Find the values of a for whch `sin^*(-1)x=|x-a|` will have at least one solution.

Explanation

To solve the equation \( \sin^{-1}(x) = |x - a| \) for values of \( a \) such that there is at least one solution, we will analyze the graphs of both sides of the equation and find the conditions under which they intersect.

### Step 1: Understand the functions involved
The function \( \sin^{-1}(x) \) (the inverse sine function) is defined for \( x \) in the interval \([-1, 1]\) and has a range of \([- \frac{\pi}{2}, \frac{\pi}{2}]\). The function \( |x - a| \) is a piecewise linear function that represents the absolute value of \( x - a \).

### Step 2: Graph the functions
1. **Graph of \( y = \sin^{-1}(x) \)**:
- This graph starts at the point \((-1, -\frac{\pi}{2})\) and ends at the point \((1, \frac{\pi}{2})\).
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