The central angle of an arc with a long radius is called 1 radian angle. Since the ratio of the length of an arc to the radius of a circle will not change because of the size of the circle, the radian is also a quantity that has nothing to do with the radius of the circle. When the angle is given in radians, radian units are usually not written. Another commonly used angle measurement method is the angle system. The essence of arc system is to unify the units for measuring arc and angle, which greatly simplifies the related formulas and operations, especially in advanced mathematics, and its advantages are particularly obvious.
Extended data:
According to the definition, the radian of a week is 2πr/r=2π, and the 360-degree angle is 2π radian, so the radian of 1 is about 57.3, that is, 57 17' 44.806'', and 1 is π/ 188.
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).
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 half 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! )