Express the following angle in degrees.
(i) `((5pi)/(12))^(c)` `" "` (ii) `-((7pi)/(12))^(c)`
(iii) `(1^(c))/(3)` `" "` (iv) `-(2pi^(c))/(9)`

Answer

To convert the given angles from radians to degrees, we will use the formula:

\[ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \]

Let's solve each part step by step.

### (i) Convert \(\frac{5\pi}{12}\) radians to degrees:

1. **Write the formula**:
\[ \text{Degrees} = \frac{5\pi}{12} \times \frac{180}{\pi} \]

2. **Cancel \(\pi\)**:
\[ = \frac{5 \times 180}{12} \]

3. **Calculate \(5 \times 180\)**:
\[ = \frac{900}{12} \]

4. **Divide \(900\) by \(12\)**:
\[ = 75 \text{ degrees} \]

### (ii) Convert \(-\frac{7\pi}{12}\) radians to degrees:

1. **Write the formula**:
\[ \text{Degrees} = -\frac{7\pi}{12} \times \frac{180}{\pi} \]

2. **Cancel \(\pi\)**:
\[ = -\frac{7 \times 180}{12} \]

3. **Calculate \(7 \times 180\)**:
\[ = -\frac{1260}{12} \]

4. **Divide \(1260\) by \(12\)**:
\[ = -105 \text{ degrees} \]

### (iii) Convert \(\frac{\pi}{3}\) radians to degrees:

1. **Write the formula**:
\[ \text{Degrees} = \frac{\pi}{3} \times \frac{180}{\pi} \]

2. **Cancel \(\pi\)**:
\[ = \frac{180}{3} \]

3. **Divide \(180\) by \(3\)**:
\[ = 60 \text{ degrees} \]

### (iv) Convert \(-\frac{2\pi}{9}\) radians to degrees:

1. **Write the formula**:
\[ \text{Degrees} = -\frac{2\pi}{9} \times \frac{180}{\pi} \]

2. **Cancel \(\pi\)**:
\[ = -\frac{2 \times 180}{9} \]

3. **Calculate \(2 \times 180\)**:
\[ = -\frac{360}{9} \]

4. **Divide \(360\) by \(9\)**:
\[ = -40 \text{ degrees} \]

### Final Answers:
(i) \(75\) degrees
(ii) \(-105\) degrees
(iii) \(60\) degrees
(iv) \(-40\) degrees