Question

将f(x)=2sinx(sinx+cosx)的图象设向量a(-π/4,-1)的方向移动,得到g(x)的图象

求g(x)解析式

Answer 1

f(x)=2sinx(sinx+cosx)
=2sin²x+2sixcosx
=2sin²x-1+sin2x+1
=sin2x-cos2x+1
=√2sin(2x-π/4)+1
图象按向量a(-π/4,-1)的方向移动
x'=x-π/4
y'=y-1
∴x=x'+π/4
y=y'+1
∴y'+1=√2sin(2(x'+π/4)-π/4)+1
y'=√2sin(2x'+π/2-π/4)
=√2sin(2x'+π/4)
g(x)=√2sin(2x+π/4)

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