Which of the following is correct ?

Options

A. `sin1^(@)gtsin1`
B. `sin1^(@)ltsin1`
C. `sin1^(@)=sin1`
D. `sin1^(@)=(pi)/(18^(@))sin1`

Explanation

To solve the question "Which of the following is correct?" regarding the sine values, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding the Conversion from Degrees to Radians:**
- We know that \( \pi \) radians is equal to \( 180 \) degrees.
- Therefore, \( 1 \) degree can be converted to radians as follows:
\[ 1 \text{ degree} = \frac{\pi}{180} \text{ radians} \]

2. **Analyzing the First Statement:**
- The first statement is: \( \sin(1 \text{ degree}) > \sin(1) \).
- Here, \( \sin(1) \) refers to \( \sin(1 \text{ radian}) \).
- Since \( 1 \text{ degree} < 1 \text{ radian} \) (because \( 1 \text{ radian} \approx 57.30 \text{ degrees} \)), and knowing that the sine function is increasing in this interval, we can conclude:
\[ \sin(1 \text{ degree}) < \sin(1 \text{ radian}) \]
- Thus, the first statement is **false**.

3. **Analyzing the Second Statement:**
- The second statement is: \( \sin(1 \text{ degree}) < \sin(1) \).
- From our previous conclusion, since \( \sin(1 \text{ degree}) < \sin(1 \text{ radian}) \), this statement is **true**.

4. **Analyzing the Third Statement:**
- The third statement is: \( \sin(1 \text{ degree}) = \sin(1) \).
- Since we have established that \( 1 \text{ degree} \) is not equal to \( 1 \text{ radian} \), this statement is **false**.

5. **Analyzing the Fourth Statement:**
- The fourth statement is: \( \sin(1 \text{ degree}) = \frac{\pi}{18} \sin(1) \).
- We already know that \( \sin(1 \text{ degree}) = \sin\left(\frac{\pi}{180}\right) \), which does not equal \( \frac{\pi}{18} \sin(1) \) because \( \frac{\pi}{18} \) is not a correct conversion factor in this context. Thus, this statement is also **false**.

### Conclusion:
The only correct statement among the options is:
- \( \sin(1 \text{ degree}) < \sin(1) \)