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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.
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to 1 / 60 of one degree. [1] Since one degree is 1 / 360 of a turn, or complete rotation, one arcminute is 1 / 21 600 of a turn.
Signed binary angle measurement. Black is traditional degrees representation, green is a BAM as a decimal number and red is hexadecimal 32-bit BAM. In this figure the 32-bit binary integers are interpreted as signed binary fixed-point values with scaling factor 2 −31, representing fractions between −1.0 (inclusive) and +1.0 (exclusive).
In degrees Description radian: 2π: ≈57°17′ 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.
The complex number z can be represented in rectangular form as = + where i is the imaginary unit, or can alternatively be written in polar form as = ( + ) and from there, by Euler's formula, [14] as = = . where e is Euler's number, and φ, expressed in radians, is the principal value of the complex number function arg applied to x + iy ...
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 binary degree, also known as the binary radian (or brad), is 1 / 256 turn. [21] The binary degree is used in computing so that an angle can be represented to the maximum possible precision in a single byte. Other measures of angle used in computing may be based on dividing one whole turn into 2 n equal parts for other values of n. [22]
Additionally, an angle that is a rational multiple of radians is constructible if and only if, when it is expressed as / radians, where a and b are relatively prime integers, the prime factorization of the denominator, b, is the product of some power of two and any number of distinct Fermat primes (a Fermat prime is a prime number one greater ...