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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.
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 degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. [4] It is not an SI unit—the SI unit of angular measure is the radian—but it is mentioned in the SI brochure as an accepted unit. [5]
The concepts of degrees, minutes, and seconds—as they relate to the measure of both angles and time—derive from Babylonian astronomy and time-keeping. Influenced by the Sumerians, the ancient Babylonians divided the Sun's perceived motion across the sky over the course of one full day into 360 degrees.
Plane angle may be defined as θ = s/r, where θ is the magnitude in radians of the subtended angle, s is circular arc length, and r is radius. One radian corresponds to the angle for which s = r, hence 1 radian = 1 m/m = 1. [33] However, rad is only to be used to express angles, not to express ratios of lengths in general. [34]
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).
Thus, in settings beyond elementary geometry, radians are regarded as the mathematically natural unit for describing angle measures. When radians (rad) are employed, the angle is given as the length of the arc of the unit circle subtended by it: the angle that subtends an arc of length 1 on the unit circle is 1 rad (≈ 57.3°), and a complete ...
Angular diameter: the angle subtended by an object. The angular diameter, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture (of ...