设α是第二象限角,sinα=3÷5,求sin(37兀÷6-2α)的值
问题描述:
设α是第二象限角,sinα=3÷5,求sin(37兀÷6-2α)的值
答
∵α是第二象限角,sinα=3/5∴cosα=-√[1-(sinα)^2]=-4/5故sin(37π/6-2α)=sin(6π+π/6-2α)=sin(π/6-2α)=sin(π/6)cos(2α)-cos(π/6)sin(2α)=(1/2)((cosα)^2-(sinα)^2)-(√3/2)(2sinαcosα)=(1/2)((-4/5...