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

Answer:

The minute hand moves $\frac{5\pi}{6}$ radians.

Step by step explanation:

We know that measure of complete circle is 360 degrees.

In a clock a complete circle means 60 minutes.

$60\text{ min }=360^{\circ}$

$1\text{ min }=\frac{360}{60}=6^{\circ}$

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

$25\text{ min }=(6\times 25)^{\circ}$

$25\text{ min }=150^{\circ}$

Therefore minute hand moves 150 degree.

Multiply $\frac{\pi}{180}$ to convert degree into radian.

$150\times \frac{\pi}{180}=\frac{5\pi}{6}$

Therefore the minute hand moves $\frac{5\pi}{6}$ radians.