Express the following angles in radians.
(i) `120^(@) " " (ii) -600^(@)`
(iii) `-144^(@)`

Answer

To express the given angles in radians, we will use the conversion factor that \(180^\circ\) is equal to \(\pi\) radians. The formula to convert degrees to radians is:

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

Now, let's solve each part step by step.

### Part (i): Convert \(120^\circ\) to Radians

1. **Write the conversion formula**:
\[ \text{Radians} = 120^\circ \times \frac{\pi}{180} \]

2. **Simplify the fraction**:
\[ = \frac{120\pi}{180} \]

3. **Reduce the fraction**:
- Both 120 and 180 can be divided by 60.
\[ = \frac{2\pi}{3} \]

### Solution for Part (i):
\[ 120^\circ = \frac{2\pi}{3} \text{ radians} \]

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### Part (ii): Convert \(-600^\circ\) to Radians

1. **Write the conversion formula**:
\[ \text{Radians} = -600^\circ \times \frac{\pi}{180} \]

2. **Simplify the fraction**:
\[ = \frac{-600\pi}{180} \]

3. **Reduce the fraction**:
- Divide both the numerator and denominator by 60.
\[ = \frac{-10\pi}{3} \]

### Solution for Part (ii):
\[ -600^\circ = -\frac{10\pi}{3} \text{ radians} \]

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### Part (iii): Convert \(-144^\circ\) to Radians

1. **Write the conversion formula**:
\[ \text{Radians} = -144^\circ \times \frac{\pi}{180} \]

2. **Simplify the fraction**:
\[ = \frac{-144\pi}{180} \]

3. **Reduce the fraction**:
- Divide both the numerator and denominator by 36.
\[ = \frac{-4\pi}{5} \]

### Solution for Part (iii):
\[ -144^\circ = -\frac{4\pi}{5} \text{ radians} \]

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### Final Answers:
1. \(120^\circ = \frac{2\pi}{3} \text{ radians}\)
2. \(-600^\circ = -\frac{10\pi}{3} \text{ radians}\)
3. \(-144^\circ = -\frac{4\pi}{5} \text{ radians}\)

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