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.) Part 2: How far does the tip of the minute hand travel during that time? You must show all of your work.

Accepted Solution

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)