# Location of negative angle on unit circle

• May 9th 2013, 06:56 PM
Unreal
Location of negative angle on unit circle
Hi!

What quadrant and location is the following angle?

$\displaystyle -\frac{11}{12}$

$\displaystyle -\frac{11}{12} = 2\pi -\frac{11\pi}{12}$

$\displaystyle \frac{13}{12} \implies$ Six and a half revolutions, stopping at $\displaystyle \pi$.

$\displaystyle \pi - \frac{\pi}{12} = \frac{11\pi}{12}$

• May 9th 2013, 07:52 PM
ibdutt
Re: Location of negative angle on unit circle
On coordinate axes remember that for angle x , 0<x<pi/2 , x is in I quadrant; pi/2<x<pi , x is in II quadrant; pi<x<3pi /2, x is in III quadrant; and 3pi/2<x<2pi , x is in IV quadrant;
Another thing we need to remember is that angle is measured positive when measure anticlockwise and negative when measured clockwise.
Even when an angle is given as negative we can change into positive, e.g., angle x = - 32/7 pi = -6pi + 10pi/7 since even multiples ( positive or negative ) of pi take the terminating line to coincide with the positive x axis we are at the starting point.
Thus we will have x = - 32/7 pi = -6pi + 10pi/7 the same as angle x = 10pi/7
It is just as simple as that
• May 9th 2013, 08:30 PM
Unreal
Re: Location of negative angle on unit circle
I'm sorry, I don't fully understand what you're saying.

For $\displaystyle -\frac{11\pi}{12}$ I changed it to a positive, $\displaystyle \frac{13\pi}{12}$.
• May 9th 2013, 09:21 PM
Prove It
Re: Location of negative angle on unit circle
Quote:

Originally Posted by Unreal
Hi!

What quadrant and location is the following angle?

$\displaystyle -\frac{11}{12}$

$\displaystyle -\frac{11}{12} = 2\pi -\frac{11\pi}{12}$

$\displaystyle \frac{13}{12} \implies$ Six and a half revolutions, stopping at $\displaystyle \pi$.

$\displaystyle \pi - \frac{\pi}{12} = \frac{11\pi}{12}$

You need to edit this post, as I expect you have left off \displaystyle \displaystyle \begin{align*} \pi \end{align*} from a few of your numbers. The \displaystyle \displaystyle \begin{align*} \pi \end{align*} is incredibly important and without it your solution would change dramatically.
• May 9th 2013, 09:25 PM
Unreal
Re: Location of negative angle on unit circle
Post edited

Quote:

Originally Posted by unreal
hi!

What quadrant and location is the following angle?

$\displaystyle -\frac{11\pi}{12}$

$\displaystyle -\frac{11\pi}{12} = 2\pi -\frac{11\pi}{12}$

$\displaystyle \frac{13\pi}{12} \implies$ six and a half revolutions, stopping at $\displaystyle \pi$.

$\displaystyle \pi - \frac{\pi}{12} = \frac{11\pi}{12}$

• May 9th 2013, 09:26 PM
Unreal
Re: Location of negative angle on unit circle
After the first response, the edit option was no longer available.

Thanks anyway.
• May 9th 2013, 09:31 PM
Prove It
Re: Location of negative angle on unit circle
A couple of things, NEVER write down that two numbers are equal when they are clearly not. \displaystyle \displaystyle \begin{align*} -\frac{11\pi}{12} \end{align*} is NOT equal to \displaystyle \displaystyle \begin{align*} 2\pi - \frac{11\pi}{12} \end{align*}. What you should be saying is that by going through a revolution of the unit circle, the point on the circle which makes an angle of \displaystyle \displaystyle \begin{align*} -\frac{11\pi}{12} \end{align*} is also made by an angle of \displaystyle \displaystyle \begin{align*} 2\pi - \frac{11\pi}{12} = \frac{13\pi}{12} \end{align*}.

I have no idea what you have done after this. \displaystyle \displaystyle \begin{align*} \frac{13\pi}{12} \end{align*} IS your angle. Notice that it is \displaystyle \displaystyle \begin{align*} \pi + \frac{\pi}{12} \end{align*}, which means it is positioned in the THIRD quadrant at an angle of \displaystyle \displaystyle \begin{align*} \frac{\pi}{12} \end{align*} below the x-axis.
• May 9th 2013, 10:35 PM
ibdutt
Re: Location of negative angle on unit circle
For - 11pi/12 i would like to change it to -2pi + 13pi/12
Thus we have the angle -11pi/12 the same as angle 13pi/12. since -2pi brings us back to the starting line.
Now 13pi/12 = pi + pi/12 that clearly indicates that the angle is in the third quadrant.