SOLUTION: Im not to sure if you can help as this is a Pre Calc/Trig question but my father highly recommended this site and this is the first time I've not been able to understand something

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Question 338589: Im not to sure if you can help as this is a Pre Calc/Trig question but my father highly recommended this site and this is the first time I've not been able to understand something in my class.
We are currently studying unit circles, and trigonometry of real numbers. The one thing I seem to be having a problem with is understanding how they figure out which quadrant a terminal angle lands in. For instance...
Angle Theta = 5(pie)/6
The reference of Angle Theta is (pie/6)
I understand that the associated point of this Angle is (square root of three/2, 1/2) but this is a generic point and has no reference to where the terminal angle lands...
so how is it known that the Angle Terminates in Quadrant II?
Thank you for your time!
Aaron
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

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Angles are measured counterclockwise starting at the positive x-axis.
The point associated with %285%2Api%29%2F6 is (-sqrt%283%29%2F2,1%2F2)
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The quadrants are divided by the x and y axes.
The positive x-axis is 0,2%2Api radians (0,360 degrees).
The positive y-axis is pi%2F2 radians (90 degrees).
The negative x-axis is pi radians (180 degrees).
The negative x-axis is %283%2Api%29%2F2 radians (270 degrees).
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So then the quadrant contain the angles in between those values,
Quadrant I : 0%3Ctheta%3Cpi%2F2 radians, 0%3Ctheta%3C90 degrees
Quadrant II : pi%2F2%3Ctheta%3Cpi radians, 90%3Ctheta%3C180 degrees
Quadrant III : pi%3Ctheta%3C%283%2Api%29%2F2 radians, 180%3Ctheta%3C270 degrees
Quadrant IV : %283%2Api%29%2F2%3Ctheta%3C2%2Api radians, 270%3Ctheta%3C360 degrees
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Since theta=%285%2Api%29%2F6 is between pi%2F2 and pi, it lands in the second quadrant.