Express (i) `45^(@),(ii) 30^(@),(iii) 9^(@)` in radians.

Answer

To express the given angles in radians, we will use the conversion factor that \(1 \text{ degree} = \frac{\pi}{180} \text{ radians}\). We will apply this conversion to each of the angles provided in the question.

### Step-by-step Solution:

**(i) Convert 45 degrees to radians:**

1. Start with the conversion formula:
\[ 1 \text{ degree} = \frac{\pi}{180} \text{ radians} \]
2. Multiply both sides by 45 degrees:
\[ 45 \text{ degrees} = 45 \times \frac{\pi}{180} \text{ radians} \]
3. Simplify the right side:
\[ = \frac{45\pi}{180} \text{ radians} \]
4. Reduce the fraction:
\[ = \frac{\pi}{4} \text{ radians} \]

**(ii) Convert 30 degrees to radians:**

1. Use the same conversion formula:
\[ 1 \text{ degree} = \frac{\pi}{180} \text{ radians} \]
2. Multiply both sides by 30 degrees:
\[ 30 \text{ degrees} = 30 \times \frac{\pi}{180} \text{ radians} \]
3. Simplify the right side:
\[ = \frac{30\pi}{180} \text{ radians} \]
4. Reduce the fraction:
\[ = \frac{\pi}{6} \text{ radians} \]

**(iii) Convert 9 degrees to radians:**

1. Again, use the conversion formula:
\[ 1 \text{ degree} = \frac{\pi}{180} \text{ radians} \]
2. Multiply both sides by 9 degrees:
\[ 9 \text{ degrees} = 9 \times \frac{\pi}{180} \text{ radians} \]
3. Simplify the right side:
\[ = \frac{9\pi}{180} \text{ radians} \]
4. Reduce the fraction:
\[ = \frac{\pi}{20} \text{ radians} \]

### Final Answers:
- \(45^{\circ} = \frac{\pi}{4} \text{ radians}\)
- \(30^{\circ} = \frac{\pi}{6} \text{ radians}\)
- \(9^{\circ} = \frac{\pi}{20} \text{ radians}\)