Evaluate each of the following:

(i)`sin^(-1)(sin((13pi)/7))`

(ii) `sin^(-1)(sin((17pi)/8))`

(iii) `sin^(-1){sin(-(17pi)/8)}`

Explanation

To evaluate the expressions given in the question, we will use the property of inverse trigonometric functions. Specifically, we will use the fact that for any angle \( \theta \), \( \sin^{-1}(\sin(\theta)) = \theta \) if \( \theta \) lies within the range \( [-\frac{\pi}{2}, \frac{\pi}{2}] \). If \( \theta \) is outside this range, we will need to find an equivalent angle within this range.

### (i) Evaluate \( \sin^{-1}(\sin(\frac{13\pi}{7})) \)

1. **Identify the angle**: The angle \( \frac{13\pi}{7} \) is greater than \( \frac{\pi}{2} \) and less than \( 2\pi \).
2. **Find a coterminal angle**: We can find a coterminal angle by subtracting \( 2\pi \):
\[
\frac{13\pi}{7} - 2\pi = \frac{13\pi}{7} - \frac{14\pi}{7} = -\frac{\pi}{7}
...