Let `f:[-pi/2,\ pi/2]->A` be defined by `f(x)=sinx` . If `f` is a bijection, write set `A` .

Explanation

To determine the set \( A \) for the function \( f: [-\frac{\pi}{2}, \frac{\pi}{2}] \to A \) defined by \( f(x) = \sin x \), we need to analyze the properties of the sine function over the given interval.

### Step-by-step Solution:

1. **Identify the Domain**: The function \( f \) is defined on the interval \( [-\frac{\pi}{2}, \frac{\pi}{2}] \). This means \( x \) can take any value from \( -\frac{\pi}{2} \) to \( \frac{\pi}{2} \).

2. **Determine the Range of \( f(x) = \sin x \)**: We need to find the values of \( \sin x \) as \( x \) varies over the interval \( [-\frac{\pi}{2}, \frac{\pi}{2}] \).
- At \( x = -\frac{\pi}{2} \), \( \sin\left(-\frac{\pi}{2}\right) = -1 \).
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