Question

Convert the angle measures from degrees to radians

150* =
40 * =

Convert the angle measures from radians to degrees

5pi/4=
Pi/5 =

Answer 1

To convert between degrees and radians, you can use the following relationships:

1. To convert degrees to radians, use the formula:
\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\]

2. To convert radians to degrees, use the formula:
\[
\text{degrees} = \text{radians} \times \frac{180}{\pi}
\]

### Converting Degrees to Radians
1. For \(150^\circ\):
\[
150^\circ \times \frac{\pi}{180} = \frac{150\pi}{180} = \frac{5\pi}{6}
\]

2. For \(40^\circ\):
\[
40^\circ \times \frac{\pi}{180} = \frac{40\pi}{180} = \frac{2\pi}{9}
\]

### Converting Radians to Degrees
1. For \(\frac{5\pi}{4}\):
\[
\frac{5\pi}{4} \times \frac{180}{\pi} = \frac{5 \times 180}{4} = \frac{900}{4} = 225^\circ
\]

2. For \(\frac{\pi}{5}\):
\[
\frac{\pi}{5} \times \frac{180}{\pi} = \frac{180}{5} = 36^\circ
\]

### Summary of Results
- \(150^\circ = \frac{5\pi}{6}\)
- \(40^\circ = \frac{2\pi}{9}\)
- \(\frac{5\pi}{4} = 225^\circ\)
- \(\frac{\pi}{5} = 36^\circ\)