Question

How can I find the angular position in radians of the minute hand of a clock at 5:00, 7:15, an 3:35?

Answer 1

Where is 0 radians, when the minute hand is pointing to 12?

Answer 2

anjulyn ,you can find angular position of minute hand with respect to any position i.e this refrence will have in your mind as jamesj said you that calculate angular position with respect to 12.it is right but it may be any 1,2,3.....12.that must be mention in your question if it is not mention then assume it 12.If it moves one minute from 12 its angular position will be 6/2pi radian...and calculate angular position which is given in your question using this concept ...

Answer 3

Ok. How did you figure the angular position as 6/2pi?

Answer 4

If the minute hand moves 1 minute, then it has moved 1/60th of a complete revolution.

As one complete revolution is 2pi radians, a one minute move is
\[ \frac{2\pi}{60} = \frac{\pi}{30} \ radians \]

Answer 5

So where is the minute hand at 7:15, at what angle?

Answer 6

Intuitively, it is a right-angle. How many radians is a right angle?

Answer 7

Because of minute hand covers 360 degree i.e 2pi radian in one rotation i.e in 60 minute .then in one minute pi/30.i am sorry for this mistake...give your one question and i am solving it by using following method..
(1)for example 5 i.e 25 minutes with respect to 12.and multiply 25 minutes in pi/30 i.e 5pi/6 is angular position with respect ton 12.

Answer 8

I know that a right angle is 90 degrees, let met covert to radians

Answer 9

90 degrees/pi= 28 radians. James, that's not correct is it?

Answer 10

since 360 degree is equal to 2pi radian.then one degree is equal to 2pi/360 rad.and for your 90 degree multiply it in 2pi/360=>90*2pi/360=pi/2...

Answer 11

No. 2 pi radians = 360 degrees
Hence
pi radians = 180 degrees
pi/2 radians = 90 degrees

Answer 12

So at 7:15 we expect the minute hand to be at angle to the vertical of pi/2 radians.

Answer 13

Now show that that results, pi/2 radians, is consistent with the fact that every minute is
pi/30 radians.

Answer 14

i think now that you can calculate other angular positions which is in your questions

Answer 15

SO James would I multiply 15minutes x pi/30 radians?

Answer 16

Yes

Answer 17

Ok, so my answer would be pi/2?

Answer 18

For what?

Answer 19

7:15

Answer 20

for 7:15, yes? pi/2. You've now shown it two ways.

Answer 21

Ok, but the answer in the back of my book says theta is equal to 0. Is pi/2 equal to 0?

Answer 22

This is why I asked you right at the beginning: where are measuring angles from? Are you measuring them from the vertical line when the minute hand points at 12?

Or are you measuring them from where the minute hand points at 3? (15 minutes)

What does the book say the answer is for the angle at 5:00? Is it 0 or something else?

Answer 23

It says pi/2

Answer 24

Ok, so you're measuring angle from the horizontal, when the minute hand points to 3.

Then yes, indeed, when the minute hand points to 12, for example at 7:00, the angle is a right angle. And hence the the answer for 5:00 is pi/2.

For 7:15, the minute hand lies right along the axis we are using to measure angle, so the answer is 0

Now you figure out 3:35

Answer 25

no oh sorry ... when it is at 5 then minute hand at 12. ie its angular position with respect to it is 0.at 7:15 its angular position is pi/2because of minute hand at 3.and at 3:35 it is at 7 i.e its angular position will be 0.7pi with respect to 12..

Answer 26

at 3:35 it will be (7/6)pi not .7pi sorry...

Answer 27

Ok. Please give me a few minutes. I have go and attend to my toddler for a moment

Answer 28

@taufique, careful. The angle now is *not* measured from the vertical. I suggest we let Anjulyn figure out this last part by themselves.

Answer 29

if refrence will be 3 then it will be 0 at 7:15 o'clock

Answer 30

Yes, read what I just wrote above!

Answer 31

Ok. If I multiply 35 times pi/30, this gives me 7pi/6. But that is not correct because my text book has a different answer.

Answer 32

No, it is not correct because we are measuring angle from the 15 minute mark, not the 0 minute mark.

Answer 33

Ok. Well James I thank you for your help. I will have to get further assistance from my Professor on Monday, but I am still not quit getting the concept. You have explained things well. However, I just need more assistance.

Answer 34

ok