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Let's break down the problem and solve each part step by step.

### a) Convert the following angles from radians into degrees:
To convert radians into degrees, we use the formula:

\[
\text{Degrees} = \text{Radians} \times \left(\frac{180^\circ}{\pi}\right)
\]

1. \(\frac{\pi}{4}\):
\[
\frac{\pi}{4} \times \frac{180^\circ}{\pi} = 45^\circ
\]

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

3. \(\frac{\pi}{2}\):
\[
\frac{\pi}{2} \times \frac{180^\circ}{\pi} = 90^\circ
\]

4. \(\frac{\pi}{10}\):
\[
\frac{\pi}{10} \times \frac{180^\circ}{\pi} = 18^\circ
\]

5. \(\frac{5\pi}{12}\):
\[
\frac{5\pi}{12} \times \frac{180^\circ}{\pi} = 75^\circ
\]

### b) Convert the following angles from degrees into radians:
To convert degrees into radians, we use the formula:

\[
\text{Radians} = \text{Degrees} \times \left(\frac{\pi}{180^\circ}\right)
\]

1. \(90^\circ\):
\[
90^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{2}
\]

2. \(60^\circ\):
\[
60^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{3}
\]

3. \(45^\circ\):
\[
45^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{4}
\]

4. \(360^\circ\):
\[
360^\circ \times \frac{\pi}{180^\circ} = 2\pi
\]

5. \(30^\circ\):
\[
30^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{6}
\]

### Summary of results:
#### a) Radians to Degrees:
- \(\frac{\pi}{4} = 45^\circ\)
- \(\pi = 180^\circ\)
- \(\frac{\pi}{2} = 90^\circ\)
- \(\frac{\pi}{10} = 18^\circ\)
- \(\frac{5\pi}{12} = 75^\circ\)

#### b) Degrees to Radians:
- \(90^\circ = \frac{\pi}{2}\)
- \(60^\circ = \frac{\pi}{3}\)
- \(45^\circ = \frac{\pi}{4}\)
- \(360^\circ = 2\pi\)
- \(30^\circ = \frac{\pi}{6}\)

Would you like further clarification on any part of the process?

### Related Questions:
1. How do you convert between radians and degrees quickly in your head?
2. What is the significance of \(\pi\) in angle conversions?
3. Can angles be measured in units other than degrees or radians?
4. What are the applications of radians in real-world problems?
5. Why do we use \(180^\circ\) as the conversion factor between degrees and radians?

### Tip:
Memorizing common radian-degree pairs, like \(\pi/6 = 30^\circ\) and \(\pi/4 = 45^\circ\), can make conversions much faster!

Convert the following angles from radians into degrees: π/4, π, π/2, π/10, 5π/12. Convert the following angles from degrees into radians: 90°, 60°, 45°, 360°, 30°.

Explore our step-by-step guide on converting radians to degrees and vice versa. This tutorial covers essential trigonometric conversions including π/4, π/2, and more, suitable for high school students.

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