Question

How many radians on the unit circle would the minute hand travel from 0° if it were to move 5π inches?

Answer 1

On the unit circle, wich is a circle of radius 1, it will move 2pi inches for 2pi radians. (because the entire circle's circumference is 2pi(radius) = 2pi(1) = 2pi).

So you want 5pi inches. I think you can now complete the problem.

Answer 2

I really dont understand this question though is how the entire circle would be 2pi but they want 5pi would 5pi be smaller than 2pi? are is it saying it went around the clock multiple times?

Answer 3

you could use cross multiplication

Answer 4

Keep in mind that if a circle has a radius of 1, then the length of the entire arc of a circle, which is its circumference, will be 2pi units. If the radius is in inches, then the entire circumference of the circle will be 2pi inches.

Answer 5

Or you can recall the formula, S = r(theta),

where S = length of the arc
r = radius of the circle
theta = # of radians in the central angle

Answer 6

I guess the thing to remember is that for every \(2\pi\) radians the minute hand moves from zero degrees, it's basically back to zero.

Answer 7

@helppls123 a drawing?

Answer 8

I marked out zero degrees, and suppose the minute hand points there initially. Now for every \(2\pi\) inches it travels, it returns to that zero-degree point, aye?

Answer 9

IMa cozy up into here

Answer 10

@Skyz
You -_-

Answer 11

well.. i feel loved

Answer 12

okay so like i was saying it is like the hand went around the clock multiple times?

Answer 13

@Skyz your fans at TC await you LOL
@help123please. that's how I understand it :D
How many \(2\pi\)'s go into \(5\pi\)?

Answer 14

twice fully and half?

Answer 15

How many times fully is all that matters, and that means twice fully.
So after it runs \(2\pi\) twice, it's again at zero degrees, with \(\pi\) more radians to go.

Answer 16

so would it be 4pi?

Answer 17

or would it be 5pi?

Answer 18

No, you misunderstand...after it travels 4pi inches, it's basically travelled 0 inches, since after 4pi, it's back where it started, leaving you with pi more inches to travel.

Answer 19

If it moved 5 pi inches, it would go around the circle 2 1/2 times. Therefore it would move 5 pi radians.

Answer 20

i think my brain is going to explode. okay so it wants me to move it from 0 to 5pi right?

Answer 21

Whoops... I must have misunderstood the question -_-

--awkward--

Thanks for sorting that out Mertsj ^_^

Answer 22

Mertsj...agree.

Answer 23

It says that a point moved 5 pi inches. If the radius is 1, the circumference is 2 pi so if it moved 5 pi that is 2 1/2 times around the circle. The number of radian in 1 revolution of any circle is 2 pi radians. So in 2 1/2 revolutions it is 5 pi radians.

Answer 24

I concede. @helppls123 apologies, it was simpler than I anticipated D:

Answer 25

So the answer is 2 1/2? o-o i'm sorry i'm so confused right now and don't worry terenz this stuff is all kinds of crazy lmao

Answer 26

The answer is 5 pi

Answer 27

No, when the unit circle is concerned, every one unit = one radian
In this case, your unit is inches.

Now, a unit circle is involved, the minute hand traveled 5pi inches, and since one inch is one radian, it would have traveled 5pi radians

Answer 28

but that is littereally in the question o-o is it really that obvious?

Answer 29

That's what threw me off too :>