Question

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

• A. $2.91 \times 10^{-4}$ rad
• B. $4.85 \times 10^{-4}$ rad
• C. $4.80 \times 10^{-6}$ rad
• D. $1.75 \times 10^{-2}$ rad

Answer 1

The Correct Option is A

To determine the angle of \(1'\) (one minute of arc) in radians, we start with the conversion relationship between degrees and radians:

\(1 \, \text{degree} \, = \, \frac{\pi}{180} \, \text{radians}\)

One degree is divided into 60 minutes, so the angle of \(1'\) is calculated as follows:

1. Since there are 60 minutes in a degree:

\[1' = \frac{1}{60} \, \text{degree}\]

1. Convert degrees to radians:

\[ 1' = \left(\frac{1}{60}\right) \times \left(\frac{\pi}{180}\right) \, \text{radians} \]

1. Calculate the value:

\[ 1' = \frac{\pi}{10800} \, \text{radians} \]

1. Approximating \(\pi \approx 3.14159\):

\[ 1' = \frac{3.14159}{10800} \approx 2.908882 \times 10^{-4} \, \text{radians} \]

This value rounds to approximately \(2.91 \times 10^{-4} \, \text{radians}\).

Therefore, the angle of \(1'\) (minute of arc) in radians is nearly \(2.91 \times 10^{-4}\) radians.

The correct answer is: \(2.91 \times 10^{-4} \, \text{rad}\).