Express (i) 1 radian, (ii) `(pi)/(3)` radians, (iii) `(pi)/(15)` radians in degrees.

Answer

To convert radians to degrees, we use the conversion factor that \(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\). Therefore, to convert any angle in radians to degrees, we multiply the angle in radians by \(\frac{180}{\pi}\).

Let's solve the given problem step by step:

### Step 1: Convert 1 radian to degrees
1. Start with the angle in radians: \(1 \text{ radian}\).
2. Use the conversion factor:
\[ 1 \text{ radian} = 1 \times \frac{180}{\pi} \text{ degrees} \]
3. Simplify the expression:
\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \]

### Step 2: Convert \(\frac{\pi}{3}\) radians to degrees
1. Start with the angle in radians: \(\frac{\pi}{3} \text{ radians}\).
2. Use the conversion factor:
\[ \frac{\pi}{3} \text{ radians} = \frac{\pi}{3} \times \frac{180}{\pi} \text{ degrees} \]
3. The \(\pi\) cancels out:
\[ = \frac{180}{3} \text{ degrees} \]
4. Simplify the expression:
\[ = 60 \text{ degrees} \]

### Step 3: Convert \(\frac{\pi}{15}\) radians to degrees
1. Start with the angle in radians: \(\frac{\pi}{15} \text{ radians}\).
2. Use the conversion factor:
\[ \frac{\pi}{15} \text{ radians} = \frac{\pi}{15} \times \frac{180}{\pi} \text{ degrees} \]
3. The \(\pi\) cancels out:
\[ = \frac{180}{15} \text{ degrees} \]
4. Simplify the expression:
\[ = 12 \text{ degrees} \]

### Final Answers
1. \(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\)
2. \(\frac{\pi}{3} \text{ radians} = 60 \text{ degrees}\)
3. \(\frac{\pi}{15} \text{ radians} = 12 \text{ degrees}\)