Can you check my work ?

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.)

my part one:
(360degrees/60minutes = 6 degrees per minute.)
1: 25 to 1: 50 is 25 minutes. 25 x 6 = 150.
150pi/180 = 5pi/6,

Your answer is correct. Indeed:

- In order to find the degrees per minute, you have to divide the full rotation angle (which is 360deg) by the number of minutes (which is 60):
360deg ÷ 60min = 6 deg/min

- In order to find how many minutes have passed, you subtract the times:
1h50m - 1h25m = 0h25m

- You then find how many degrees correspond to 25minutes:
6 deg/min × 25 min = 150deg

- Lastly, you transform degrees into radiants, through the proportion:
deg : 180 = rad : π
Therefore,
150 : 180 = rad : π
rad = (150×π)/180 = 5π/6