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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 topology, it is often denoted as S1 because it is a one-dimensional unit n -sphere.
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius. [2]
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.
54′. 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. [2] [3] [4] It is equivalent to 1 400 of a turn, [5] 9 10 of a degree, or ...
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]
While a radian is defined as an angle on the unit circle where the arc and radius have equal length, a milliradian is defined as the angle where the arc length is one thousandth of the radius. Therefore, when using milliradians for range estimation, the unit used for target distance needs to be thousand times as large as the unit used for ...
The turn (symbol tr or pla) is a unit of plane angle measurement equal to the angular measure subtended by a complete circle at its center. It is equal to 2 π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) [1] or to one revolution (symbol rev or r ). [2]
One radian corresponds to the angle for which s = r, hence 1 radian = 1 m/m. However, rad is only to be used to express angles, not to express ratios of lengths in general. A similar calculation using the area of a circular sector θ = 2A/r 2 gives 1 radian as 1 m 2 /m 2. The key fact is that the radian is a dimensionless unit equal to 1.