Question

已知一圆内,1弧度的圆心角所对的弦长为2,则这个圆心角所对的弧长为 sin1/2是个什么东西?

Answer 1

设那1rad的角所对的弦为AB,圆心为O,则角AOB是1rad,AB=2,半径R＝OA=OB,由正弦定理OA/sin[(π-1)/2]=AB/sin1,将AB=2代入,则OA=2sin[(π－1)/2]/sin1,OA=2[sin(π/2)cos(1/2)-cos(π/2)sin(1/2)]/[2sin(1/2)cos(1/2)]=1/sin(1/2),即R=1/sin(1/2)