Azimuth in the context of "Origin (mathematics)"

The four cardinal directions or cardinal points are the four main compass directions: north (N), east (E), south (S), and west (W). The corresponding azimuths (clockwise horizontal angle from north) are 0°, 90°, 180°, and 270°.

The four ordinal directions or intercardinal directions are northeast (NE), southeast (SE), southwest (SW), and northwest (NW).The corresponding azimuths are 45°, 135°, 225°, and 315°.

A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat plate (the dial) and a gnomon, which casts a shadow onto the dial. As the Sun appears to move through the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The style is the time-telling edge of the gnomon, though a single point or nodus may be used. The gnomon casts a broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude.

The term sundial can refer to any device that uses the Sun's altitude or azimuth (or both) to show the time. Sundials are valued as decorative objects, metaphors, and objects of intrigue and mathematical study.

A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It typically consists of a magnetized needle or another element, such as a compass card or compass rose, that pivots to align itself with magnetic north. Other methods may be used, including gyroscopes, magnetometers, and GPS receivers.

Compasses often show angles in degrees: north corresponds to 0°, and the angles increase clockwise, so east is 90°, south is 180°, and west is 270°. These numbers allow the compass to show azimuths or bearings which are commonly stated in degrees. If local variation between magnetic north and true north is known, then direction of magnetic north also gives direction of true north.

Radar is a system that uses radio waves to determine the distance (ranging), direction (azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations and terrain. The term RADAR was coined in 1940 by the United States Navy as an acronym for "radio detection and ranging". The term radar has since entered English and other languages as an anacronym, a common noun, losing all capitalization.

A radar system consists of a transmitter producing electromagnetic waves in the radio or microwave domain, a transmitting antenna, a receiving antenna (often the same antenna is used for transmitting and receiving) and a receiver and processor to determine properties of the objects. Radio waves (pulsed or continuous) from the transmitter reflect off the objects and return to the receiver, giving information about the objects' locations and speeds. This device was developed secretly for military use by several countries in the period before and during World War II. A key development was the cavity magnetron in the United Kingdom, which allowed the creation of relatively small systems with sub-meter resolution.

A compass rose or compass star, sometimes called a wind rose or rose of the winds, is a polar diagram displaying the orientation of the cardinal directions (north, east, south, and west) and their intermediate points. It is used on compasses (including magnetic ones), maps (such as compass rose networks), or monuments. It is particularly common in navigation systems, including nautical charts, non-directional beacons (NDB), VHF omnidirectional range (VOR) systems, satellite navigation devices ("GPS").

The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and azimuth.Therefore, the horizontal coordinate system is sometimes called the az/el system, the alt/az system, or the alt-azimuth system, among others. In an altazimuth mount of a telescope, the instrument's two axes follow altitude and azimuth.

In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:

• Absolute bearing refers to the clockwise angle between the magnetic north (magnetic bearing) or true north (true bearing) and an object. For example, an object to due east would have an absolute bearing of 90 degrees. Thus, it is the same as azimuth.
• Relative bearing refers to the angle between the craft's forward direction (heading) and the location of another object. For example, an object relative bearing of 0 degrees would be immediately in front; an object relative bearing 180 degrees would be behind. Bearings can be measured in mils, points, or degrees. Thus, it is the same as an azimuth difference (modulo +/- 360 degrees).

In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are

• the point's distance from a reference point called the pole, and
• the point's direction from the pole relative to the direction of the polar axis, a ray drawn from the pole.

The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. The pole is analogous to the origin in a Cartesian coordinate system.