Quadrant (plane geometry)


The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.
The axes themselves are, in general, not part of the respective quadrants.
These are often numbered from 1st to 4th and denoted by Roman numerals: I coordinates are I, II, III, and IV. When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right quadrant.

Mnemonic

In the above graphic, the words in quotation marks are a mnemonic for remembering which three trigonometric functions are positive in each quadrant. The expression reads "All Science Teachers Crazy" and proceeding counterclockwise from the upper right quadrant, we see that "All" functions are positive in quadrant I, "Science" is positive in quadrant II, "Teachers" is positive in quadrant III, and "Crazy" is positive in quadrant IV. There are several variants of this mnemonic.