Question 1141182: What is the angle in radians through which the hour hand of a clock turns between 6:00am to 6:40 am. Found 2 solutions by josmiceli, Theo:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! there are 360 degrees in one complete revolution of the hour hand.
that would be 12 hours, or 12 * 60 = 720 minutes.
6:00 am would be 6 * 60 = 360 minutes.
6:40 am would be 6 * 60 + 40 = 400 minutes.
since there are 720 minutes in one complete revolution, then each degree is equal to 2 minutes.
therefore 360 minutes is equal to 180 degrees and 400 minutes is equal to 200 degrees.
the angle between these two position would therefore be equal to 20 degrees.
radians are equal to degrees times pi / 180.
therefore 20 degrees is equal to 20 * pi / 180 = pi / 9 radians which can also be shown as 1/9 * pi radians.
i believe that's your answer.
the angle formed is 1/9 * pi radians.
if your worked it from radians rather than working it from degrees and then converting to radians, you should wind up with the same answer.
one complete revolution is 2 * pi radians.
there are 720 minutes in one complete revolution of the hour hand.
therefore, each minute is worth 2 * pi / 720 = pi / 360 radians.
the difference between 6:00 and 6:40 is 40 minutes.
each minute is worth pi / 360 radians, therefore 40 minutes is worth 40 * pi / 360 radians.
simplify to get pi / 9 radians.
it looks like pi / 9 radians is your answer in radians.
