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° if it were to move 3π inches?
Part 4: What is the coordinate point associated with this radian measure? @mathmale

Answer 1

First, woohoo, how many minutes are there in one hour?

Answer 2

60minutes

Answer 3

hello

Answer 4

Right. And how many minutes are there between 3:35 and 3:55, when we're reading time?

Answer 5

20mins

Answer 6

Right. so, the time period from 3:35 to 3:55 is what fraction of an hour?

Answer 7

uhh1/3

Answer 8

Good.
and one full circle, measured in radians, is 2pi radians.

What is 1/3 of 2pi rad?

Answer 9

idk

Answer 10

@mathmale

Answer 11

Just write\[\frac{ 2\pi }{ 3 }\], followed by the units of measurement (radians).
The time span 3:35-3:55 is represented by a central angle of 2pi/3 radians.

Answer 12

2.093333

Answer 13

summary:
1. Find the number of minutes between 3:35 and 3:55.
2. Divide that by 60 minutes to obtain the fraction of a full circle represented by that time period.
3. Multiply the resulting faction by 2pi, to obtain the number of radians represented.

You could type the answer as 2.093, or (better) leave it as 2Pi/3 radians.

Answer 14

For the next part of this problem, write out the formula for arc length in terms of the radius and the central angle.

Answer 15

thats for part one right

Answer 16

The central angle is 2pi/3; that's the answer to Part One.
We need to move on to Part Two. Can you write out the formula for arc length?

Answer 17

hold up

Answer 18

i dont know it

Answer 19

Strongly suggest that you always look up words you don't know. I did a quick Internet search for "arc length formula" and found the following:

http://www.mathsisfun.com/definitions/arc-length.html

Arc length is most often represented by the letter " s ":

s = r (theta),
where s= arc length
r = the radius of the circle
theta = the central angle (we've already found this angle; it's 2pi/3)

Answer 20

i had a question for part one we were converting degress to radians right?

Answer 21

Unfortunately, Part B does not tell you that it's "arc length" that we're looking for. Instead, it asks how far the tip of the minute hand moves (in the arc from 3:35 to 3:55).

Answer 22

so we have part 2 already?

Answer 23

To answer your question about Part A: I asked you to multiply the radian representation of one full circle (2Pi) by 1/3 (which represents 20 minutes). So we were already dealing in radians and did not have to convert from degrees to radians.

Answer 24

For the purpose of review: Type out the formula for arc length here:

Answer 25

\[\theta*4\]

Answer 26

OK. I was hoping for \[s=r*\theta\]

Answer 27

oh ok so now what do we do

Answer 28

but what you have written would be ok, so long as you include the units of measurement of the radius.

\[s=(central.\angle) * (radius)\]

Answer 29

Can you now find the arc length, s, using this formula?
Go back and obtain the central angle and the radius, using appropriate units of measurement.

Answer 30

i dont know what to putor plug in

Answer 31

20 mins is the arc but i dont know whats the radius

Answer 32

what is the central angle (theta)? Just review our discussion, above; all the info you need is there.

Regarding the radius: Look at the original question: what is the length of the clock's minute hand?

Answer 33

Review: \[s=r*\theta\] where theta is the central angle in radians (not degrees) and r is the radius of the circle in question.

What is theta?
What is the radius?

Answer 34

theta=2pi/3
radius=?

Answer 35

The length of the minute had is 4 inches; that's your radius. We want to know how far the TIP of the minute hand travels in an arc/circle as it moves from 3:35 to 3:55.

Answer 36

So theta= 2pi/3 (radians)
and r = radius = ?

Answer 37

it had to travel 20 minutes

Answer 38

radius =4

Answer 39

It was in motion for 20 minutes, but it also traced out a distance. What was that distance?
sorry to continue to be picky, but we must include units of measurement with every measurement. Thus, the radius is 4 inches.
the central angle is 2pi/3 radians.

Therefore, using \[s=r*\theta\] the arc length (the distance traveled by the tip of the minute hand) is what?

Answer 40

8.3732

Answer 41

I haven't actually tried the calculation. What I'd most like to see would look like this:

distance traveled = arc length = (radius)*(central angle) = ( ? )* ( ? )

Please fill in the blanks.

Answer 42

4*2pi/3

Answer 43

@mathmale

Answer 44

I'm not going to abandon you. If I don't respond immediately, it means either that OpenStudy is slow or down or that I had something else to do while waiting for your response.

Please label your result: arc length = distance traveled = 8Pi/3 inches.

Answer 45

Part C. Please type in the formula for arc length. (Repetition does help us learn and remember things like this.)

Answer 46

why would it be 8 pi

Answer 47

2*4=8, right?

Answer 48

yeah ok gotcha

Answer 49

Part C. Please type in the formula for arc length. (Repetition does help us learn and remember things like this.)

Answer 50

ok \[s=\theta*4\]

Answer 51

In Part C you are given the distance traveled and need to find the central angle. Please solve that arc length formula for the central angle.

