1, the definition of arc system
The radian is the unit of measurement of angle, which indicates the ratio of arc length to radius corresponding to the central angle. In the radian system, the angle corresponding to a complete circle is 2π (or 360), and the radian number corresponding to the central angle with arc length equal to radius length is 1 radian.
2. Sector area formula (arc system):
The formula of sector area (arc system) can be calculated by the following formula: sector area =0.5* radius? * radians. Where the radius is the radius length of the sector and the radian is the number of radians corresponding to the central angle.
3, radian calculation:
To calculate the area of a sector, we must first determine the size of the central angle. If the degree of central angle is given, it needs to be converted into radian system. The conversion formula is radian = (angle *π)/ 180. Where π is pi, which is approximately equal to 3. 14 159. The sector area can be calculated by substituting the radian number into the sector area formula.
4. Example calculation:
Take a sector with a radius of 5 meters and a central angle of 60 as an example. First, the degree of the central angle is converted into radian system: radian = (60 * π)/180 ≈1.047 radian. Then, substitute it into the sector area formula to calculate: sector =0.5*5? * 1.047≈ 13.09 m2.
5, the advantages of arc system:
Compared with the degree system, the arc system has more advantages in mathematical calculation. The expressions of many trigonometric functions are more concise and convenient when calculating in radians. In addition, the circular arc system is also beneficial to the research of circular motion, calculus and other mathematical fields.
To sum up, the sector area formula (radian system) is to calculate the sector area in radians. In the radian system, the angle corresponding to a complete circle is 2π, and the radian number corresponding to a central angle with arc length equal to radius length is 1 radian. The sector area can be calculated by substituting the radius length and the central angle (converted into radians) into the sector area formula.