圆心角公式
圆是一个圆形图形，其边界与其中心点等距。圆心到边界的距离称为圆的半径。圆的两个半径所成的角称为圆心角。圆完成了 360° 的角度。圆心角的值介于 0 到 360° 之间。以弧度表示，圆心角的值介于 0 和 2π 之间。
圆心角公式
如果圆上的两点正好相对，则形成180°的内角。否则，形成的角度始终小于 180° 或 π 弧度。一个半圆对着 180° 的最大角度。类似地，四边形圆对向最大角度 90°。
小于180°的角称为凸角，大于180°的角称为反角。中心角 theta 的示例如下所示：
O是圆的中心点，AB是圆弧。
圆心角的计算公式如下：
Length of arc = 2πr × (θ/360)
θ = 360L/2πr
Where,
r is the radius of the circle
Theta is the angle in degrees.
L = Arc length
Or
L = r θ
θ = L/r
Where,
r is the radius of the circle
Theta is the angle in radians.
L = Arc length
示例问题
问题1：求半径为5m，弧长为8m的圆的圆心角，单位为弧度。
解决方案：
The formula to calculate the central angle in radians is given by:
θ = L/r
Where,
L is the arc length
r is the radius
L = 8m
r = 5m
θ = 8/5 = 1.6 radians
Thus, the central angle of the circle of radius 5m and arc length of 8m is 1.6 radians.
问题2：求半径为2m、弧长为4m的圆的圆心角。
解决方案：
The formula to calculate the central angle in degrees is given by:
θ = 360L/2πr
Where,
L is the arc length
r is the radius
L = 4m
r = 2m
θ = 360 × 4/ (2 × 3.1415 × 2)
(π = 3.1415)
θ = 114.6°
Thus, the central angle of the circle of radius 2m and arc length of 4m is 114.6°.
问题3：求半径为6m、弧长为18m的圆的圆心角，单位为弧度。
解决方案：
The formula to calculate the central angle in radians is given by:
θ = L/r
where,
L is the arc length
r is the radius
L = 18m
r = 6m
θ = 18/6 = 3 radians
Thus, the central angle of the circle of radius 6m and arc length of 18m is 3 radians.
问题4：求半径10cm、弧长30cm的圆的圆心角。
解决方案：
The formula to calculate the central angle in degrees is given by:
θ = 360L/2πr
where,
L is the arc length
r is the radius
L = 30cm
r = 10cm
θ = 360 × 30/ (2 × 3.1415 × 10)
(π = 3.1415)
θ = 171.9°
Thus, the central angle of the circle of radius 10cm and arc length of 30cm is 171.9°.
问题5：求半径为7m、弧长为280cm的圆的圆心角，单位为弧度。
解决方案：
The formula to calculate the central angle in radians is given by:
θ = L/r
Where,
L is the arc length
r is the radius
L = 280cm
r = 7m
Both the dimensions are in different units. We need to first convert the dimensions into the same unit.
L = 2.8m
(1m = 100cm)
r = 7m
θ = 2.8/7 = 0.4 radians
Or
L = 280cm
r = 7m = 700cm
(1m = 100cm)
θ = 280/700 = 0.4 radians
Thus, the central angle of the circle of radius 7m and arc length of 280cm is 0.4 radians.