To convert an angle measured in radians into seconds of arc, the value in radians must be multiplied by which of the following exact factors?

Step-by-step solution

We know the relationship between radians and degrees is rad = 180^ . Therefore, 1 rad = 180 degrees . Since 1^ = 60' (minutes of arc) and 1' = 60'' (seconds of arc), we have 1^ = 3600'' . Substituting this into the radian conversion gives 1 rad = 180 3600'' . Thus, to convert an angle from radians to seconds of arc, the value must be multiplied by the factor 180 3600 . Answer: 180 3600