60-529: (Redirected from Rad ) [REDACTED] Look up rad or Appendix:Variations of "rad" in Wiktionary, the free dictionary. RAD or Rad may refer to: Arts, entertainment and media [ edit ] Rad (film) , a 1986 American sports film Rad (character) , a villain in AC Comics's "Femforce" Rad Spencer , fictional character in
120-646: A 1986 American sports film Rad (character) , a villain in AC Comics's "Femforce" Rad Spencer , fictional character in the Bionic Commando video game series Bradley "Rad" White, fictional character in the Transformers Unicron Trilogy Rad ( My-Otome ) , a fictional manga character Rad (video game) , 2019 Robot Alchemic Drive , a video game Rad (journal) , a Croatian academic journal Businesses and organisations [ edit ] Rad Aviation ,
180-506: A World Bank multidisciplinary network of researchers Rules for Archival Description , the Canadian archival descriptive standard FK Rad , a Serbian football club See also [ edit ] All pages with titles beginning with Rad Radiator , a heat exchanger Gerhard von Rad (1901–1971), German theologian Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
240-450: A World Bank multidisciplinary network of researchers Rules for Archival Description , the Canadian archival descriptive standard FK Rad , a Serbian football club See also [ edit ] All pages with titles beginning with Rad Radiator , a heat exchanger Gerhard von Rad (1901–1971), German theologian Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
300-1351: A constant η equal to 1 inverse radian (1 rad ) in a fashion similar to the introduction of the constant ε 0 . With this change the formula for the angle subtended at the center of a circle, s = rθ , is modified to become s = ηrθ , and the Taylor series for the sine of an angle θ becomes: Sin θ = sin x = x − x 3 3 ! + x 5 5 ! − x 7 7 ! + ⋯ = η θ − ( η θ ) 3 3 ! + ( η θ ) 5 5 ! − ( η θ ) 7 7 ! + ⋯ , {\displaystyle \operatorname {Sin} \theta =\sin \ x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots =\eta \theta -{\frac {(\eta \theta )^{3}}{3!}}+{\frac {(\eta \theta )^{5}}{5!}}-{\frac {(\eta \theta )^{7}}{7!}}+\cdots ,} where x = η θ = θ / rad {\displaystyle x=\eta \theta =\theta /{\text{rad}}}
360-403: A consultation with James Thomson, Muir adopted radian . The name radian was not universally adopted for some time after this. Longmans' School Trigonometry still called the radian circular measure when published in 1890. In 1893 Alexander Macfarlane wrote "the true analytical argument for the circular ratios is not the ratio of the arc to the radius, but the ratio of twice the area of
420-1193: A defunct British aircraft manufacturer RAD Group , a number of independent companies in the networking and telecommunications industry RAD Data Communications , an Israeli networking equipment manufacturer RAD Game Tools , a video game developer Reich Labour Service ( Reichsarbeitsdienst ), a paramilitary organization in Nazi Germany Rezvani Automotive Designs , American performance car manufacturer Rite Aid , New York Stock Exchange stock symbol RAD Royal Academy of Dance , British examination board for dance education and training Royal Association for Deaf people , British charity People [ edit ] Given name or nickname [ edit ] Rad Dougall (Robert Anthony Dougall, born 1951), South African racing driver Rad Hourani (born 1982), Canadian fashion designer and artist Rad Kortenhorst (Leonardus Gerardus Kortenhorst, 1886–1963), Dutch politician Rad Martinez (born 1978), American mixed martial artist Sydney Valpy Radley-Walters (1920–2015), nicknamed Rad, Canadian Army officer Rad Radford ,
480-637: A length equal to the radius of the circle, 1 = 2 π ( 1 rad 360 ∘ ) {\textstyle 1=2\pi \left({\tfrac {1{\text{ rad}}}{360^{\circ }}}\right)} . This can be further simplified to 1 = 2 π rad 360 ∘ {\textstyle 1={\tfrac {2\pi {\text{ rad}}}{360^{\circ }}}} . Multiplying both sides by 360° gives 360° = 2 π rad . The International Bureau of Weights and Measures and International Organization for Standardization specify rad as
540-1040: A number of independent companies in the networking and telecommunications industry RAD Data Communications , an Israeli networking equipment manufacturer RAD Game Tools , a video game developer Reich Labour Service ( Reichsarbeitsdienst ), a paramilitary organization in Nazi Germany Rezvani Automotive Designs , American performance car manufacturer Rite Aid , New York Stock Exchange stock symbol RAD Royal Academy of Dance , British examination board for dance education and training Royal Association for Deaf people , British charity People [ edit ] Given name or nickname [ edit ] Rad Dougall (Robert Anthony Dougall, born 1951), South African racing driver Rad Hourani (born 1982), Canadian fashion designer and artist Rad Kortenhorst (Leonardus Gerardus Kortenhorst, 1886–1963), Dutch politician Rad Martinez (born 1978), American mixed martial artist Sydney Valpy Radley-Walters (1920–2015), nicknamed Rad, Canadian Army officer Rad Radford ,
