y=3sin(2x+10)+5sin(2x+70)最大值

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y=3sin(2x+10)+5sin(2x+70)最大值
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y=3sin(2x+10)+5sin(2x+70)最大值
y=3sin(2x+10)+5sin(2x+70)最大值

y=3sin(2x+10)+5sin(2x+70)最大值
设t=2x+10,则
y=3sint + 5sin(t+60)
=3sint + 5sint*cos60 + 5cost*sin60
=5.5sint + (5√3/2)cost
=√(5.5^2+25*3/4)sin(t+α)
其中tanα=5.5/(5√3/2);因为x∈R,所以t+α∈R,所以sin(t+α)最大值为1
所以y的最大值为y=√(5.5^2+25*3/4)=7