Answer 52

hold the phone Math male what do i pput for part2 ?

Answer 53

@mathmale

Answer 54

You tell me. What does Part B / Part 2 ask you for?

Answer 55

so thats all i write for part 2? 4*2pi/3

Answer 56

As before, please label your answers and please include the appropriate units of measurement. In Part 2 we were supposed to do what?
Have you seen the image I just uploaded?

Answer 57

@mathmale i know im annoying soo pls jst bare and im sorry

Answer 58

distanced traveled = "20" arc length = radius *central angle

Answer 59

all of what we're discussing now we'd discussed earlier, so I'd hope you'd go back and review that material. In Part 2 we're supposed to find the distance that the tip of the minute hand travels. That's arc length. Please write your answer with a label, in simplified form, with units of measurement:

Distance traveled by tip of minute hand = S = arc length = ???

Answer 60

is 4 =arc length

Answer 61

@mathmale

Answer 62

\[s=r*\theta\] represents arc length; theta is the central angle (in radians) and r is the radius of the circle along which the tip of the minute hand travels. So, no, 4 is not the arc length. Try again. Solve s = r*theta for theta.

Answer 63

but you said earlier that its 4 inches the radius

Answer 64

Divde both sides of \[s=r*\theta\] by r, to solve for theta.

Answer 65

Yes, but you were asking me whether 4 is the arc length. (See your comment, above.)

Answer 66

4=radius and 2pi/3 = arc length

Answer 67

@mathmale

Answer 68

@mathmale you there??

Answer 69

That's a bit better: 4 inches is the radius, BUT 2pi/3 is the central angle.

Would you please copy down this formula and note what each letter represents:\[s=r*\theta\]

Answer 70

can you pls jst tell me because this has been a drag

Answer 71

I'd like for you to have something to review, because we're going over the same thing repeatedly and losing time that way.
Please define for me:

s:
r:
theta:

Answer 72

Please start taking notes, so you have something to refer to. You will need this formula s=r*theta again and again.

Answer 73

s is length
r is 4
theta is 2.093

Answer 74

the formula for arc length is \[s=r*\theta\]

If we divide both sides by r, we get a formula for theta, the central angle:\[\frac{ s }{ r }=\theta\]

This is the formula you need to answer Part 3.
In this last formula, let s=arc length = 3pi inches, and let r=radius=4 inches.
Determine theta, the central angle.

Answer 75

2.355

Answer 76

is theta

Answer 77

@mathmale

Answer 78

Yes, and that's the central angle, and the answer to Part 3.
I really do expect you to learn these formulas and to know what each letter (s, r, theta) represents.

Let's move on to Part 4.

Answer 79

You tell me, in your own words, what y ou think Part 4 calls for.

Answer 80

ok

Answer 81

its asking what point is is in this radian range? idk

Answer 82

It's asking for the coordinates of the tip of the minute hand when the central angle is 2.355 radians and the radius is 4 inches.

(2,4) is a point in cartesian coordinates; it means that x=2 and y=4.

In Part 4 we're dealing with polar coordinates, so instead of x and y, we use r (radius) and theta (central angle). What experience have you had so far with polar coordinates?

Answer 83

none

Answer 84

Please stop tagging me. I explained earlier that I will not abandon you. Many of the delays in my responses stem from OpenStudy's being overloaded and thus very slow.

How do you normally learn new material? It would be grossly unfair if you were asked to find a point in polar coordinates without having had any introduction to polar coordinates. Do you have a textbook? Is there material in your online materials about polar coordinates?

Answer 85

If, in Part 3, the central angle is (3pi/4) radians (you typed 2.355 radians), and the radius is 4 inches, then the coordinates of the point in question in Part 4 is just (4 inches, 3pi/4 rad).

Coordinates of a point in polar coordinates are (r, theta), where r= radius and theta=central angle.

Can you find this information in your textbook or in your online materials?

Answer 86

mathmale are you recieving the messages im sending you?

Answer 87

In review:

Part 1: That 20-minute time change is represented by (20/60)*2Pi radians, or 2Pi/3 rad.
Part 2:

Answer 88

Yes, I've received many of your private messages and believe I'm receiving your messages in this chat.

Answer 89

then pls reply

Answer 90

Part 1: That 20-minute time change is represented by (20/60)*2Pi radians, or 2Pi/3 rad.
Part 2: during that 20-minute interval, the tip of the minute hand travels s = r*theta inches,
or s = (4 inches)(2pi/3 rad).

Please stop tagging me. I explained earlier that I will not abandon you. Many of the delays in my responses stem from OpenStudy's being overloaded and thus very slow.

How do you normally learn new material? It would be grossly unfair if you were asked to find a point in polar coordinates without having had any introduction to polar coordinates. Do you have a textbook? Is there material in your online materials about polar coordinates?

Do you want to tackle that new problem you've posted, or do you want to finish this current problem?

Answer 91

@mathmale I would like to know how to find the coordinates.

Answer 92

@mathmale. part 4 please!