Question

一个扇形面积为2,周长为6,求该扇形圆心角的弧度数,并求相应的弓形面积

Answer 1

设半径为r,圆心角为a弧度,则弧长=ar,依题意
(1/2)ar^2=2,①
2r+ar=6.a=(6-2r)/r,②
代入①,(3-r)r=2,
r^2-3r+2=0,r=1或2.
代入②,a=4或1.
r=1,a=4时所求弓形面积=2+(1/2)sin(2π-4).
r=2,a=1时所求弓形面积=2-2sin1≈0.317.