Solve the following inequality:
`sin^(-1)xgt-1`

Explanation

To solve the inequality \( \sin^{-1} x > -1 \), we will follow these steps:

### Step 1: Rewrite the Inequality
The given inequality is:
\[ \sin^{-1} x > -1 \]
This can be rewritten as:
\[ -1 < \sin^{-1} x \]

### Step 2: Apply the Sine Function
To eliminate the inverse sine, we apply the sine function to both sides of the inequality. Remember that the sine function is increasing in the range of \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\):
\[ \sin(-1) < x \]
This means we need to find the value of \(\sin(-1)\).

### Step 3: Calculate \(\sin(-1)\)
Using the property of sine, we know:
\[ \sin(-\theta) = -\sin(\theta) \]
Thus,
\[ \sin(-1) = -\sin(1) \]

### Step 4: Write the Final Inequality
Now substituting back, we have:
\[ -\sin(1) < x \]
or equivalently,
\[ x > -\sin(1) \]

### Step 5: Determine the Range of \(x\)
Since the domain of \(\sin^{-1} x\) is \([-1, 1]\), we also need to consider this constraint. Therefore, the final solution combines both the inequality and the domain:
\[ -\sin(1) < x \leq 1 \]

### Final Answer
Thus, the solution to the inequality \( \sin^{-1} x > -1 \) is:
\[ x \in (-\sin(1), 1] \]