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A circle with an equilateral chord (red). One sixtieth of this arc is a degree. Six such chords complete the circle. [6] The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year.
A great circle transforms to another great circle under rotations, leaving always a diameter of the sphere in its original position. Figure 2 : A rotation represented by an Euler axis and angle. In three dimensions, angular displacement is an entity with a direction and a magnitude.
The angle expressed by another angular unit may then be obtained by multiplying the angle by a suitable conversion constant of the form k / 2 π , where k is the measure of a complete turn expressed in the chosen unit (for example, k = 360° for degrees or 400 grad for gradians):
A standard Brunton compass, used commonly by geologists and surveyors to obtain a bearing in the field. 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:
An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to a full turn, or approximately 6.28 radians, which is expressed here using the Greek letter tau (τ). Some special angles in radians, stated in terms of 𝜏. A comparison of angles expressed in degrees and radians.
The unit for radial distance is usually determined by the context, as occurs in applications of the 'unit sphere', see applications. When the system is used to designate physical three-space, it is customary to assign positive to azimuth angles measured in the counterclockwise sense from the reference direction on the reference plane—as seen ...
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A standard Brunton Geo compass, commonly used by geologists and surveyors to measure azimuth The cartographical azimuth or grid azimuth (in decimal degrees) can be calculated when the coordinates of 2 points are known in a flat plane ( cartographical coordinates ):