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Even with these restrictions, if the polar angle (inclination) is 0° or 180°—elevation is −90° or +90°—then the azimuth angle is arbitrary; and if r is zero, both azimuth and polar angles are arbitrary. To define the coordinates as unique, the user can assert the convention that (in these cases) the arbitrary coordinates are set to zero.
The azimuth is the angle formed between a reference direction (in this example north) and a line from the observer to a point of interest projected on the same plane as the reference direction orthogonal to the zenith. An azimuth (/ ˈ æ z ə m ə θ / ⓘ; from Arabic: اَلسُّمُوت, romanized: as-sumūt, lit.
Azimuth is measured eastward from the north point (sometimes from the south point) of the horizon; altitude is the angle above the horizon. 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.
The bearing angle value will always be less than 90 degrees. [1] For example, if Point B is located exactly southeast of Point A, the bearing from Point A to Point B is "S 45° E". [ 3 ] For example, if the bearing between Point A and Point B is S 45° E, the azimuth between Point A and Point B is 135°.
The solar azimuth angle is the azimuth (horizontal angle with respect to north) of the Sun's position. [1] [2] [3] This horizontal coordinate defines the Sun's relative direction along the local horizon, whereas the solar zenith angle (or its complementary angle solar elevation) defines the Sun's apparent altitude.
Euler angles, normally in the Tait–Bryan convention, are also used in robotics for speaking about the degrees of freedom of a wrist. They are also used in electronic stability control in a similar way. Gun fire control systems require corrections to gun-order angles (bearing and elevation) to compensate for deck tilt (pitch and roll).
It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane. [1] [2] At solar noon, the zenith angle is at a minimum and is equal to latitude minus solar declination angle. This is the basis by which ancient mariners navigated the oceans. [3]
The problem was the lack of an azimuth instrument to enable it; clinometers for elevation already existed. The Germans solved this problem by inventing the lining-plane in about 1890. This was a gun-mounted rotatable open sight, mounted in alignment with the bore, and able to measure large angles from it.