1
f(x)=a·b=(2sin(wx)+cos(wx),2sin(wx)-cos(wx))·(sin(wx),cos(wx))
=(2sin(wx)+cos(wx))sin(wx)+(2sin(wx)-cos(wx))cos(wx)
=2sin(wx)^2+sin(wx)cos(wx)+2sin(wx)cos(wx)-cos(wx)^2
=3sin(2wx)/2+(1-cos(2wx))-(1+cos(2wx))/2
=3sin(2wx)/2-3cos(2wx)/2+1/2
=(3√2/2)sin(2wx-π/4)+1/2
f(x)圖像相鄰的兩條對(duì)稱軸的距離為π/2
即f(x)的最小正周期：T=π
即：2π/(2w)=π
即：w=1
即：f(x)=(3√2/2)sin(2x-π/4)+1/2
2
增區(qū)間：2x-π/4∈[2kπ-π/2,2kπ+π/2]
即：x∈[kπ-π/8,kπ+3π/8],k∈Z
減區(qū)間：2x-π/4∈[2kπ+π/2,2kπ+3π/2]
即：x∈[kπ+3π/8,kπ+7π/8],k∈Z
x∈[0,π/2],故當(dāng)k=0時(shí),增區(qū)間：x∈[0,3π/8]
減區(qū)間：x∈[3π/8,π/2]
x∈[0,π/2],2x-π/4∈[-π/4,3π/4]
sin(2x-π/4)∈[-√2/2,1]
故：(3√2/2)sin(2x-π/4)+1/2∈[-1,(3√2+1)/2]
即：fmax=(3√2+1)/2
fmin=-1