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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.
[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]
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 values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
One radian corresponds to the angle for which s = r, hence 1 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 radian as 1 m 2 /m 2 = 1. [30] The key fact is that the radian is a dimensionless ...
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.
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
Shows the conversion between degrees and radians, along with the signs of the major trigonometric functions in each quadrant. Date: 29 September 2011: Source: