Question

Value of 1 Radian is:

• A. \( 47^\circ 15' 17'' \)
• B. \( 60^\circ 30' 15'' \)
• C. \( 180^\circ \)
• D. \( 57^\circ 17' 45'' \)

Hint:

To convert radians to degrees, multiply by \( \frac{180}{\pi} \). If needed, convert the decimal part into minutes and seconds.

Answer 1

The Correct Option is D

We know that \( 1 \text{ radian} = \frac{180^\circ}{\pi} \). Using the approximate value \( \pi \approx 3.1416 \), we get: \[ 1 \text{ radian} = \frac{180^\circ}{3.1416} \approx 57.2958^\circ. \] Converting the decimal part \( 0.2958 \) into minutes and seconds: \[ 0.2958^\circ \times 60 = 17.748' \quad \text{(minutes)}, \] \[ 0.748 \times 60 = 44.88'' \quad \text{(seconds)}. \] Thus, \( 1 \text{ radian} \approx 57^\circ 17' 45'' \), which is the correct answer (D).