## anonymous one year ago Freddie is at chess practice waiting on his opponent's next move. He 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 3:35 to 3:55? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time? Part 3: How many radians on the unit circle would the minute hand travel from 0 degrees if it were to move 3pi inches? Part 4: What is the coordinate point associated with this radian measure?

1. anonymous

I got the first part I just need help on the second. The answer for the first part is 2π/3 radians

2. anonymous

@jim_thompson5910 ?

3. jim_thompson5910

I'm getting 2pi/3 as well

4. jim_thompson5910

what is the circumference of the entire circle?

5. anonymous

360°

6. jim_thompson5910

that's the number of degrees in a full rotation

7. jim_thompson5910

I want the perimeter of the circle

8. anonymous

It doesn't give one. I can only think of 360

9. jim_thompson5910

formula C = 2*pi*r

10. anonymous

This is the circle

11. jim_thompson5910

the clock's minute hand has a length of 4 so r = 4

12. jim_thompson5910

I'm talking about the minute hand's circle, not the unit circle

13. anonymous

I got 25.12

14. jim_thompson5910

good

15. jim_thompson5910

that's the distance around the whole circle

16. jim_thompson5910

but we only want a piece of that circle (from 35 min to 55 min)

17. anonymous

Okay how would we find that?

18. jim_thompson5910

how did you find 2pi/3 from the previous part?

19. anonymous

$360\div60=6$ $6\times20=120$ so 120° on the circle has 2π/3 radians

20. jim_thompson5910

good, so 120 degrees is 120/360 = 1/3 of the full circle

21. jim_thompson5910

multiply 1/3 by the circumference to get the distance just from 35 to 55

22. anonymous

I got 8.37 (rounded)

23. jim_thompson5910

me too

24. jim_thompson5910

that's the approximate distance around the circle edge from 35 to 55

25. anonymous

Okay thank you :) could you help me with part three too?

26. jim_thompson5910

sure

27. jim_thompson5910

The exact circumference is C = 2*pi*4 = 8pi agreed?

28. anonymous

Yes

29. jim_thompson5910

8pi inches is a full circle the minute hand travels 3pi inches what fraction of the circle does it travel?

30. anonymous

8pi/3pi?

31. jim_thompson5910

it's the other way around 3pi/8pi = 3/8

32. jim_thompson5910

so it travels 3/8 around the circle

33. jim_thompson5910

3/8 of 2pi radians = ???

34. anonymous

$\frac{ 2π }{ 1 }\times \frac{ 3 }{ 8 }?$ $\frac{ 6π }{ 8 }=\frac{ 3π }{ 4 }?$

35. jim_thompson5910

36. anonymous

Oh and the points would be$(\frac{ -√2 }{ 2 }, \frac{ √2 }{ 2 })$

37. jim_thompson5910

very close

38. jim_thompson5910

keep in mind that the radius is not 1 it's 4

39. anonymous

I thought we were looking for the radian measure. The next part is the points of that radian measure.

40. jim_thompson5910

yes it's points on a circle with radius 4