函数y=Asin(wx+ )(-π/6,0)(7π/6,0)A=2最大值也是2求解析式
解析:∵y=Asin(wx+φ ),A=2
∴y=2sin(wx+φ )
∵过点(-π/6,0)(7π/6,0)(认为是相邻零点)
∴T/2=7π/6+π/6=4π/3==>T=8π/3==>w=2π/(8π/3)=3/4
∴y=2sin(3/4x+φ )==>y(-π/6)=2sin(-π/8+φ )=0
-π/8+φ=2kπ==>φ=2kπ+π/8
-π/8+φ=2kπ+π==>φ=2kπ+9π/8
∴y=2sin(3/4x+π/8 )或y=2sin(3/4x+9π/8 )