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?

Question

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?

anonymous · Answer

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

anonymous · Answer

@jim_thompson5910 ?

jim_thompson5910 · Answer

I'm getting 2pi/3 as well

jim_thompson5910 · Answer

what is the circumference of the entire circle?

anonymous · Answer

360°

jim_thompson5910 · Answer

that's the number of degrees in a full rotation

jim_thompson5910 · Answer

I want the perimeter of the circle

anonymous · Answer

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

jim_thompson5910 · Answer

formula

C = 2*pi*r

anonymous · Answer

This is the circle

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

I got 25.12

jim_thompson5910 · Answer

good

jim_thompson5910 · Answer

that's the distance around the whole circle

jim_thompson5910 · Answer

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

anonymous · Answer

Okay how would we find that?

jim_thompson5910 · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

I got 8.37 (rounded)

jim_thompson5910 · Answer

me too

jim_thompson5910 · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

sure

jim_thompson5910 · Answer

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

anonymous · Answer

Yes

jim_thompson5910 · Answer

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

anonymous · Answer

8pi/3pi?

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

so it travels 3/8 around the circle

jim_thompson5910 · Answer

3/8 of 2pi radians = ???

anonymous · Answer

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

jim_thompson5910 · Answer

that is the radian measure

anonymous · Answer

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

jim_thompson5910 · Answer

very close

jim_thompson5910 · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

yes it's points on a circle with radius 4