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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
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
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...
: I (where the signs of the (''x''; ''y'') 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 ("northeast") quadrant.
Mnemonic
In the above graphic, the words in quotation marks are amnemonic
A mnemonic device ( ), memory trick or memory device is any learning technique that aids information retention or retrieval in the human memory, often by associating the information with something that is easier to remember.
It makes use of e ...
for remembering which three trigonometric functions (sine, cosine, tangent and their reciprocals) 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" (for sine) is positive in quadrant II, "Teachers" (for tangent) is positive in quadrant III, and "Crazy" (for cosine) is positive in quadrant IV. There are several variants of this mnemonic.
See also
* Half-plane * Orthant * Octant (solid geometry) * Ray (geometry)External links
* * {{PlanetMath, urlname=quadrant, title=Quadrant Euclidean plane geometry