Find the value of `sin^(-1)(sin7)` and `sin^(-1)(sin(-5))`

Explanation

To solve the problem of finding the values of \( \sin^{-1}(\sin 7) \) and \( \sin^{-1}(\sin(-5)) \), we will follow a systematic approach based on the properties of the inverse sine function.

### Step 1: Understanding the Range of \( \sin^{-1}(x) \)
The function \( \sin^{-1}(x) \) (or arcsin) is defined for values of \( x \) in the range \([-1, 1]\) and its output lies in the range \([- \frac{\pi}{2}, \frac{\pi}{2}]\).

### Step 2: Finding \( \sin^{-1}(\sin 7) \)
1. **Identify the angle**: The angle \( 7 \) radians is outside the range \([- \frac{\pi}{2}, \frac{\pi}{2}]\).
2. **Adjust the angle**: We need to find an equivalent angle within the range. We can use the periodic property of the sine function, which has a period of \( 2\pi \):
...