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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.
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.
The radian is determined by the circumference of a circle that is equal in length to the radius of the circle (n = 2 π = 6.283...). It is the angle subtended by an arc of a circle that has the same length as the circle's radius. The symbol for radian is rad. One turn is 2 π radians, and one radian is 180° / π , or about 57.2958 degrees.
If the angle subtended by the chord at the centre is 90°, then ℓ = r √2, where ℓ is the length of the chord, and r is the radius of the circle. If two secants are inscribed in the circle as shown at right, then the measurement of angle A is equal to one half the difference of the measurements of the enclosed arcs (⌢ and ⌢).
A half-turn may refer to: One half of a full turn, an angle measure equivalent to 180 degrees or π radians Considering only points in a plane, a half turn is equivalent to a point reflection; Pi (π), a mathematical constant representing a half-turn in radians; A U-turn: a driving maneuver used to reverse direction
For a semicircle with a diameter of a + b, the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter ...
The metric system counterpart of the MOA is the milliradian (mrad or 'mil'), being equal to 1 ⁄ 1000 of the target range, laid out on a circle that has the observer as centre and the target range as radius. The number of milliradians on a full such circle therefore always is equal to 2 × π × 1000, regardless the target range. Therefore, 1 ...
The radian is specified in the SI as a derived unit in terms of the base unit of metre as a ratio of lengths, rad:=1m/m=1, which is remarked in ISO 80000-3 as follows: "The radian is the angle between two radii of a circle that cuts off on the circumference an arc equal in length to the radius of the circle".