Find the principal values of each of the following:
(i) `"cosec"^(-1)(-sqrt(2))`
(ii) `"cosec"^(-1)(-2)`

Explanation

To find the principal values of the given inverse cosecant functions, we will follow a systematic approach.

### Solution:

**(i) Finding \( \text{cosec}^{-1}(-\sqrt{2}) \)**

1. **Set up the equation**: Let \( \theta = \text{cosec}^{-1}(-\sqrt{2}) \). This implies that \( \text{cosec}(\theta) = -\sqrt{2} \).

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