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  1. The quadrants are numbered counterclockwise one through four, beginning with the quadrant in which both the x- and y-coordinates are positive (usually the upper right quadrant). An instrument with an arc of 90°, used to measure the angle between a celestial object and the horizon.
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  3. Quadrant II – long-term development and strategizing The second quadrant is for items that are important without requiring immediate action. Covey points out that this quadrant should be used for long-term strategizing. Quadrant III – distractions with high urgency The third quadrant is reserved for tasks that are urgent, without being.
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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.

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Signs of the coordinates in a quadrant

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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.

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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?

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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.

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Learn about this topic in these articles:

invention by Hadley

  • In John Hadley

    …of Philadelphia, Hadley invented a quadrant (actually a double-reflecting octant) for measuring the altitude of the Sun or a star above the horizon to find geographic position at sea. His double-reflecting principle made accurate determinations of location much easier. Hadley also fixed a spirit level to the instrument so that…

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use in navigation

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Quadrantanopia Neural Pathways

  • In navigation: Latitude measurements

    …seem to have been the quadrant and the astrolabe, long known to astronomers. For both devices the reference direction was actually the vertical, rather than the horizontal, but conversion of the readings was an elementary matter. The mariner’s astrolabe, however, was less widely used than its 16th-century successor, the cross-staff,…

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