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. **Understand the Relationship Between Degrees and Radians**:
- We know that \( \pi \) radians is equivalent to 180 degrees. This gives us the conversion factor between degrees and radians.

2. **Convert Minutes to Degrees**:
- One degree is divided into 60 minutes. Therefore, 1 minute is equal to \( \frac{1}{60} \) degrees.

3. **Convert Degrees to Radians**:
- Using the relationship from step 1, we can convert degrees to radians. The conversion formula is:
\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
- Substituting \( \frac{1}{60} \) degrees into the formula gives:
\[ \text{radians} = \left(\frac{1}{60}\right) \times \frac{\pi}{180} \]

4. **Simplify the Expression**:
- Now, we simplify the expression:
\[ \text{radians} = \frac{\pi}{60 \times 180} \]
- Calculating \( 60 \times 180 = 10800 \):
\[ \text{radians} = \frac{\pi}{10800} \]

5. **Calculate the Numerical Value**:
- Using \( \pi \approx 3.14 \):
\[ \text{radians} \approx \frac{3.14}{10800} \]
- Performing the division:
\[ \text{radians} \approx 0.000290 \]

6. **Express in Scientific Notation**:
- The value \( 0.000290 \) can be expressed in scientific notation as:
\[ \text{radians} \approx 2.90 \times 10^{-4} \]

### Final Answer:
The angle of 1 minute of arc in radians is approximately \( 2.90 \times 10^{-4} \) radians.

---