Find the values of :
(i) `tan (-30^(@))`
(ii) `sin 120^(@)`
(iii) `sin 135^(@)`
(iv) `cos 150^(@)`
(v) `sin 270^(@)`
(vi) `cos 270^(@)`

Explanation

Let's solve the given problems step by step:

### (i) Find `tan (-30°)`

1. **Use the property of tangent**:
\[ \tan(-\theta) = -\tan(\theta) \]
Therefore,
\[ \tan(-30°) = -\tan(30°) \]

2. **Find `tan(30°)`**:
\[ \tan(30°) = \frac{1}{\sqrt{3}} \]

3. **Substitute back**:
\[ \tan(-30°) = -\frac{1}{\sqrt{3}} \]

**Final Answer**:
\[ \tan(-30°) = -\frac{1}{\sqrt{3}} \]

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### (ii) Find `sin(120°)`

1. **Use the sine addition formula**:
\[ \sin(120°) = \sin(90° + 30°) \]

2. **Apply the sine property**:
\[ \sin(90° + \theta) = \cos(\theta) \]
Thus,
\[ \sin(120°) = \cos(30°) \]

3. **Find `cos(30°)`**:
\[ \cos(30°) = \frac{\sqrt{3}}{2} \]

**Final Answer**:
\[ \sin(120°) = \frac{\sqrt{3}}{2} \]

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### (iii) Find `sin(135°)`

1. **Use the sine addition formula**:
\[ \sin(135°) = \sin(90° + 45°) \]

2. **Apply the sine property**:
\[ \sin(90° + \theta) = \cos(\theta) \]
Thus,
\[ \sin(135°) = \cos(45°) \]

3. **Find `cos(45°)`**:
\[ \cos(45°) = \frac{1}{\sqrt{2}} \]

**Final Answer**:
\[ \sin(135°) = \frac{1}{\sqrt{2}} \]

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### (iv) Find `cos(150°)`

1. **Use the cosine addition formula**:
\[ \cos(150°) = \cos(90° + 60°) \]

2. **Apply the cosine property**:
\[ \cos(90° + \theta) = -\sin(\theta) \]
Thus,
\[ \cos(150°) = -\sin(60°) \]

3. **Find `sin(60°)`**:
\[ \sin(60°) = \frac{\sqrt{3}}{2} \]

4. **Substitute back**:
\[ \cos(150°) = -\frac{\sqrt{3}}{2} \]

**Final Answer**:
\[ \cos(150°) = -\frac{\sqrt{3}}{2} \]

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### (v) Find `sin(270°)`

1. **Use the sine addition formula**:
\[ \sin(270°) = \sin(180° + 90°) \]

2. **Apply the sine property**:
\[ \sin(180° + \theta) = -\sin(\theta) \]
Thus,
\[ \sin(270°) = -\sin(90°) \]

3. **Find `sin(90°)`**:
\[ \sin(90°) = 1 \]

4. **Substitute back**:
\[ \sin(270°) = -1 \]

**Final Answer**:
\[ \sin(270°) = -1 \]

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### (vi) Find `cos(270°)`

1. **Use the cosine addition formula**:
\[ \cos(270°) = \cos(180° + 90°) \]

2. **Apply the cosine property**:
\[ \cos(180° + \theta) = -\cos(\theta) \]
Thus,
\[ \cos(270°) = -\cos(90°) \]

3. **Find `cos(90°)`**:
\[ \cos(90°) = 0 \]

4. **Substitute back**:
\[ \cos(270°) = -0 = 0 \]

**Final Answer**:
\[ \cos(270°) = 0 \]

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