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

1 Answer
MathFact-orials.blogspot.com
Dec 28, 2016

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).

![mathisfun.com](useruploads.socratic.org)

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.

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