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To complete the table and show the solutions, we'll need to convert between degree measure and radian measure using the following relationship:

\[
\text{Radians} = \text{Degrees} \times \left( \frac{\pi}{180^\circ} \right)
\]

And for the reverse:

\[
\text{Degrees} = \text{Radians} \times \left( \frac{180^\circ}{\pi} \right)
\]

Let's go step by step and fill in the table based on the given information:

### 1. \( 600^\circ \) to Radians:
\[
600^\circ \times \frac{\pi}{180^\circ} = \frac{600 \pi}{180} = \frac{10 \pi}{3}
\]
So, the radian measure for \( 600^\circ \) is \( \frac{10 \pi}{3} \).

### 2. \( -1900^\circ \) to Radians:
\[
-1900^\circ \times \frac{\pi}{180^\circ} = \frac{-1900 \pi}{180} = \frac{-95 \pi}{9}
\]
So, the radian measure for \( -1900^\circ \) is \( \frac{-95 \pi}{9} \).

### 3. \( 1.040^\circ \) to Radians:
\[
1.040^\circ \times \frac{\pi}{180^\circ} \approx 0.01814 \pi \, \text{radians}
\]
So, the radian measure for \( 1.040^\circ \) is approximately \( 0.01814 \pi \).

### 4. \( 6 \pi / 5 \) to Degrees:
\[
6 \pi / 5 \times \frac{180^\circ}{\pi} = 6 \times 36 = 216^\circ
\]
So, the degree measure for \( 6 \pi / 5 \) is \( 216^\circ \).

### 5. \( 972^\circ \) to Radians:
\[
972^\circ \times \frac{\pi}{180^\circ} = \frac{972 \pi}{180} = \frac{27 \pi}{5}
\]
So, the radian measure for \( 972^\circ \) is \( \frac{27 \pi}{5} \).

### 6. \( 11 \pi / 2 \) to Degrees:
\[
11 \pi / 2 \times \frac{180^\circ}{\pi} = 11 \times 90 = 990^\circ
\]
So, the degree measure for \( 11 \pi / 2 \) is \( 990^\circ \).

### Final Table:
| Degree Measure  | Radian Measure     |
|-----------------|--------------------|
| \( 600^\circ \) | \( \frac{10 \pi}{3} \) |
| \( -1900^\circ \) | \( \frac{-95 \pi}{9} \) |
| \( 1.040^\circ \) | \( 0.01814 \pi \)  |
| \( 216^\circ \) | \( \frac{6 \pi}{5} \) |
| \( 972^\circ \) | \( \frac{27 \pi}{5} \) |
| \( 990^\circ \) | \( \frac{11 \pi}{2} \) |

Would you like more details on any of the steps? 

Here are some related questions:
1. What is the general formula for converting degrees to radians?
2. How do negative angle measures affect trigonometric calculations?
3. Why is \( \pi \) used in radian measure?
4. How do we simplify fractions in radian conversions?
5. What are practical applications of degree and radian conversions?

**Tip:** Remember, when converting degrees to radians, always multiply by \( \frac{\pi}{180^\circ} \).

Complete the table by converting between degree and radian measures, showing all solutions.

Learn how to convert degree measures like 600° and -1,900° to radians, and radian measures such as 5π/4 and 11π/2 to degrees with a step-by-step solution. Suitable for high school students studying trigonometry.

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