 Convert the following radian measures to degrees and degree measures to radians. -5pi over 6 Radian Degree 120° 8π −315° 4 585°

Let's convert each of the given radian measures to degrees and each degree measure to radians.

### Conversion Formulas:
- To convert radians to degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\)
- To convert degrees to radians: \(\text{Radians} = \text{Degrees} \times \frac{\pi}{180}\)

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

### 2. 120° to Radians:
\[
\text{Radians} = 120^\circ \times \frac{\pi}{180} = \frac{120\pi}{180} = \frac{2\pi}{3} \text{ Radians}
\]

### 3. \(8\pi\) to Degrees:
\[
\text{Degrees} = 8\pi \times \frac{180}{\pi} = 8 \times 180 = 1440^\circ
\]

### 4. \(-315^\circ\) to Radians:
\[
\text{Radians} = -315^\circ \times \frac{\pi}{180} = -\frac{315\pi}{180} = -\frac{7\pi}{4} \text{ Radians}
\]

### 5. \(4\) Radians to Degrees:
\[
\text{Degrees} = 4 \times \frac{180}{\pi} \approx 229.18^\circ
\]

### 6. \(585^\circ\) to Radians:
\[
\text{Radians} = 585^\circ \times \frac{\pi}{180} = \frac{585\pi}{180} = \frac{13\pi}{4} \text{ Radians}
\]

### Summary of Conversions:
1. \(-\frac{5\pi}{6}\) Radians = \(-150^\circ\)
2. \(120^\circ\) = \(\frac{2\pi}{3}\) Radians
3. \(8\pi\) Radians = \(1440^\circ\)
4. \(-315^\circ\) = \(-\frac{7\pi}{4}\) Radians
5. \(4\) Radians ≈ \(229.18^\circ\)
6. \(585^\circ\) = \(\frac{13\pi}{4}\) Radians

Would you like more details or have any questions?

### Follow-up Questions:
1. How do you convert degrees to radians in the general case?
2. What is the significance of the unit circle in radian and degree conversions?
3. Why do we use \(\pi\) in the conversion between radians and degrees?
4. Can you convert \(450^\circ\) to radians?
5. What is the radian measure of \(270^\circ\)?
6. How many degrees are in \(\frac{\pi}{2}\) radians?
7. Convert \(2\pi\) radians to degrees.
8. What is the degree equivalent of \(-\frac{3\pi}{2}\) radians?

#### Tip:
Always remember that \(360^\circ\) is equal to \(2\pi\) radians, which is a helpful reference for conversions.

Learn how to convert radians to degrees and degrees to radians with detailed examples. Solve conversions like -5π/6 radians to degrees (-150°) and 120° to radians (2π/3 radians). Explore why π is used in these conversions and the significance of the unit circle.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation