已知函数

问题补充说明：已知函数f﹙x﹚=√3sin^2x+sinxcosx. ﹙1﹚求f﹙25π/6﹚的值; ﹙2﹚设 α∈ ﹙0,π﹚,f ﹙a/2﹚=1/4- ﹙√3﹚/2,求sinα 的值.

(1)f(x)=√3(sinx)^+sinxcosx

=sinx(√3s斗假查司里括先屋排inx+cosx)=2sinxsin(x+π/6),

f(来自25π/6)=2sin(25π/6)sin(25π/6+π/6)

=2sin(4π+π/360问答6)sin(4π+π/3)=2sin(π/6)sin(π/3)

=2×(1/2)×√3/2=√3/2

(2）f(α/2)=2sin(α/2)sin(α/2+π/6)=(√3/2)-(1/4),积化差得

cos(π/6)-cos(α+π/6)=(√3/2)-(1/4),∴cos(α+π/6)=1/4>0,

∴孙花弦广坚九结二如诉田sin(α+π/6)=√[1-(1/16)=√15/4,又α=(α+π/6)-(π/6),

∴sinα战曲间亚搞理师黑房要革=sin(α+π/6)院越训封自斗明呀cos(π/6)-cos(α+π/6)sin(π/6)

=(√15/4)×(√3/2)-(1/4)×(1/2)=(每话般资伟使观古组类振3√5-1)/8

说明:我改为f(α/2)=(√3/2)-(1/4)计算的.∵若f(α/2)=(1/4)-(√3/2),则可得cos(α+π/6)=√3-(1/4)>1,这是不可能的.

标签：已知,函数