^\circ\) in radians is \(-\frac{95 \pi}{9}\).

3. **Convert \(\frac{7 \pi}{3}\) to Degrees:**
   \[
   \frac{7 \pi}{3} \times \frac{180^\circ}{\pi} = \frac{7 \times 180^\circ}{3} = 420^\circ
   \]
   So, \(\frac{7 \pi}{3}\) in degrees is \(420^\circ\).

4. **Convert \(1040^\circ\) to Radians:**
   \[
   1040^\circ \times \frac{\pi}{180^\circ} = \frac{1040 \pi}{180} = \frac{52 \pi}{9}
   \]
   So, \(1040^\circ\) in radians is \(\frac{52 \pi}{9}\).

5. **Convert \(\frac{6 \pi}{5}\) to Degrees:**
   \[
   \frac{6 \pi}{5} \times \frac{180^\circ}{\pi} = \frac{6 \times 180^\circ}{5} = 216^\circ
   \]
   So, \(\frac{6 \pi}{5}\) in degrees is \(216^\circ\).

6. **Convert \(972^\circ\) to Radians:**
   \[
   972^\circ \times \frac{\pi}{180^\circ} = \frac{972 \pi}{180} = \frac{27 \pi}{5}
   \]
   So, \(972^\circ\) in radians is \(\frac{27 \pi}{5}\).

7. **Convert \(\frac{11 \pi}{2}\) to Degrees:**
   \[
   \frac{11 \pi}{2} \times \frac{180^\circ}{\pi} = \frac{11 \times 180^\circ}{2} = 990^\circ
   \]
   So, \(\frac{11 \pi}{2}\) in degrees is \(990^\circ\).

### Completed Table:

| Degree Measure | Radian Measure        |
|----------------|------------------------|
| 600°           | \(\frac{10 \pi}{3}\)  |
| -1900°         | \(-\frac{95 \pi}{9}\) |
| 420°           | \(\frac{7 \pi}{3}\)   |
| 1040°          | \(\frac{52 \pi}{9}\)  |
| 216°           | \(\frac{6 \pi}{5}\)   |
| 972°           | \(\frac{27 \pi}{5}\)  |
| 990°           | \(\frac{11 \pi}{2}\)  |

Would you like more details on any specific conversions, or have any questions?

---

### Further Related Questions:
1. How do you convert between radians and degrees for negative angles?
2. What is the significance of using \(\pi\) in radian measurements?
3. How would you convert radians to degrees for non-standard angles (e.g., \(\frac{\pi}{7}\))?
4. What is the smallest positive angle that is coterminal with \(600^\circ\)?
5. How does understanding radians help in trigonometric functions?

### Tip:
Always simplify fractions in radian conversions to ensure your answers are in the simplest form possible.

Complete the table by converting between degrees and radians.

Learn to convert angles between degrees and radians using key formulas, such as Degrees = Radians × 180 / π. This table includes examples like 600°, -1900°, and their equivalent radian measures.

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