If `x=sinphi`, then which among the following correctly represents the range of x?

Options

A. `-1lexle1`
B. `-1ltxlt1`
C. `0ltxlt1`
D. `0lexle1`

Answer

To solve the problem, we need to determine the range of the function \( x = \sin \phi \).

### Step-by-Step Solution:

1. **Understanding the Sine Function**:
The sine function, denoted as \( \sin \phi \), is a periodic function that oscillates between -1 and 1 for all real values of \( \phi \).

2. **Identifying the Maximum and Minimum Values**:
- The maximum value of \( \sin \phi \) occurs at \( \phi = \frac{\pi}{2} \) (90 degrees), where \( \sin \frac{\pi}{2} = 1 \).
- The minimum value of \( \sin \phi \) occurs at \( \phi = \frac{3\pi}{2} \) (270 degrees), where \( \sin \frac{3\pi}{2} = -1 \).

3. **Establishing the Range**:
From the above points, we can conclude that:
\[ -1 \leq \sin \phi \leq 1 \]
This means that the sine function can take any value from -1 to 1, inclusive.

4. **Expressing the Range in Terms of \( x \)**:
Since we have defined \( x = \sin \phi \), we can express the range of \( x \) as:
\[ -1 \leq x \leq 1 \]

5. **Selecting the Correct Option**:
Among the given options:
- Option A: \( -1 \leq x \leq 1 \) (This is correct)
- Option B: \( -1 < x < 1 \) (This is incorrect as it excludes -1 and 1)
- Option C: \( 0 < x < 1 \) (This is incorrect as it excludes negative values)
- Option D: \( 0 \leq x \leq 1 \) (This is incorrect as it excludes negative values)

Therefore, the correct answer is **Option A**.