If `sin^(-1)x=y`,then :

Options

A. `o le y le pi `
B. `-(pi)/(2) le y le (pi)/(2)`
C. `o lt y lt pi `
D. `-(pi)/(2) lt y lt (pi)/(2)`

Explanation

To solve the problem, we need to analyze the function given in the question, which is the inverse sine function, denoted as \( \sin^{-1}(x) \) or \( \arcsin(x) \).

### Step-by-Step Solution:

1. **Understanding the Function**:
We start with the equation given in the question:
\[ \sin^{-1}(x) = y \]
This means that \( y \) is the angle whose sine is \( x \).

2. **Identifying the Domain**:
The inverse sine function \( \sin^{-1}(x) \) is defined only for \( x \) values in the range:
\[ -1 \leq x \leq 1 \]
This is the domain of the function.

3. **Identifying the Range**:
The range of the function \( \sin^{-1}(x) \) (or \( y \)) is determined by the possible output values of the function. For the inverse sine function, the range is:
\[ -\frac{\pi}{2} \leq y \leq \frac{\pi}{2} \]
This means that \( y \) can take any value from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\).

4. **Conclusion**:
Therefore, the correct answer to the question is that the range of \( y \) is:
\[ y \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \]

### Final Answer:
The range of \( y \) is:
\[ -\frac{\pi}{2} \leq y \leq \frac{\pi}{2} \]