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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]
A simple arithmetic calculator was first included with Windows 1.0. [6]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
Additionally, an angle that is a rational multiple of radians is constructible if and only if, when it is expressed as / radians, where a and b are relatively prime integers, the prime factorization of the denominator, b, is the product of some power of two and any number of distinct Fermat primes (a Fermat prime is a prime number one greater ...
Angles are computed using radians; degree values must be converted to radians by dividing by 57.2958. As an example, to calculate 25 sin (600×0.05°) one would enter C 6 E 2 + 0 0 5 × 5 7 2 9 5 8 E 1 ÷ + 2 5 E 1 × to get a result of 1.2500 01 (representing 12.5 which is equal to 25 sin(30°) ).
Elevation is 90 degrees (= π / 2 radians) minus inclination. Thus, if the inclination is 60 degrees (= π / 3 radians), then the elevation is 30 degrees (= π / 6 radians). In linear algebra, the vector from the origin O to the point P is often called the position vector of P.
In degrees Description radian: 2π: ≈57°17′ The radian is determined by the circumference of a circle that is equal in length to the radius of the circle (n = 2 π = 6.283...). It is the angle subtended by an arc of a circle that has the same length as the circle's radius. The symbol for radian is rad.