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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 ]
Quantity Unit Remarks Name Symbol Name Symbol Definition angle, (plane angle) α, β, γ, θ, φ radian: rad: 1 rad = 1 m ⁄ m = 1 degree ° 1° = π ⁄ 180 rad There is no space between the number and these superscript-style unit symbols.
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]
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This means that the SI steradian is the number of square radians in a solid angle equal to one square radian, which of course is the number one. It is useful to distinguish between dimensionless quantities of a different kind , such as the radian (in the SI, a ratio of quantities of dimension length), so the symbol sr is used.
Mathematically, this represents an arc of angle ϕ N − ϕ S swept around a sphere by θ E − θ W radians. When longitude spans 2 π radians and latitude spans π radians, the solid angle is that of a sphere. A latitude-longitude rectangle should not be confused with the solid angle of a rectangular pyramid.
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As an example, let A be an angle whose measure is 22.50°. In Madhava's table, the entry corresponding to 22.50° is the measure in arcminutes, arcseconds and sixtieths of an arcsecond of the angle whose radian measure is the value of sin 22.50°, which is 0.3826834; multiply 0.3826834 radians by 180/ π to convert to 21.92614 degrees, which is