Question

Tammy is at the dentist's office waiting on her appointment. She notices that the 6-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 1:20 to 1:55? (Hint: Find the number of degrees per minute first.)
Part 2: How far does the tip of the minute hand travel during that time?

You must show all of your work.

Answer 1

@Hero I have the first answer but I need help on the second part

Answer 2

Just so we're on the same page, what did you get for the first part?

Answer 3

@Kabbed

Answer 4

sorry I thought i had the answer for part 1 but im still figuring it out

Answer 5

Okay, would you like me to help you out with it?

Answer 6

@Kabbed

Answer 7

So the first step is to determine how many degrees there are per minute. To do this, divide the degrees in a circle by the number of minutes in an hour since one hour represents one revolution of the minute hand. In other words compute 360/60 = 6. So one minute is 6 degrees. Next, figure out how many minutes has transpired from 1:20 to 1:55. You are correct that it is 35 minutes. The angle between 1:20 and 1:55 can be found by multiplying 6 times 35 to get 210 degrees. Next convert the degrees to radians by multiplying 210 by \(\pi/180\). Finally, use the formula \(s = r\theta\) to find the the distance, \(s\), the minute hand moved. Remember \(r\) is the length of the minute hand.

Answer 8

s = 6θ

Answer 9

Looks good so far. By the way, when you find \(\theta\) it is standard to find the fractional expression, not the decimal expression.

Answer 10

You can convert to decimal at the very end of your computation.

Answer 11

what

Answer 12

Have you attempted to find \(\theta\) yet? If so, post your work here.

Answer 13

how do I find it

Answer 14

You have to multiply the number of degrees between A (the minute hand at 1:20 ) to B (the minute hand at 1:55) by the conversion factor \(\pi/180\) to get \(\theta\)

Answer 15

s = 60

Answer 16

what is the symbol called

Answer 17

How did you get "60" for s? explain

Answer 18

0 is the symbol but I can't write the symbol down

Answer 19

were trying to convert 3.6 radians to degrees

Answer 20

3.6 * 180/pi

Answer 21

\(\theta = 210 \times \dfrac{\pi}{180} = \dfrac{7 \pi}{6}\)

\(s = r\theta = 6 \times \dfrac{7\pi}{6} = 7\pi\) now convert \(7\pi\) to decimal to get the approximate answer in inches.

Answer 22

how do you convert

Answer 23

with a calculator. Do you have one?

Answer 24

yes okay

Answer 25

Usually you would use 3.14 for pi if necessary

Answer 26

21.991

Answer 27

Finally

Answer 28

i thought 210 * 180/pi was going to convert the degrees to radians but then it became 7pi/6 somehow or is 6 the radians

Answer 29

The 21.99 approximates to an exact number

Answer 30

so the tip of the minute hand travels 21.99 inches

Answer 31

\(\dfrac{7\pi}{6}\) is the radian value of \(210^{\circ}\)

Answer 32

okay

Answer 33

21.99 can be approximated to an exact whole number value

Answer 34

how does s = rtheta = 6 * 7pi/6 happen

Answer 35

oh wait nevermind

Answer 36

1:20 to 1:55 in degrees is 210 right

Answer 37

Yes, but you still have not acknowledged my very last comment.

Answer 38

so the answer is the exact whole number value

Answer 39

I would round to the whole number. Do you know what that is?

Answer 40

So the answer is 21

Answer 41

No, it rounds UP to the next whole number.

Answer 42

You've never rounded up before?

Answer 43

22

Answer 44

Yes. Unless it says to approximate the answer to two decimal places, I would just put the whole number as the answer. "22 inches" to be specific. Always include units.