函数y=3sin(x/3)+4cos(x/3)的最大值.

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函数y=3sin(x/3)+4cos(x/3)的最大值.

函数y=3sin(x/3)+4cos(x/3)的最大值.
函数y=3sin(x/3)+4cos(x/3)的最大值.

函数y=3sin(x/3)+4cos(x/3)的最大值.
y=3sin(x/3)+4cos(x/3)
=5[(3/5)sin(x/3)+(4/5)cos(x/3)]
=5sin(x/3 + α ) (其中cosα=3/5,sinα=4/5)
∈[-5,5]

y=3sin(x/3)+4cos(x/3)
=5[3/5sin(x/3)+4/5cos(x/3)]
设cosθ=3/5(0<θ<π/2),则sinθ=4/5
y=5sin(x/3+θ)
则y的最大值为5