Question

设α是第二象限角,sinα＝3÷5,求sin（37兀÷6－2α）的值

Answer 1

∵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)^2-(3/5)^2)-(√3/2)(2(3/5)(-4/5))

=(7+24√3)/50.