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.

Answer 1

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.)
Part 2: How far does the tip of the minute hand travel during that time?
Part 3: How many radians on the unit circle would the minute hand travel from 0° if it were to move 5π inches?
Part 4: What is the coordinate point associated with this radian measure?

Answer 2

@Hero @phi @jim_thompson5910 @wio

Answer 3

Part 1:
Degrees per minute = 360 degrees/60 minutes = 6 degrees/min.
From 1:25 to 1:50, 25 minutes has passed, so the minute hand has moved 25*6 = 150 degrees or 150*pi/180 = 5pi/6 radians.

Part 2:
Total distance the tip of minute hand has traveled in this time = 2pi*(4 in) * (5pi/6)/(2pi) = 10pi/3 inches.

Part 3:
2pi * (x/2pi) = 5pi
x = 5pi radians

Part 4:
Coordinate point is (-1, 0).

Answer 4

Thanks