600-430: A ring name of American wrestler Louis Mucciolo Jr. (1971–1998) Surname [ edit ] Jahon Rad (born 2001), American soccer player, twin brother of Kaveh Rad Jovana Rad (born 1987), Serbian basketball player Kaveh Rad (born 2001), American soccer player, twin brother of Jahon Rad Taras Rad (born 1999), Ukrainian Paralympic cross-country skier and biathlete Places [ edit ] Rád ,
660-430: A ring name of American wrestler Louis Mucciolo Jr. (1971–1998) Surname [ edit ] Jahon Rad (born 2001), American soccer player, twin brother of Kaveh Rad Jovana Rad (born 1987), Serbian basketball player Kaveh Rad (born 2001), American soccer player, twin brother of Jahon Rad Taras Rad (born 1999), Ukrainian Paralympic cross-country skier and biathlete Places [ edit ] Rád ,
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#1732776517844720-471: A scientific instrument on board the Curiosity rover Radical of an integer , rad ( x ) , in number theory Rapid application development , a software development approach Reactive attachment disorder , an emotional disorder Reflex anal dilation , the reflexive dilation of the human anus Relative abundance distribution , a measure of biodiversity Restriction site associated DNA markers ,
780-415: A scientific instrument on board the Curiosity rover Radical of an integer , rad ( x ) , in number theory Rapid application development , a software development approach Reactive attachment disorder , an emotional disorder Reflex anal dilation , the reflexive dilation of the human anus Relative abundance distribution , a measure of biodiversity Restriction site associated DNA markers ,
840-534: A sector to the square on the radius." However, the paper was withdrawn from the published proceedings of mathematical congress held in connection with World's Columbian Exposition in Chicago (acknowledged at page 167), and privately published in his Papers on Space Analysis (1894). Macfarlane reached this idea or ratios of areas while considering the basis for hyperbolic angle which is analogously defined. As Paul Quincey et al. write, "the status of angles within
900-415: A type of genetic marker Right axis deviation , a heart condition .rad file format, for Radiance (software) Other uses [ edit ] Rad (rune) , an Anglo-Saxon rune Rade language , ISO 639-3 language code rad Radley railway station , England, station code RAD Rental Assistance Demonstration , an American federal public housing program Researchers Alliance for Development ,
960-415: A type of genetic marker Right axis deviation , a heart condition .rad file format, for Radiance (software) Other uses [ edit ] Rad (rune) , an Anglo-Saxon rune Rade language , ISO 639-3 language code rad Radley railway station , England, station code RAD Rental Assistance Demonstration , an American federal public housing program Researchers Alliance for Development ,
1020-686: A village in Pest county, Hungary Rad (village) , in Trebišov District, Slovakia Radnorshire , historic county in Wales Allegheny Regional Asset District , a special purpose unit of local government in Pennsylvania, U.S. Science and technology [ edit ] Radian , symbol rad, a unit of angle Rad (radiation unit) , a unit of absorbed radiation dose Radiation assessment detector ,
1080-417: A village in Pest county, Hungary Rad (village) , in Trebišov District, Slovakia Radnorshire , historic county in Wales Allegheny Regional Asset District , a special purpose unit of local government in Pennsylvania, U.S. Science and technology [ edit ] Radian , symbol rad, a unit of angle Rad (radiation unit) , a unit of absorbed radiation dose Radiation assessment detector ,
1140-493: Is "pedagogically unsatisfying". In 1993 the American Association of Physics Teachers Metric Committee specified that the radian should explicitly appear in quantities only when different numerical values would be obtained when other angle measures were used, such as in the quantities of angle measure (rad), angular speed (rad/s), angular acceleration (rad/s ), and torsional stiffness (N⋅m/rad), and not in
1200-430: Is a thousandth of a radian (0.001 rad), i.e. 1 rad = 10 mrad . There are 2 π × 1000 milliradians (≈ 6283.185 mrad) in a circle. So a milliradian is just under 1 / 6283 of the angle subtended by a full circle. This unit of angular measurement of a circle is in common use by telescopic sight manufacturers using (stadiametric) rangefinding in reticles . The divergence of laser beams
1260-409: Is also usually measured in milliradians. The angular mil is an approximation of the milliradian used by NATO and other military organizations in gunnery and targeting . Each angular mil represents 1 / 6400 of a circle and is 15 / 8 % or 1.875% smaller than the milliradian. For the small angles typically found in targeting work, the convenience of using
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#17327765178441320-421: Is appropriate that the arguments of the functions are treated as (dimensionless) numbers—without any reference to angles. The trigonometric functions of angles also have simple and elegant series expansions when radians are used. For example, when x is the angle expressed in radians, the Taylor series for sin x becomes: If y were the angle x but expressed in degrees, i.e. y = π x / 180 , then
