In mathematics and physics, radian is the unit of measurement of angle. It is a unit derived from the international system of units, abbreviated as rad. Definition: an arc whose arc length is equal to the radius and whose central angle is 1 radian. (that is, two rays shoot from the center of the circle to the circumference, forming an arc with an angle opposite to the angle. When the arc length is exactly equal to the radius of the circle, the radian of the included angle between two rays is 1).

According to the definition, the number of radians in a week is 2πr/r=2π, and the 360-degree angle is 2π radians. Therefore, the radian of 1 is about 57.3, the approximate value is 0.0 1745 radian, the fillet is 2π radian, and the flat angle (that is, 180 degree angle) is π radian.

In the concrete calculation, when the angle is given in radians, the radian unit is usually not written, but the numerical value is written directly. The most typical example is trigonometric function, such as sin 8π, tan (3π/2).

Extended data

In junior high school mathematics, we learned the formula of arc length:

Arc length =nπr/ 180, where n is the number of angles, that is, the arc length corresponding to the central angle n.

But if we use radians, the above formula will become simpler: (note that radians are positive and negative)

L=|α| r, that is, the product of the size and radius of α.

Similarly, we can simplify the sector area formula:

S = | α| r 2/2 (the product of the size of α angle and the square of radius, from which we can see that when |α|=2π, that is, the fillet, the formula becomes S = π r 2, the formula of circular area! )

In the scientific calculation method of calculator program attached to Windows operating system (starting from the lower left corner of computer → program → attachment → calculator), radian can be called for calculation.