Find the value of the following :-
`{:((a)sin((pi)/(6)),(b)cos ((pi)/(4))), ((c)tan((pi)/(3)),(d)cos ((pi)/(2))), ((e)cot ((3pi)/(4)),(f)sin((5pi)/(6))),((g)sin pi,(h)cos pi),((i)sin((pi)/(2)),(j)sin((3pi)/(2))),((k)cos((3pi)/(2)),):}`

Answer

To solve the problem, we will evaluate each trigonometric function step by step.

1. **Evaluate \( \sin\left(\frac{\pi}{6}\right) \)**:
\[ \sin\left(\frac{\pi}{6}\right) = \sin(30^\circ) = \frac{1}{2} \]

2. **Evaluate \( \cos\left(\frac{\pi}{4}\right) \)**:
\[ \cos\left(\frac{\pi}{4}\right) = \cos(45^\circ) = \frac{1}{\sqrt{2}} \]

3. **Evaluate \( \tan\left(\frac{\pi}{3}\right) \)**:
\[ \tan\left(\frac{\pi}{3}\right) = \tan(60^\circ) = \sqrt{3} \]

4. **Evaluate \( \cos\left(\frac{\pi}{2}\right) \)**:
\[ \cos\left(\frac{\pi}{2}\right) = \cos(90^\circ) = 0 \]

5. **Evaluate \( \cot\left(\frac{3\pi}{4}\right) \)**:
\[ \cot\left(\frac{3\pi}{4}\right) = \cot\left(\pi - \frac{\pi}{4}\right) = -\cot\left(\frac{\pi}{4}\right) = -1 \]

6. **Evaluate \( \sin\left(\frac{5\pi}{6}\right) \)**:
\[ \sin\left(\frac{5\pi}{6}\right) = \sin\left(\pi - \frac{\pi}{6}\right) = \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} \]

7. **Evaluate \( \sin(\pi) \)**:
\[ \sin(\pi) = 0 \]

8. **Evaluate \( \cos(\pi) \)**:
\[ \cos(\pi) = -1 \]

9. **Evaluate \( \sin\left(\frac{\pi}{2}\right) \)**:
\[ \sin\left(\frac{\pi}{2}\right) = 1 \]

10. **Evaluate \( \sin\left(\frac{3\pi}{2}\right) \)**:
\[ \sin\left(\frac{3\pi}{2}\right) = \sin\left(\pi + \frac{\pi}{2}\right) = -1 \]

11. **Evaluate \( \cos\left(\frac{3\pi}{2}\right) \)**:
\[ \cos\left(\frac{3\pi}{2}\right) = \cos\left(\pi + \frac{\pi}{2}\right) = 0 \]

Now, we can summarize the values we found:
- \( \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} \)
- \( \cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} \)
- \( \tan\left(\frac{\pi}{3}\right) = \sqrt{3} \)
- \( \cos\left(\frac{\pi}{2}\right) = 0 \)
- \( \cot\left(\frac{3\pi}{4}\right) = -1 \)
- \( \sin\left(\frac{5\pi}{6}\right) = \frac{1}{2} \)
- \( \sin(\pi) = 0 \)
- \( \cos(\pi) = -1 \)
- \( \sin\left(\frac{\pi}{2}\right) = 1 \)
- \( \sin\left(\frac{3\pi}{2}\right) = -1 \)
- \( \cos\left(\frac{3\pi}{2}\right) = 0 \)

### Final Values:
- \( \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} \)
- \( \cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} \)
- \( \tan\left(\frac{\pi}{3}\right) = \sqrt{3} \)
- \( \cos\left(\frac{\pi}{2}\right) = 0 \)
- \( \cot\left(\frac{3\pi}{4}\right) = -1 \)
- \( \sin\left(\frac{5\pi}{6}\right) = \frac{1}{2} \)
- \( \sin(\pi) = 0 \)
- \( \cos(\pi) = -1 \)
- \( \sin\left(\frac{\pi}{2}\right) = 1 \)
- \( \sin\left(\frac{3\pi}{2}\right) = -1 \)
- \( \cos\left(\frac{3\pi}{2}\right) = 0 \)