1380-420: Is arc length, and r is radius. A right angle is exactly π 2 {\displaystyle {\frac {\pi }{2}}} radians. One complete revolution , expressed as an angle in radians, is the length of the circumference divided by the radius, which is 2 π r r {\displaystyle {\frac {2\pi r}{r}}} , or 2 π . Thus, 2 π radians
1440-439: Is because radians have a mathematical naturalness that leads to a more elegant formulation of some important results. Results in analysis involving trigonometric functions can be elegantly stated when the functions' arguments are expressed in radians. For example, the use of radians leads to the simple limit formula which is the basis of many other identities in mathematics, including Because of these and other properties,
1500-413: Is clear that the complete form is meant. Current SI can be considered relative to this framework as a natural unit system where the equation η = 1 is assumed to hold, or similarly, 1 rad = 1 . This radian convention allows the omission of η in mathematical formulas. Defining radian as a base unit may be useful for software, where the disadvantage of longer equations is minimal. For example,
1560-400: Is different from Wikidata All article disambiguation pages All disambiguation pages rad (Redirected from Rad ) [REDACTED] Look up rad or Appendix:Variations of "rad" in Wiktionary, the free dictionary. RAD or Rad may refer to: Arts, entertainment and media [ edit ] Rad (film) ,
1620-476: Is different from Wikidata All article disambiguation pages All disambiguation pages Radian 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
1680-496: Is equal in length to the radius. The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit , defined in the SI as 1 rad = 1 and expressed in terms of the SI base unit metre (m) as rad = m/m . Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing. One radian is defined as
1740-418: Is equal to 180 degrees as the radius of a circle to the semicircumference , this is as 1 to 3.141592653589" –, and recognized its naturalness as a unit of angular measure. In 1765, Leonhard Euler implicitly adopted the radian as a unit of angle. Specifically, Euler defined angular velocity as "The angular speed in rotational motion is the speed of that point, the distance of which from the axis of gyration
1800-413: Is equal to 360 degrees. The relation 2 π rad = 360° can be derived using the formula for arc length , ℓ arc = 2 π r ( θ 360 ∘ ) {\textstyle \ell _{\text{arc}}=2\pi r\left({\tfrac {\theta }{360^{\circ }}}\right)} . Since radian is the measure of an angle that is subtended by an arc of
1860-417: Is expressed by one." Euler was probably the first to adopt this convention, referred to as the radian convention, which gives the simple formula for angular velocity ω = v / r . As discussed in § Dimensional analysis , the radian convention has been widely adopted, while dimensionally consistent formulations require the insertion of a dimensional constant, for example ω = v /( ηr ) . Prior to
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1920-431: Is often radian per second per second (rad/s ). For the purpose of dimensional analysis , the units of angular velocity and angular acceleration are s and s respectively. Likewise, the phase angle difference of two waves can also be expressed using the radian as the unit. For example, if the phase angle difference of two waves is ( n ⋅2 π ) radians, where n is an integer, they are considered to be in phase , whilst if
1980-562: 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 = 2 A / r gives 1 radian as 1 m /m = 1. The key fact is that the radian is a dimensionless unit equal to 1 . In SI 2019, the SI radian is defined accordingly as 1 rad = 1 . It is a long-established practice in mathematics and across all areas of science to make use of rad = 1 . Giacomo Prando writes "the current state of affairs leads inevitably to ghostly appearances and disappearances of
2040-707: Is the angle corresponding to a revolution) by dividing the number of radians by 2 π . One revolution is 2 π {\displaystyle 2\pi } radians, which equals one turn , which is by definition 400 gradians (400 gons or 400 ). To convert from radians to gradians multiply by 200 g / π {\displaystyle 200^{\text{g}}/\pi } , and to convert from gradians to radians multiply by π / 200 rad {\displaystyle \pi /200{\text{ rad}}} . For example, In calculus and most other branches of mathematics beyond practical geometry , angles are measured in radians. This
2100-462: Is the angle in radians. The capitalized function Sin is the "complete" function that takes an argument with a dimension of angle and is independent of the units expressed, while sin is the traditional function on pure numbers which assumes its argument is a dimensionless number in radians. The capitalised symbol Sin {\displaystyle \operatorname {Sin} } can be denoted sin {\displaystyle \sin } if it
