Question

Tammy is at the dentist's office waiting on her appointment. She notices that the 6-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:20 to 1:55? (Hint: Find the number of degrees per minute first.)

Answer 1

Part 1:

In order to find how many radians the minute hand moves from 1:20 to 1:55, we need to remember that there are 60 minutes in an hour (clock) and there are 360 degrees in the clock since the clock is a circle. After dividing 360 by 60, we find that each minute is equal to 6 degrees. After that, we can subtract the times, which tells us that there are 35 minutes between 1:20 and 1:55. Using this we can just multiply this out, to get 35 times 6, which is equal to 210 degrees. We can get our final answer by converting this into degrees. Since one 1 degree is about 0.0174, we can set up a proportion. After solving, we will get that the minutes hand moves 3.555 radians in total.

Answer 2

There are 12 five minutes in one hour and 1 hour correspond to 360°, then each 5 minutes represents 360/12 = 30°

From 1:20 to 1: 55 we have 35 minutes or 7 x 5 minutes or

7 x 30° = 210°

To convert degree into radian, we apply the following formula:

degree/180° = radian/π

210/180 = r/π or (cross multiplication) →Radian = (π x 210/180

→ Radian = 7π/6 (simplify by 30)