Find the domain and the range of the function `y=f(x)`, where `f(x)` is given by
`sinx`

Answer

To find the domain and range of the function \( y = f(x) \), where \( f(x) = \sin x \), we will follow these steps:

### Step 1: Understand the Function
The function \( f(x) = \sin x \) is a trigonometric function that oscillates between -1 and 1.

### Step 2: Determine the Domain
The domain of a function is the set of all possible input values (x-values) for which the function is defined.

For the sine function:
- The sine function is defined for all real numbers.
- Therefore, the domain of \( f(x) = \sin x \) is:
\[ \text{Domain} = (-\infty, \infty) \]

### Step 3: Determine the Range
The range of a function is the set of all possible output values (y-values) that the function can produce.

For the sine function:
- The sine function oscillates between -1 and 1.
- Therefore, the range of \( f(x) = \sin x \) is:
\[ \text{Range} = [-1, 1] \]

### Final Result
- **Domain**: \( (-\infty, \infty) \)
- **Range**: \( [-1, 1] \)

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