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

Explanation

To find the values of \( \sin^{-1}(\sin(7)) \) and \( \sin^{-1}(\sin(-5)) \), we will use the properties of the inverse sine function and the periodicity of the sine function.

### Step 1: Finding \( \sin^{-1}(\sin(7)) \)

1. **Identify the range of the sine inverse function**: The function \( \sin^{-1}(x) \) is defined for \( x \) in the range \([-1, 1]\) and its output is in the range \([- \frac{\pi}{2}, \frac{\pi}{2}]\).

2. **Determine the equivalent angle for 7 radians**: Since \( 7 \) radians is greater than \( \frac{\pi}{2} \) (approximately \( 1.57 \) radians), we need to find an equivalent angle within the range of \( \sin^{-1} \).

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