Question

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

Answer 1

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? `pi/12`

The negative y-axis is at `-pi/2`, or rotated `pi/2=90^o` in the negative, clockwise, downward direction. `pi/12 < 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.