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:

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.