To solve the problem of identifying the graph of the function \( y = \sin x \) from the given options, we can follow these steps:
### Step 1: Understand the Function
The function given is \( y = \sin x \). The sine function is a periodic function that oscillates between -1 and 1.
### Step 2: Identify Key Features of the Graph
- **Amplitude**: The amplitude of \( y = \sin x \) is 1, meaning the maximum value is 1 and the minimum value is -1.
- **Period**: The period of \( y = \sin x \) is \( 2\pi \), meaning it repeats every \( 2\pi \).
- **Key Points**: The sine function starts at (0,0), reaches its maximum at \( \left(\frac{\pi}{2}, 1\right) \), returns to zero at \( (\pi, 0) \), reaches its minimum at \( \left(\frac{3\pi}{2}, -1\right) \), and completes one cycle at \( (2\pi, 0) \).
### Step 3: Analyze the Options
Given the options, we need to find which graph matches the characteristics of \( y = \sin x \):
- **Option A**: Should show the sine wave starting from the origin, reaching a peak of 1 at \( \frac{\pi}{2} \), and returning to 0 at \( \pi \).
- **Option B**: Represents \( y = -\sin x \), which would be the reflection of the sine wave across the x-axis.
- **Option C**: Represents \( y = \cos x \), which starts at its maximum value of 1 at \( x = 0 \).
- **Option D**: Represents \( y = -\cos x \), which is also a reflection but starting from the maximum.
### Step 4: Compare Each Option
- **Option A**: Matches the characteristics of \( y = \sin x \).
- **Option B**: Does not match, as it is \( y = -\sin x \).
- **Option C**: Does not match, as it is \( y = \cos x \).
- **Option D**: Does not match, as it is \( y = -\cos x \).
### Step 5: Conclusion
The correct option that represents the graph of \( y = \sin x \) is **Option A**.
