10 angle system
It is stipulated that the 360th point of a fillet is an angle of 1 degree, and the unit system for measuring angles in degrees is called angular system. Note that "degree" is a unit, not "1 degree", because the definition of unit is the name of the standard quantity to measure things.
Under this definition, the degree of fillet is 360, the angle is180 and the right angle is 90.
In the angle system, 1 = 60',1'= 60 ",1'=( 1/60),1"= (1/60)'.
The angle system is an example of using the hexadecimal system.
Two angles are added, 0 and 0 are added,' and' are added,' and' are added, where if it exceeds 60, enter 1.
When two angles are subtracted, negative 0 and negative 0, negative 0 and negative 0, where 1 of the previous unit is taken as 60 if it is not enough.
2 arc system
The central angle whose arc length is equal to the radius is called 1 radian, and recorded as 1 radian.
A=l/r, (l is arc length and r is radius)
180 = π rad。
1 degree =π/180 radians
30 degrees is converted into radian value: radian =30*π/180.
Interchange between angle system and circular arc system
180 =π radian
1 degree =π/180 radians
1 radian ≈ 57 18'
The difference between two kinds of angle systems
Usually, a protractor is used as a measuring tool when measuring angles, which is inconvenient due to the limitation of shape and size. Curvature system can use scale and compass instead of protractor to measure angle. This method is simple to operate, and the measurement accuracy can meet the engineering requirements, so it has practical value. The essence of radian system is to unify the units for measuring arc and radius, which greatly simplifies the related formulas and operations. Because the ratio of arc length to radian radius is a real number, it can establish a one-to-one relationship with real numbers, and its advantages are particularly obvious in the study of functions, especially in advanced mathematics.