Answer:
3/2π and π/480
Step-by-step explanation:
The question given says that the <u><em>minute hand</em></u> on a clock moves through complete circle in 1 hour, that is <em><u>360° or 2π</u></em>. It also says that the <em><u>hour hand</u></em> moves through 1/12 of a circle, that means 30° <em><u>or π/6</u></em>.
To know how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m, it's necessary to calculate how many radians move them per minute.
Between 1:00 p.m. and 1:45 p.m 45 minutes have passed. With that information, the radians can be calculated using multiplication and division.
Minute hand: To know how many radians move the minute hand per minute division wil be used.
Movement in an hour/ minutes in an hour
2π rad/60 min= π/30 rad-min
That means the minute hand move π/30 radians in a minute.
Now, multiplication can be used to calculate how many radians move the minute hand in 1h.
(π/30 rad-min)(45 minutes)= 3/2π rad
<u>The minute hand moves 3/2π radians between 1:00 p.m. and 1:45 p.m.</u>
Hour hand: To know how many radians move the hour hand per minute division wil be used.
Movement in an hour/ minutes in an hour
2π rad/(60 min x 12 hours)= π/360 rad-min
That means the minute hand move π/360 radians in a minute.
Now, multiplication can be used to calculate how many radians move the hour hand in 1h.
(π/360 rad-min)(45 minutes)= π/8 rad
<u>The minute hand moves π/8 radians between 1:00 p.m. and 1:45 p.m.</u>
