Consider the following statements :
1. `1^(@)` in radian measure is less than 0.02 radians .
2. 1 radian in degree measure is greater then `45^(@)`.
Which of the above statements is / are correct ?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Explanation

To determine the correctness of the given statements, we will convert between degrees and radians and compare the values.

### Step 1: Convert 1 degree to radians
To convert degrees to radians, we use the formula:
\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
For 1 degree:
\[ 1 \text{ degree} = 1 \times \frac{\pi}{180} = \frac{\pi}{180} \text{ radians} \]

### Step 2: Calculate the value of \(\frac{\pi}{180}\)
Using the approximation \(\pi \approx 3.14\):
\[ \frac{\pi}{180} \approx \frac{3.14}{180} \approx 0.01746 \text{ radians} \]

### Step 3: Compare \(0.01746\) radians with \(0.02\) radians
Now we compare:
\[ 0.01746 < 0.02 \]
This shows that the first statement is true.

### Step 4: Convert 1 radian to degrees
To convert radians to degrees, we use the formula:
\[ \text{degrees} = \text{radians} \times \frac{180}{\pi} \]
For 1 radian:
\[ 1 \text{ radian} = 1 \times \frac{180}{\pi} \text{ degrees} \]

### Step 5: Calculate the value of \(\frac{180}{\pi}\)
Using the approximation \(\pi \approx 3.14\):
\[ \frac{180}{\pi} \approx \frac{180}{3.14} \approx 57.3 \text{ degrees} \]

### Step 6: Compare \(57.3\) degrees with \(45\) degrees
Now we compare:
\[ 57.3 > 45 \]
This shows that the second statement is also true.

### Conclusion
Both statements are correct. Therefore, the answer is:
**Option C: Both 1 and 2 are correct.**

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