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The problem asks to draw the angles α and β in the standard position and then express each angle as a fraction of a complete rotation. Let's solve each part of the problem:

### Part a:
- **Given:** 
  - α = 10° 
  - β = 10 rad

1. **For α (in degrees):**
   - A complete rotation is 360°.
   - To express α as a fraction of a complete rotation:
     \[
     \frac{α}{360°} = \frac{10°}{360°} = \frac{1}{36}
     \]

2. **For β (in radians):**
   - A complete rotation in radians is \( 2\pi \) radians (approximately 6.28 rad).
   - To express β as a fraction of a complete rotation:
     \[
     \frac{β}{2\pi} = \frac{10}{2\pi} \approx \frac{10}{6.28} \approx 1.59
     \]

### Part b:
- **Given:** 
  - α = 20° 
  - β = 20 rad

1. **For α (in degrees):**
   - To express α as a fraction of a complete rotation:
     \[
     \frac{α}{360°} = \frac{20°}{360°} = \frac{1}{18}
     \]

2. **For β (in radians):**
   - To express β as a fraction of a complete rotation:
     \[
     \frac{β}{2\pi} = \frac{20}{2\pi} \approx \frac{20}{6.28} \approx 3.18
     \]

### Summary:
- For α = 10°: it represents \(\frac{1}{36}\) of a full rotation.
- For β = 10 rad: it represents approximately 1.59 full rotations.
- For α = 20°: it represents \(\frac{1}{18}\) of a full rotation.
- For β = 20 rad: it represents approximately 3.18 full rotations.

Would you like further details or have any questions about these calculations?

Here are 5 related questions to expand on this topic:
1. How do you convert an angle from degrees to radians?
2. What is the significance of the standard position for an angle?
3. How do you express angles greater than \(2\pi\) radians or 360° as a fraction of a full rotation?
4. What is the relationship between the radian and degree measures of an angle?
5. How would you graph angles in standard position on the unit circle?

**Tip:** When converting angles between radians and degrees, remember that \( 180° = \pi \) radians.

Dibuja los ángulos α y β en posición normal, luego escribe cada ángulo como una parte de una rotación completa. a) α = 10° y β = 10 rad, b) α = 20° y β = 20 rad

Learn how to express angles in degrees and radians as fractions of a full rotation. This problem demonstrates the conversion of 10° and 10 radians, and 20° and 20 radians, using basic trigonometric concepts. Suitable for Grades 9-12.

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