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:

  • \( \frac{5\pi}{4} = 225° \)
  • \( \frac{\pi}{5} = 36° \)