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Hence an angle of 1.2 radians would be written today as 1.2 rad; archaic notations could include 1.2 r, 1.2 rad, 1.2 c, or 1.2 R. In mathematical writing, 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.
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]
One SI radian corresponds to the angle expressed in radians for which s = r, hence 1 SI radian = 1 m/m = 1. [28] However, rad is only to be used to express angles, not to express ratios of lengths in general. [29] A similar calculation using the area of a circular sector θ = 2A/r 2 gives 1 SI radian as 1 m 2 /m 2 = 1. [30]
A minute of arc is π/10800 of a radian. A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol ″, [ 2 ] is 1/60 of an arcminute, 1/3600 of a degree, [ 1 ]1/1296000 of a turn, and π/648000 (about 1/206264.8) of a radian. These units originated in Babylonian astronomy as sexagesimal (base ...
square degrees. 1802 / π2 deg2. ≈ 3 282.8 deg 2. The steradian (symbol: sr) or square radian[1][2] is the unit of solid angle in the International System of Units (SI). It is used in three dimensional geometry, and is analogous to the radian, which quantifies planar angles. A solid angle in steradians, projected onto a sphere, gives the ...
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 ...
The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [1] In the table below, the label "Undefined" represents a ratio If the codomain of the trigonometric functions is taken to be the real numbers these entries ...