电梯限速器动作范围:求值cos2π/9cos4π/9cos8π/9

来源:百度文库 编辑:高校问答 时间:2024/05/07 15:18:25

cos2π/9cos4π/9cos8π/9
分子分母同时乘以sin2π/9,
就行了
(8sin2π/9cos2π/9cos4π/9cos8π/9)/8sin2π/9
分子变为sin16π /9
所以为-1/8

cos2π/9cos4π/9cos8π/9=(sin2π/9*cos2π/9cos4π/9cos8π/9)/sin2π/9=((1/2)*sin4π/9*cos4π/9*cos8π/9)/sin2π/9=(1/8sin16π/9)/(sin2π/9)
因为sin16π/9=-sin2π/9

所以=g-

1/729
由于cos2π cos4π cos8π的值都为1.所以cos2π/9cos4π/9cos8π/9=1/9/9/9=1/729.

1/729