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Currently studying trigonometric functions and the book has the quadrants labeled for (+x,+y) is quadrant I, quadrant 2 is (+x,-y), quadrant 3 is (-x,-y), and quadrant 4 is (-x,y). While I conventionally are used to and learned that quadrant I is (+x,+y) and then increment counter clockwise : quadrant II (-x,+y) ..... What is the correct label?

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1 Answer

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It's debatable which is "correct".

But, in my experience, it's more common to refer to the $(x<0, y>0)$ region as the "second" quadrant.

And I think this labeling makes sense, because angles in the $xy$ plane are usually measured in a counterclockwise direction from the $x$-axis. If you start at the $x$-axis, and travel counterclockwise, the $(x<0, y>0)$ quadrant will be the second one you encounter on your journey.

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