2160-424: The Bionic Commando video game series Bradley "Rad" White, fictional character in the Transformers Unicron Trilogy Rad ( My-Otome ) , a fictional manga character Rad (video game) , 2019 Robot Alchemic Drive , a video game Rad (journal) , a Croatian academic journal Businesses and organisations [ edit ] Rad Aviation , a defunct British aircraft manufacturer RAD Group ,
2220-1067: The Boost units library defines angle units with a plane_angle dimension, and Mathematica 's unit system similarly considers angles to have an angle dimension. As stated, one radian is equal to 180 ∘ / π {\displaystyle {180^{\circ }}/{\pi }} . Thus, to convert from radians to degrees, multiply by 180 ∘ / π {\displaystyle {180^{\circ }}/{\pi }} . For example: Conversely, to convert from degrees to radians, multiply by π / 180 rad {\displaystyle {\pi }/{180}{\text{ rad}}} . For example: 23 ∘ = 23 ⋅ π 180 rad ≈ 0.4014 rad {\displaystyle 23^{\circ }=23\cdot {\frac {\pi }{180}}{\text{ rad}}\approx 0.4014{\text{ rad}}} Radians can be converted to turns (one turn
2280-545: The International System of Units (SI) has long been a source of controversy and confusion." In 1960, the CGPM established the SI and the radian was classified as a "supplementary unit" along with the steradian . This special class was officially regarded "either as base units or as derived units", as the CGPM could not reach a decision on whether the radian was a base unit or a derived unit. Richard Nelson writes "This ambiguity [in
2340-484: The area of a circle , π r . The other option is to introduce a dimensional constant. According to Quincey this approach is "logically rigorous" compared to SI, but requires "the modification of many familiar mathematical and physical equations". A dimensional constant for angle is "rather strange" and the difficulty of modifying equations to add the dimensional constant is likely to preclude widespread use. In particular, Quincey identifies Torrens' proposal to introduce
2400-499: The radian measure is normally credited to Roger Cotes , who died in 1716. By 1722, his cousin Robert Smith had collected and published Cotes' mathematical writings in a book, Harmonia mensurarum . In a chapter of editorial comments, Smith gave what is probably the first published calculation of one radian in degrees, citing a note of Cotes that has not survived. Smith described the radian in everything but name – "Now this number
2460-405: The CGPM allowed the freedom of using them or not using them in expressions for SI derived units, on the basis that "[no formalism] exists which is at the same time coherent and convenient and in which the quantities plane angle and solid angle might be considered as base quantities" and that "[the possibility of treating the radian and steradian as SI base units] compromises the internal coherence of
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2520-525: The SI based on only seven base units". In 1995 the CGPM eliminated the class of supplementary units and defined the radian and the steradian as "dimensionless derived units, the names and symbols of which may, but need not, be used in expressions for other SI derived units, as is convenient". Mikhail Kalinin writing in 2019 has criticized the 1980 CGPM decision as "unfounded" and says that the 1995 CGPM decision used inconsistent arguments and introduced "numerous discrepancies, inconsistencies, and contradictions in
2580-422: The angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. 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, θ = s r {\displaystyle \theta ={\frac {s}{r}}} , where θ is the magnitude in radians of the subtended angle, s
2640-423: The arguments of these functions are (dimensionless, possibly complex) numbers—without any reference to physical angles at all. The radian is widely used in physics when angular measurements are required. For example, angular velocity is typically expressed in the unit radian per second (rad/s). One revolution per second corresponds to 2 π radians per second. Similarly, the unit used for angular acceleration
2700-506: The classification of the supplemental units] prompted a spirited discussion over their proper interpretation." In May 1980 the Consultative Committee for Units (CCU) considered a proposal for making radians an SI base unit, using a constant α 0 = 1 rad , but turned it down to avoid an upheaval to current practice. In October 1980 the CGPM decided that supplementary units were dimensionless derived units for which
2760-453: The curvature is negligible). Prefixes smaller than milli- are useful in measuring extremely small angles. Microradians (μrad, 10 rad ) and nanoradians (nrad, 10 rad ) are used in astronomy, and can also be used to measure the beam quality of lasers with ultra-low divergence. More common is the arc second , which is π / 648,000 rad (around 4.8481 microradians). The idea of measuring angles by
2820-435: The length of the arc was in use by mathematicians quite early. For example, al-Kashi (c. 1400) used so-called diameter parts as units, where one diameter part was 1 / 60 radian. They also used sexagesimal subunits of the diameter part. Newton in 1672 spoke of "the angular quantity of a body's circular motion", but used it only as a relative measure to develop an astronomical algorithm. The concept of
