(1)
1/2 sinx+√3/2 cosx=-a/2
∴sin(x+π/3)=-a/2
畫(huà)出sinx曲線可得若直線y=-a/2與正弦函數(shù)y=sin(x+π/3)在(0,2π)內(nèi)有兩個(gè)不同的交點(diǎn)需要滿足
-1＜-a/2＜√3/2或√3/2＜-a/2＜1
∴-2＜a＜2且a≠√3
(2)
兩點(diǎn)在y=sin(x+π/3)曲線上一定關(guān)于x=π/2 -π/3=π/6或x=3π/2 -π/3=7π/6對(duì)稱
∴兩點(diǎn)之和=π/3或7π/3