how many radians are displaced by the minute hand of a clock between 1:00 pm and 6:45 pm of the same day
the minute hand would have gone around 5 3/4 times
= 5.75(2π)radians or 23π/2 radians
it goes around 5.75 times
=5.75*2PI
radians
for some reason i am gettin 23pi/24
To calculate the number of radians displaced by the minute hand of a clock between 1:00 pm and 6:45 pm, we need to determine the angle covered by the minute hand for each hour.
In a 12-hour period, the minute hand completes a full rotation of 360 degrees or 2π radians. This means that for each hour, the minute hand moves 360 degrees divided by 12, or 30 degrees, or π/6 radians.
Between 1:00 pm and 6:00 pm, there are six hours. Therefore, during this time, the minute hand moves 6 times π/6 radians, which equals 6π/6 radians.
Between 6:00 pm and 6:45 pm, there are 45 minutes. In one hour, which consists of 60 minutes, the minute hand moves π/6 radians. We can find the angle covered by the minute hand in 45 minutes by multiplying π/6 radians by 45/60, which simplifies to 3π/12 or π/4 radians.
To find the total number of radians displaced by the minute hand between 1:00 pm and 6:45 pm, we add the two values we calculated:
6π/6 + π/4 = 6π/6 + 3π/12
To simplify, we can combine the two fractions by finding a common denominator:
6π/6 + 3π/12 = 12π/12 + 3π/12 = 15π/12
So, the minute hand of the clock is displaced by 15π/12 radians between 1:00 pm and 6:45 pm of the same day.