2880-536: The number 6400 in calculation outweighs the small mathematical errors it introduces. In the past, other gunnery systems have used different approximations to 1 / 2000 π ; for example Sweden used the 1 / 6300 streck and the USSR used 1 / 6000 . Being based on the milliradian, the NATO mil subtends roughly 1 m at a range of 1000 m (at such small angles,
2940-404: The phase angle difference of two waves is ( n ⋅2 π + π ) radians, with n an integer, they are considered to be in antiphase. A unit of reciprocal radian or inverse radian (rad ) is involved in derived units such as meter per radian (for angular wavelength ) or newton-metre per radian (for torsional stiffness). Metric prefixes for submultiples are used with radians. A milliradian (mrad)
3000-437: The quantities of torque (N⋅m) and angular momentum (kg⋅m /s). At least a dozen scientists between 1936 and 2022 have made proposals to treat the radian as a base unit of measurement for a base quantity (and dimension) of "plane angle". Quincey's review of proposals outlines two classes of proposal. The first option changes the unit of a radius to meters per radian, but this is incompatible with dimensional analysis for
3060-404: The radian in the dimensional analysis of physical equations". For example, an object hanging by a string from a pulley will rise or drop by y = rθ centimetres, where r is the magnitude of the radius of the pulley in centimetres and θ is the magnitude of the angle through which the pulley turns in radians. When multiplying r by θ , the unit radian does not appear in the product, nor does
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#17327765178443120-411: The series would contain messy factors involving powers of π /180: In a similar spirit, if angles are involved, mathematically important relationships between the sine and cosine functions and the exponential function (see, for example, Euler's formula ) can be elegantly stated when the functions' arguments are angles expressed in radians (and messy otherwise). More generally, in complex-number theory,
3180-439: The symbol "rad" is often omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and when degrees are meant, the degree sign ° is used. 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. However, rad
3240-429: The symbol for the radian. Alternative symbols that were in use in 1909 are (the superscript letter c, for "circular measure"), the letter r, or a superscript , but these variants are infrequently used, as they may be mistaken for a degree symbol (°) or a radius (r). Hence an angle of 1.2 radians would be written today as 1.2 rad; archaic notations include 1.2 r, 1.2 , 1.2 , or 1.2 . In mathematical writing,
3300-508: The term radian becoming widespread, the unit was commonly called circular measure of an angle. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson (brother of Lord Kelvin ) at Queen's College , Belfast . He had used the term as early as 1871, while in 1869, Thomas Muir , then of the University of St Andrews , vacillated between the terms rad , radial , and radian . In 1874, after
3360-474: The title RAD . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=RAD&oldid=1230480555 " Categories : Disambiguation pages Disambiguation pages with surname-holder lists Disambiguation pages with given-name-holder lists Place name disambiguation pages Nicknames Hidden categories: Short description
3420-474: The title RAD . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=RAD&oldid=1230480555 " Categories : Disambiguation pages Disambiguation pages with surname-holder lists Disambiguation pages with given-name-holder lists Place name disambiguation pages Nicknames Hidden categories: Short description
3480-578: The trigonometric functions appear in solutions to mathematical problems that are not obviously related to the functions' geometrical meanings (for example, the solutions to the differential equation d 2 y d x 2 = − y {\displaystyle {\tfrac {d^{2}y}{dx^{2}}}=-y} , the evaluation of the integral ∫ d x 1 + x 2 , {\displaystyle \textstyle \int {\frac {dx}{1+x^{2}}},} and so on). In all such cases, it
3540-489: The unit centimetre—because both factors are magnitudes (numbers). Similarly in the formula for the angular velocity of a rolling wheel, ω = v / r , radians appear in the units of ω but not on the right hand side. Anthony French calls this phenomenon "a perennial problem in the teaching of mechanics". Oberhofer says that the typical advice of ignoring radians during dimensional analysis and adding or removing radians in units according to convention and contextual knowledge
3600-519: The wordings of the SI". At the 2013 meeting of the CCU, Peter Mohr gave a presentation on alleged inconsistencies arising from defining the radian as a dimensionless unit rather than a base unit. CCU President Ian M. Mills declared this to be a "formidable problem" and the CCU Working Group on Angles and Dimensionless Quantities in the SI was established. The CCU met in 2021, but did not reach
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