Question

函数y=3sin(x/3)+4cos(x/3)的最大值。请高手写出过程。

Answer 1

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]

Answer 2

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