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Binary angular measurement (BAM) [1] (and the binary angular measurement system, BAMS [2]) is a measure of angles using binary numbers and fixed-point arithmetic, in which a full turn is represented by the value 1. The unit of angular measure used in those methods may be called binary radian (brad) or binary degree.
One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.
Left: An angle of 1 radian (marked green, approximately 57.3°) corresponds to an angle where the length of the arc (blue) is equal to the radius of the circle (red). Right: A milliradian corresponds to 1 / 1000 of the angle of a radian. (The image on the right is exaggerated for illustration, as a milliradian is much smaller in reality).
In astronomy, the angular size or angle subtended by the image of a distant object is often only a few arcseconds (denoted by the symbol ″), so it is well suited to the small angle approximation. [6] The linear size (D) is related to the angular size (X) and the distance from the observer (d) by the simple formula:
The point from which the object is viewed is called the apex of the solid angle, and the object is said to subtend its solid angle at that point. In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr), which is equal to one square radian, sr = rad 2.
In trigonometry, the gradian – also known as the gon (from Ancient Greek γωνία (gōnía) ' angle '), grad, or grade [1] – is a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees.
A chart to convert between degrees and radians. In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more "natural" properties when their arguments are expressed in radians. These ...
The three coordinates (ρ, φ, z) of a point P are defined as: The radial distance ρ is the Euclidean distance from the z-axis to the point P.; The azimuth φ is the angle between the reference direction on the chosen plane and the line from the origin to the projection of P on the plane.