Question

根号下（5/4cos方α+3/2sin方α+（根号下3）/4 sin2α）怎么化简

就是化成y=Acos(wx+u)+B的形式

Answer 1

cos²α=1/2(1+cos2α)
sin²α=1/2(1-cos2α)

√（5/4cos²α+3/2sin²α+√3/4 sin2α）
=√[5/4*1/2(1+cos2α)+3/2*1/2(1-cos2α)+√3/4sin2α]
=√[5/8cos2α-3/4cos2α+11/8+√3/4sin2α]
=√[√3/4sin2α-1/8cos2α+11/8]
=√[1/8(2√3sin2α-cos2α)+11/8]
=√[√13/8(2√3/√13sin2α-1/√13cos2α)+11/8]
=√[√13/8sin(2α-φ)+11/8]

其中sinφ=√13/13,cosφ=2√39/13

Answer 2

答的真好呀，梅花出自苦寒来，童鞋你要努力呦