# Between 0 and 2pi? So 0 and 2pi consider?

1. Jun 16, 2009

### matttan

Hi,

I was doing trigonometry and I came across this problem when they said "between".

If they said between 0 to 2pie radians, do they include 0 and 2pie or it is 0 < x < 2pie ?

Thanks

2. Jun 16, 2009

### dx

Re: Between 0 and 2pie? So 0 and 2pie consider?

Could be either, but it's usually 0 ≤ x < 2pi.

3. Jun 16, 2009

### Gregg

Re: Between 0 and 2pie? So 0 and 2pie consider?

< is less than so no, but usually there will be a less than or equal to somewhere in there. PI PI PI PI PI. Not pie.

$\Pi \pi$

4. Jun 16, 2009

### Staff: Mentor

Re: Between 0 and 2pie? So 0 and 2pie consider?

"Between" is somewhat ambiguous, so some people will write "strictly between" to indicate that the endpoints aren't included.

5. Jun 16, 2009

### Ouabache

Re: Between 0 and 2pie? So 0 and 2pie consider?

I like pie :tongue2:

I would state your assumptions based upon the wording of the question.
For example: My solution for this problem is based on the given condition [itex]0< x < 2\pi[/tex].

If this were an exam question, I would ask the teacher/professor, to clarify their meaning.

Last edited: Jun 16, 2009
6. Jun 17, 2009

### matttan

Re: Between 0 and 2pie? So 0 and 2pie consider?

Thanks for all the reply (:

Refer: http://mathworld.wolfram.com/Between.html
" All points on a line segment excluding the endpoints lie between the endpoints. "

So I guess Between 0 and 2Pi means 0 < x < 2Pi?

Because the author is confusing me as for the 1st example, the question states between 0 and 2pi and in his solution he writes 0 < x < 2Pi. And the other qs(example 2). which also says between 0 and 2pi but he writes as 0 <= x <= 2Pi in his solution? Is the author 1st example the correct one?

Lets say if a qs states find all the possible solutions/angle for Sin x = 0 where x is between 0 and 2Pi so if example 1 came in, there will be only 1 solutions which is 1Pi as 0 and 2Pi is out of the range 0 < x < 2Pi. But is example 2 is used, then there will be 3 solutions which is 0, 1Pi and 2Pi as the range is 0 <= x <= 2Pi.

Last edited: Jun 17, 2009
7. Jun 18, 2009

### thrill3rnit3

Re: Between 0 and 2pie? So 0 and 2pie consider?

I've always thought that the word "between" meant < or > (unless it said inclusive), while "from...to" had the equal sign below the > and <.

8. Jul 10, 2009

### Ouabache

Re: Between 0 and 2pi?

You are correct, the solution depends on interpretation of the given information.
It appears your author is not consistent with the use of "between" in that context.
If you have the opportunity, I would ask your teacher to clarify this sort of ambiguity
before solving your problems. If not, then state your assumptions (as you interpret the question),
and solve the problem based on those assumptions.