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Let's complete the table step by step, using the relationships between "vueltas" (turns), degrees, and radians. The key conversions are:

- 1 full turn \( = 360^\circ = 2\pi \) radians.
- To convert between turns, degrees, and radians:
  \[
  \text{Degrees} = \text{Turns} \times 360^\circ
  \]
  \[
  \text{Radians} = \text{Turns} \times 2\pi
  \]

### 1. First Column (Vueltas = 1):
- Grados: \( 1 \times 360^\circ = 360^\circ \)
- Radianes: \( 1 \times 2\pi = 2\pi \)

### 2. Second Column (Vueltas = \( \frac{1}{3} \)):
- Grados: \( \frac{1}{3} \times 360^\circ = 120^\circ \)
- Radianes: \( \frac{1}{3} \times 2\pi = \frac{2\pi}{3} \)

### 3. Third Column (Vueltas = \( \frac{1}{2} \)):
- Grados: \( \frac{1}{2} \times 360^\circ = 180^\circ \)
- Radianes: \( \frac{1}{2} \times 2\pi = \pi \)

### 4. Fourth Column (Grados = 270°):
- Vueltas: \( \frac{270^\circ}{360^\circ} = \frac{3}{4} \)
- Radianes: \( \frac{3}{4} \times 2\pi = \frac{3\pi}{2} \)

### 5. Fifth Column (Grados = 30°):
- Vueltas: \( \frac{30^\circ}{360^\circ} = \frac{1}{12} \)
- Radianes: \( \frac{1}{12} \times 2\pi = \frac{\pi}{6} \)

### 6. Sixth Column (Radianes = \( \frac{7\pi}{4} \)):
- Vueltas: \( \frac{\frac{7\pi}{4}}{2\pi} = \frac{7}{8} \)
- Grados: \( \frac{7}{8} \times 360^\circ = 315^\circ \)

### 7. Seventh Column (Radianes = \( \frac{2\pi}{3} \)):
- Vueltas: \( \frac{\frac{2\pi}{3}}{2\pi} = \frac{1}{3} \)
- Grados: \( \frac{1}{3} \times 360^\circ = 120^\circ \)

---

### Final Table:
| Vueltas       | Grados    | Radianes      |
|---------------|-----------|---------------|
| 1             | 360°      | \( 2\pi \)    |
| \( \frac{1}{3} \) | 120°      | \( \frac{2\pi}{3} \) |
| \( \frac{1}{2} \) | 180°      | \( \pi \)     |
| \( \frac{3}{4} \) | 270°      | \( \frac{3\pi}{2} \) |
| \( \frac{1}{12} \) | 30°       | \( \frac{\pi}{6} \)  |
| \( \frac{7}{8} \) | 315°      | \( \frac{7\pi}{4} \) |
| \( \frac{1}{3} \)  | 120°      | \( \frac{2\pi}{3} \) |

Would you like further explanation on any of these conversions?

### Related Questions:
1. How do you convert from radians to degrees?
2. What is the difference between a full turn and a half-turn in radians?
3. How do fractional turns relate to degrees?
4. What is the significance of \( 2\pi \) radians in terms of angular measurement?
5. How can you convert from degrees to turns?

### Tip:
When converting between radians and degrees, always remember \( 180^\circ = \pi \) radians.

Complete the table with the missing values for turns, degrees, and radians.

Learn how to complete a table by converting between turns, degrees, and radians. This problem involves key trigonometry concepts, including the formulas for converting between angular units. Suitable for high school students in Grades 9-12.

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