Find the value of:
(i) `cos 210^(@)`
(ii)`"sin" 225^(@)`
(iii)`"tan" 330^(@)`
(iv)`cot(-315^(@))`
(v) `"sec"(11pi)/(4)`

Answer

Let's solve the given trigonometric values step by step.

### (i) Find `cos 210°`

1. **Identify the angle**:
- \( 210° = 180° + 30° \)

2. **Use the cosine addition formula**:
- \( \cos(180° + \theta) = -\cos(\theta) \)
- Therefore, \( \cos(210°) = -\cos(30°) \)

3. **Calculate \( \cos(30°) \)**:
- \( \cos(30°) = \frac{\sqrt{3}}{2} \)

4. **Final calculation**:
- \( \cos(210°) = -\frac{\sqrt{3}}{2} \)

### (ii) Find `sin 225°`

1. **Identify the angle**:
- \( 225° = 180° + 45° \)

2. **Use the sine addition formula**:
- \( \sin(180° + \theta) = -\sin(\theta) \)
- Therefore, \( \sin(225°) = -\sin(45°) \)

3. **Calculate \( \sin(45°) \)**:
- \( \sin(45°) = \frac{1}{\sqrt{2}} \)

4. **Final calculation**:
- \( \sin(225°) = -\frac{1}{\sqrt{2}} \)

### (iii) Find `tan 330°`

1. **Identify the angle**:
- \( 330° = 360° - 30° \)

2. **Use the tangent subtraction formula**:
- \( \tan(360° - \theta) = -\tan(\theta) \)
- Therefore, \( \tan(330°) = -\tan(30°) \)

3. **Calculate \( \tan(30°) \)**:
- \( \tan(30°) = \frac{1}{\sqrt{3}} \)

4. **Final calculation**:
- \( \tan(330°) = -\frac{1}{\sqrt{3}} \)

### (iv) Find `cot(-315°)`

1. **Identify the angle**:
- \( -315° = 360° - 315° = 45° \)

2. **Use the cotangent property**:
- \( \cot(-\theta) = -\cot(\theta) \)
- Therefore, \( \cot(-315°) = -\cot(45°) \)

3. **Calculate \( \cot(45°) \)**:
- \( \cot(45°) = 1 \)

4. **Final calculation**:
- \( \cot(-315°) = -1 \)

### (v) Find `sec(11π/4)`

1. **Identify the angle**:
- \( \frac{11\pi}{4} = 2\pi + \frac{3\pi}{4} \)

2. **Use the secant property**:
- \( \sec(\theta + 2\pi) = \sec(\theta) \)
- Therefore, \( \sec\left(\frac{11\pi}{4}\right) = \sec\left(\frac{3\pi}{4}\right) \)

3. **Calculate \( \sec\left(\frac{3\pi}{4}\right) \)**:
- \( \sec\left(\frac{3\pi}{4}\right) = -\sec\left(\frac{\pi}{4}\right) \)

4. **Calculate \( \sec\left(\frac{\pi}{4}\right) \)**:
- \( \sec\left(\frac{\pi}{4}\right) = \sqrt{2} \)

5. **Final calculation**:
- \( \sec\left(\frac{11\pi}{4}\right) = -\sqrt{2} \)

### Summary of Answers:
1. \( \cos(210°) = -\frac{\sqrt{3}}{2} \)
2. \( \sin(225°) = -\frac{1}{\sqrt{2}} \)
3. \( \tan(330°) = -\frac{1}{\sqrt{3}} \)
4. \( \cot(-315°) = -1 \)
5. \( \sec\left(\frac{11\pi}{4}\right) = -\sqrt{2} \)