Which angle is pi over 5



unit
standard SI system of units
Unit name Radians
Unit symbol wheel
Described size (s) flat angle, angle of rotation
Size symbol (s) α, β, γ, ...1)
Dimension name 1 (dimensionless)
In SI units
See also:Degree, full angle, gon, line, hour, percent
Note 1) all small Greek letters except π
(Pi is a given value, the circle number Pi)

The Radians (Unit symbol: wheel) is an auxiliary unit of measurement that indicates that the above dimension is to be understood as an indication of the size of a flat angle in radians.

The flat angle of 1 radian encloses an arc 1 meter long on the circumference of a circle with a 1 meter radius. The full angle is 2π radians: 1 full angle = 2 π radians.

Note due to possible risk of confusion: Until December 31, 1977, the wheel with the unit symbol rd was the legal unit of energy and equivalent dose in Germany; 1 rd = 1 cGy = 1 cJ / kg.

Radians in SI

In the International System of Units (SI) is Radians the special name for the dimensionless, coherent, derived SI unit m / m. Because of these properties, it can simply be replaced by 1 in calculations, i.e. H. 1 rad = 1. It can also be combined with the SI prefixes, e.g. B. as Milliradian (mrad)[1]. The unnecessary but deliberate addition of the unit symbol rad in size values ​​can be used in some cases to indicate which physical quantity is meant without specifying it by name.

Example:

size unit
job Nm
Torque Nm / rad

The formula shows the difference between these quantities: Work = torque * (turned) angle. With a magnitude of 5.25 Nmrad-1 then apparently a torque, but no work is meant.

Conversion between radians and degrees

The full angle is 2π radians or 360 degrees; therefore the following applies:

or:

So the factor for converting between radians and degrees is

Examples:

Frequently required values ​​can be found in the following table:

Conversion between radians and other angular dimensions

To do this, replace the number "360" in the above formulas with the corresponding number of the full angle in the other angle, and the number "180" with half the full angle. So instead then or. or. .

Calculator and computer

Scientific pocket calculators calculate trigonometric functions either in radians or in degrees, sometimes also in gons. The mode for calculating in radians is marked with "RAD" on most pocket calculators.

In mathematical libraries for programming languages, the trigonometric functions always use radians. In order to obtain degrees, the above conversion formulas must be used.

Historical

In the SI it was initially left open whether radians and steradian are derived units or base units; the class of “complementary units” was created for both. In 1980 the CIPM recommended that these supplementary units be interpreted as derived. This was followed in 1995 by the 20th CGPM and resolved in resolution 8 to abolish the class of supplementary units.

See also

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  1. BIPM - SI Brochure, 8th Edition, March 2006, Section 2.2.2, Table 3: Coherent derived SI units with special names and symbols. [1]

Categories: Unit of Measure | SI unit