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[18] [19] Today, the degree, 1 / 360 of a turn, or the mathematically more convenient radian, 1 / 2 π of a turn (used in the SI system of units) is generally used instead. In the 1970s – 1990s, most scientific calculators offered the gon (gradian), as well as radians and degrees, for their trigonometric functions . [ 23 ]
≡ 1 ⁄ 400 of a revolution ≡ π ⁄ 200 rad ≡ 0.9° ≈ 15.707 963 × 10 −3 rad: octant: ≡ 45° ≈ 0.785 398 rad: quadrant: ≡ 90° ≈ 1.570 796 rad: radian (SI unit) rad The angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. One full revolution encompasses 2π radians. = 1 rad ...
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 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]
Date/Time Thumbnail Dimensions User Comment; current: 00:15, 9 February 2009: 700 × 700 (188 KB): Inductiveload {{Information |Description={{en|1=A chart for the conversion between degrees and radians, along with the signs of the major trigonometric functions in each quadrant.}} |Source=Own work by uploader |Author=Inductiveload |Date=2009/02
provided the angle is measured in radians. Angles measured in degrees must first be converted to radians by multiplying them by / . These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science.
English: A chart showing the relationships between pi, tau, and radians with a circle. Shows the conversion between degrees and radians, along with the signs of the major trigonometric functions in each quadrant.
A similar calculation using the area of a circular sector θ = 2A/r 2 gives 1 radian as 1 m 2 /m 2 = 1. [35] 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. [36] It is a long-established practice in mathematics and across all areas of science to make use of rad ...