# How do you determine the quadrant in which -pi/12 lies?

Q4

#### Explanation:

First off we know there are 4 quadrants and rotation starts from the positive x-axis. Positive rotation moves counter-clockwise up towards the positive y-axis and negative rotation moves clockwise down towards the negative y-axis. The diagram below shows positive rotation (negative rotation goes in the opposite direction).

We have negative rotation, so we move clockwise, downwards towards the negative y-axis.

How far do we move in that direction? $\frac{\pi}{12}$

The negative y-axis is at $- \frac{\pi}{2}$, or rotated $\frac{\pi}{2} = {90}^{o}$ in the negative, clockwise, downward direction. $\frac{\pi}{12} < \frac{\pi}{2}$ and so hasn't rotated as far as the negative y-axis - and so rotates into Q4 but not as far as Q3, and so that is where it lies - Q4.