y=sin(x+π/4)+sin2x的值域y=sin(x+π/4)+sin2x的值域
问题描述：
y=sin(x+π/4)+sin2x的值域
y=sin(x+π/4)+sin2x的值域
答
y=sin(x+π/4)+sin2x∵ sin(x+π/4)=√2/2(sinx+cosx)∴sin²(x+π/4)=1/2(sin²x+cos²x+2sinxcosx)=1/2(1+sin2x)∴sin2x=2sin²(x+π/4)-1令t= sin(x+π/4)∈[-√2,√2]∴y=2t²+t-1=2(t+1/4)...