Question

将函数sin=x的图像向右平移π/3,再将所得图像上各点的横坐标不变,纵坐标伸长到原来4倍,这样就得到函数f(x

Answer 1

解；
y=sinx
右移π/3个单位：y=sin(x-π/3)
纵坐标伸长为原来的4倍：f(x)=4sin(x-π/3)
g(x)=f(x)cosx+√3
=(4sinxcosπ/3-4cosxsinπ/3)cosx+√3
=(2sinx-2√3cosx)cosx+√3
=sin2x-2√3cos²x+√3
=sin2x-√3(2cos²x-1)
=sin2x-√3cos2x
=2sin(2x-π/3)
x∈[-π/12,θ]
2x∈[-π/6.2θ]
2x-π/3∈[-π/2,2θ-π/3]
∵g(x)最大值为2
∴当2x-π/2=π/2+2kπ时
g(x)取得最大值2
∴2θ-π/3>=π/2+2kπ
∴θ最小值为：
2θ-π/3=π/2
θ=5π/12