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?
Part 3: How many radians on the unit circle would the minute hand travel from 0° if it were to move 5π inches?
Part 4: What is the coordinate point associated with this radian measure?

Answer 1

@satellite73 you have some time to help me answer these four parts? :/

Answer 2

@campbell_st

Answer 3

well 60 minutes = 2 pi radians on the clockface

so

1 minute = 2pi/60 radians

then 1:20 to 1:55 = 35 mins

35 minutes = 35 * 2pi/60

Answer 4

(b) the arc length is

\[l = r \theta\]

you have theta from the previous part and the minute hand is 6 inches... so r = 6

Answer 5

(C) you will have to use arc length again

\[5\pi = 6 \times \theta\]

find theta

this will give the angle in radian

hope it helps

Answer 6

by c you mean 3?

Answer 7

how do i find theta?

Answer 8

yep

Answer 9

and divide both sides of the equation by 6

Answer 10

theta=5pi/6

Answer 11

yes

Answer 12

for #2 how do i find what there asking for? l=6*theta

Answer 13

how to find the lenght?

Answer 14

well 1 minute = 2pi/60

so the 35 minutes through with the minute hand travels form and angle

35*2pi/60 or 7pi/6

thats the value of theta

Answer 15

so.l=6*7pi/6?

Answer 16

yes

Answer 17

can that be simplified?

Answer 18

well there is an obvious common factor to cancel

Answer 19

l=7pi?

Answer 20

yes

Answer 21

thank you for being patient... would that answer #2

Answer 22

its is

Answer 23

ok going back to question one..35*2pi/60=219.8?

Answer 24

no... leave the answer in terms of pi....

you are working in radian

its

\[\frac{35 \times 2\pi}{60}\]

simplify it

Answer 25

can we simplify 7*2pi/12 ?

Answer 26

sure its 14pi/12 they are both even...

Answer 27

7pi/6 then?

Answer 28

now we have answered #1 and 2

Answer 29

yes

Answer 30

if you go back and read the posts you have the answers to 1, 2, and 3

Answer 31

yes i meant 3 also :) so how will we find #4

Answer 32

just pick up a calculator adnd find the values of x and y