Find the inclination of the line whose slope is :
`(i) 0` `(ii) (1)/(4)` `(iii) 3`.

Answer

To find the inclination of a line given its slope, we can use the relationship between the slope \( m \) and the angle of inclination \( \theta \):

\[ m = \tan(\theta) \]

Now, we will solve for the inclination \( \theta \) for each given slope.

### Step-by-Step Solution:

#### (i) Slope \( m = 0 \)

1. **Identify the slope**: We have \( m = 0 \).
2. **Use the relationship**: We know that \( m = \tan(\theta) \).
3. **Set up the equation**:
\[ \tan(\theta) = 0 \]
4. **Find \( \theta \)**: The angle whose tangent is 0 is:
\[ \theta = 0^\circ \]

#### (ii) Slope \( m = \frac{1}{4} \)

1. **Identify the slope**: We have \( m = \frac{1}{4} \).
2. **Use the relationship**:
\[ \tan(\theta) = \frac{1}{4} \]
3. **Find \( \theta \)**: To find \( \theta \), we take the inverse tangent:
\[ \theta = \tan^{-1}\left(\frac{1}{4}\right) \]

#### (iii) Slope \( m = 3 \)

1. **Identify the slope**: We have \( m = 3 \).
2. **Use the relationship**:
\[ \tan(\theta) = 3 \]
3. **Find \( \theta \)**: To find \( \theta \), we take the inverse tangent:
\[ \theta = \tan^{-1}(3) \]

### Summary of Results:

1. For \( m = 0 \), \( \theta = 0^\circ \)
2. For \( m = \frac{1}{4} \), \( \theta = \tan^{-1}\left(\frac{1}{4}\right) \) (approximately \( 14.04^\circ \))
3. For \( m = 3 \), \( \theta = \tan^{-1}(3) \) (approximately \( 71.57^\circ \))