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Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
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.
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 turn (360°) is an angle of 2 π (≈ 6.28) rad.
The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
Unit Value Symbol Abbreviations In radians, approx. Degree 1 / 360 turn ° Degree: deg: 17.453 2925 mrad: Arcminute 1 / 60 degree ′ Prime: arcmin, amin, am, MOA: 290.888 2087 μrad: Arcsecond 1 / 60 arcminute = 1 / 3600 degree ″ Double prime: arcsec, asec, as: 4.848 1368 μrad: Milliarcsecond 0.001 arcsecond ...
Convert that point back to polar coordinates. The angle is a reasonable mean of the input angles. The resulting radius will be 1 if all angles are equal. If the angles are uniformly distributed on the circle, then the resulting radius will be 0, and there is no circular mean.
A related unit of angular measure equal to 1 ⁄ 256 of a circle, represented by 8 bits, has found some use in machinery control where fine precision is not required, most notably crankshaft and camshaft position in internal combustion engine controllers, and in video game programming. There is no consensus as to its name, but it has been ...
The magnitude of an object's solid angle in steradians is equal to the area of the segment of a unit sphere, centered at the apex, that the object covers. Giving the area of a segment of a unit sphere in steradians is analogous to giving the length of an arc of a unit circle in radians. Just as the magnitude of a plane angle in radians at the ...