求函数y=3sin(x+π/9)+5sin(x+4π/9)的最大值

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求函数y=3sin(x+π/9)+5sin(x+4π/9)的最大值求函数y=3sin(x+π/9)+5sin(x+4π/9)的最大值求函数y=3sin(x+π/9)+5sin(x+4π/9)的最大值y

求函数y=3sin(x+π/9)+5sin(x+4π/9)的最大值
求函数y=3sin(x+π/9)+5sin(x+4π/9)的最大值

求函数y=3sin(x+π/9)+5sin(x+4π/9)的最大值
y=3sin(x+π/9)+5sin(x+4π/9)
=3sin(x+π/9)+5sin(x+π/9+π/3)
=3sin(x+π/9)+5/2*sin(x+π/9)+(5√3)/2*cos(x+π/9)
=11/2*sin(x+π/9)+(5√3)/2*cos(x+π/9) (辅助角公式)
=7sin(x+π/9+θ)
故最大值是7