已知cos(α+5π/12)=1/3，且-π<α<-π/2，求下列格式的值

显示全部楼层 · 2010-7-19 20:23:48

已知cos(α+5π/12)=1/3，且-π<α<-π/2，求下列格式的值
(1)cos(π/12-α) (2)cos(7π/12-α)
(3)cos(α+17π/12)
要有过程！

千问 · 2010-7-19 20:23:48

-π<α<-π/2，-π+5π/12<α+5π/12<-π/2+5π/12-7π/12<α+5π/12<-π/12cos(α+5π/12)=1/3-π/2<α+5π/12<-π/12cos(π/12-α)=cos[(π/2-5π/12)-α] =cos[π/2-(5π/12+α)]=sin(5π/12+α)=-2√2/3cos(7π/12-α) =cos[(π-5π/12)-α]=cos[π-(5π/12+α)]=-cos(α+5π/12)=-1/3cos(α+17π/12)=cos(π+α+5π/12)=-cos(α+5π/12)=-1/3