Concept:A radian is the standard unit of angular measure. To convert radians to degrees, minutes, and seconds, we multiply by the conversion factor \( 180/\pi \).
Formula:$$ 1 \text{ rad} = \frac{180^\circ}{\pi} $$
Solution:- We know \( 1 \text{ rad} \approx 57.2958^\circ \).
- This can be split into exactly \( 57^\circ \) and a fractional remainder of \( 0.2958^\circ \).
- To find the minutes, multiply the fraction by 60: \( 0.2958 \times 60 \approx 17.75' \).
- Rounding to the nearest whole minute gives \( 18' \) (18 arcminutes).
- Thus, \( 1 \text{ radian} \approx 57^\circ 18' \).
Why other options are incorrect:- Option A incorrectly mistakes the '.3' in 57.3 degrees for 3 minutes. (0.3 degrees is \( 0.3 \times 60 = 18 \) minutes).
- Option B and Option D use the symbol for arcseconds (double prime) instead of arcminutes (single prime).
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