The angle of 1' (minute of arc) in radian is nearly equal to

Options

A. `2.91 x 10^-4 rad`
B. `4.85 x 10^-4 rad`
C. `4.80 x 10^-6 rad`
D. `1.75 x 10^-2 rad`

Answer

To find the angle of 1 minute of arc in radians, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Minutes and Degrees**:
- We know that 60 minutes (arc) is equal to 1 degree.
- Therefore, 1 minute is equal to \( \frac{1}{60} \) degrees.

2. **Convert Degrees to Radians**:
- We know the conversion factor between degrees and radians:
\[ 180 \text{ degrees} = \pi \text{ radians} \]
- To find out how many radians are in 1 degree, we can rearrange this to:
\[ 1 \text{ degree} = \frac{\pi}{180} \text{ radians} \]

3. **Calculate Radians for 1 Minute**:
- Since 1 minute is \( \frac{1}{60} \) degrees, we can convert this to radians:
\[ 1 \text{ minute} = \frac{1}{60} \text{ degrees} = \frac{1}{60} \times \frac{\pi}{180} \text{ radians} \]

4. **Simplifying the Expression**:
- Now we simplify the expression:
\[ 1 \text{ minute} = \frac{\pi}{60 \times 180} \text{ radians} \]
- This simplifies to:
\[ 1 \text{ minute} = \frac{\pi}{10800} \text{ radians} \]

5. **Calculating the Numerical Value**:
- Using \( \pi \approx 3.14 \):
\[ 1 \text{ minute} \approx \frac{3.14}{10800} \text{ radians} \]
- Performing the division:
\[ 1 \text{ minute} \approx 2.9 \times 10^{-4} \text{ radians} \]

### Final Answer:
Thus, the angle of 1 minute of arc in radians is approximately \( 2.9 \times 10^{-4} \) radians.

---