函数y=sin(θ-π/2)cos(θ+π/2),θ∈[0,2π/3]的最小值

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函数y=sin(θ-π/2)cos(θ+π/2),θ∈[0,2π/3]的最小值
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函数y=sin(θ-π/2)cos(θ+π/2),θ∈[0,2π/3]的最小值
函数y=sin(θ-π/2)cos(θ+π/2),θ∈[0,2π/3]的最小值

函数y=sin(θ-π/2)cos(θ+π/2),θ∈[0,2π/3]的最小值
y=sin(θ-π/2)cos(θ+π/2)
=-sin(π/2-θ)cos(π/2+θ)
=cosθsinθ
=(sin2θ)/2
θ∈[0,2π/3],2θ∈[0,4π/3],-√2/2≤sin2θ≤1
所以 -√2/4≤y≤1/2
则y最小值为-√2/4

可以化简为y=-1/2*sin(2θ)
则最小值为-1/2