Question

Celia is staring at the clock waiting for school to end so that she can go to track practice. She notices that the 4-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 1:25 to 1:50? (Hint: Find the number of degrees per minute first.)

Answer 1

How many radians does the minute hand move from 1:25 to 1:50?

Calculations are done as follows:

360 ° /60 minutes = 6° per minute
1:25 to 1:50 = 25 minutes

25 minutes x 6° per minute = 150°
150° (π/180) = 5π/6

Answer 2

The minute hand moves
`(5\pi)/(6)` radians.

Step by step explanation:

We know that measure of complete circle is 360 degrees.

In a clock a complete circle means 60 minutes.

`60\text{ min }=360^(\circ)`

`1\text{ min }=(360)/(60)=6^(\circ)`

The minute hand move from 1:25 to 1:50, it means the minute have cover 25 minutes.

`25\text{ min }=(6* 25)^(\circ)`

`25\text{ min }=150^(\circ)`

Therefore minute hand moves 150 degree.

Multiply
`(\pi)/(180)` to convert degree into radian.

`150* (\pi)/(180)=(5\pi)/(6)`

Therefore the minute hand moves
`(5\pi)/(6)` radians.