Find the principal value of the following
(i) `sin^(-1).(1)/(2)`
(ii) `tan ^(-1).(1)/sqrt(3)`
(iii) `cot ^(-1)(-sqrt3)`

Explanation

To find the principal values of the given inverse trigonometric functions, we will solve each part step by step.

### (i) Find `sin^(-1)(1/2)`

1. **Identify the value**: We need to find the angle whose sine is \( \frac{1}{2} \).
2. **Recall the sine values**: We know that \( \sin(\frac{\pi}{6}) = \frac{1}{2} \).
3. **Principal value**: Therefore, the principal value of \( \sin^{-1}(\frac{1}{2}) \) is \( \frac{\pi}{6} \).

...