Which of the following is correct?

Options

A. `sin 1^(@) gt sin 1`
B. `sin 1^(@) lt sin 1`
C. `sin 1^(@) = sin 1`
D. `sin 1^(@) =(pi)/(18^(@)) sin 1`

Answer

To solve the question of comparing \( \sin(1^\circ) \) and \( \sin(1) \) (where \( 1 \) is in radians), we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Values**:
- We need to compare \( \sin(1^\circ) \) and \( \sin(1) \).
- Here, \( 1^\circ \) is an angle in degrees, while \( 1 \) is an angle in radians.

2. **Convert Degrees to Radians**:
- To convert degrees to radians, we use the conversion factor:
\[ \text{Radians} = \text{Degrees} \times \frac{\pi}{180} \]
- Thus, \( 1^\circ \) in radians is:
\[ 1^\circ = 1 \times \frac{\pi}{180} \approx 0.01745 \text{ radians} \]

3. **Evaluate the Sine Values**:
- Now we need to find the values of \( \sin(1^\circ) \) and \( \sin(1) \):
- \( \sin(1^\circ) \) can be calculated using a calculator or sine table:
\[ \sin(1^\circ) \approx 0.017452 \]
- \( \sin(1) \) (where \( 1 \) is in radians):
\[ \sin(1) \approx 0.841471 \]

4. **Comparison**:
- Now we compare the two values:
\[ \sin(1^\circ) \approx 0.017452 \quad \text{and} \quad \sin(1) \approx 0.841471 \]
- Clearly, \( \sin(1) > \sin(1^\circ) \).

5. **Conclusion**:
- From the comparison, we conclude:
\[ \sin(1) > \sin(1^\circ) \]
- Therefore, the correct statement is:
\[ \sin(1) \text{ is greater than } \sin(1^\circ). \]

### Final Answer:
The correct option is that \( \sin(1) > \sin(1^\circ) \).

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