Quadrant

In mathematics, a quadrant is one of the four sections of a rectangular coordinate plane. The quadrants are separated by the x- and y-axes and are labeled I through IV, starting in the upper right quadrant and going counterclockwise, as shown in the figure below.

Signs of the coordinates in a quadrant

The signs of coordinates of any point plotted in a particular quadrant are the same. A point cannot lie on both a quadrant and an axis. Points that lie on either axis have one coordinate that is 0, which is neither positive nor negative. The diagram below shows the signs of coordinates in different quadrants.

Example:

Determine which quadrant each of the following points are located in. A: (2, 2); B: (-3, 1); C: (-1, -2); D: (3, -4).

Point A is in quadrant I since its coordinates are (+, +).

Point B is in quadrant II since its coordinates are (-, +).

Points C is in quadrant III since its coordinates are (-, -).

Point D is in quadrant IV since its coordinates are (+, -).

Quadrants in Trigonometry

The signs of the three basic trigonometric functions, sin, cos, and tan, vary based on which quadrant they are in. The sign of each trigonometric function in each quadrant can be determined using the signs of the coordinates along with basic trigonometric relationships. The diagram below shows the signs of these functions in different quadrants.


Did you know?

The first part of the word "quadrant" is from a Latin root meaning four.

A popular name for an all-terrain vehicle (ATV) is "quad," named for its four large tires.

Other words based on the same root include: quadrilateral, quadruplets, quadrillion.