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

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- anonymous

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

- anonymous

@jim_thompson5910 ?

- jim_thompson5910

I'm getting 2pi/3 as well

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## More answers

- jim_thompson5910

what is the circumference of the entire circle?

- anonymous

360°

- jim_thompson5910

that's the number of degrees in a full rotation

- jim_thompson5910

I want the perimeter of the circle

- anonymous

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

- jim_thompson5910

formula
C = 2*pi*r

- anonymous

This is the circle

##### 1 Attachment

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

I got 25.12

- jim_thompson5910

good

- jim_thompson5910

that's the distance around the whole circle

- jim_thompson5910

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

- anonymous

Okay how would we find that?

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

I got 8.37 (rounded)

- jim_thompson5910

me too

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

sure

- jim_thompson5910

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

- anonymous

Yes

- jim_thompson5910

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

- anonymous

8pi/3pi?

- jim_thompson5910

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

- jim_thompson5910

so it travels 3/8 around the circle

- jim_thompson5910

3/8 of 2pi radians = ???

- anonymous

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

- jim_thompson5910

that is the radian measure

- anonymous

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

- jim_thompson5910

very close

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

yes it's points on a circle with radius 4

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