Question

Convert the angle measures from degrees to radians.(2 points) 150° = 40° = Question 2 Convert the angle measures from radians to degrees.(2 points) 5π4 = π5 =

Answer 1

### Question 1: Convert degrees to radians

To convert degrees to radians, you can use the conversion factor:
\[
1 \text{ degree} = \frac{\pi}{180} \text{ radians}
\]

1. **Convert 150° to radians:**
\[
150° = 150 \times \frac{\pi}{180} = \frac{150\pi}{180} = \frac{5\pi}{6} \text{ radians}
\]

2. **Convert 40° to radians:**
\[
40° = 40 \times \frac{\pi}{180} = \frac{40\pi}{180} = \frac{2\pi}{9} \text{ radians}
\]

### Question 2: Convert radians to degrees

To convert radians to degrees, you can use the conversion factor:
\[
1 \text{ radian} = \frac{180}{\pi} \text{ degrees}
\]

1. **Convert \( \frac{5\pi}{4} \) to degrees:**
\[
\frac{5\pi}{4} = \frac{5\pi}{4} \times \frac{180}{\pi} = \frac{5 \times 180}{4} = \frac{900}{4} = 225°
\]

2. **Convert \( \frac{\pi}{5} \) to degrees:**
\[
\frac{\pi}{5} = \frac{\pi}{5} \times \frac{180}{\pi} = \frac{180}{5} = 36°
\]

### Final Answers

- **Degrees to Radians:**
- \( 150° = \frac{5\pi}{6} \) radians
- \( 40° = \frac{2\pi}{9} \) radians

- **Radians to Degrees:**
- \( \frac{5\pi}{4} = 225° \)
- \( \frac{\pi}{5} = 36° \)