求y=cos^2x+2sinx-1/2的值域,X属于[π/6,5π/6]

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求y=cos^2x+2sinx-1/2的值域,X属于[π/6,5π/6]求y=cos^2x+2sinx-1/2的值域,X属于[π/6,5π/6]求y=cos^2x+2sinx-1/2的值域,X属于[π

求y=cos^2x+2sinx-1/2的值域,X属于[π/6,5π/6]
求y=cos^2x+2sinx-1/2的值域,X属于[π/6,5π/6]

求y=cos^2x+2sinx-1/2的值域,X属于[π/6,5π/6]
由y=cos²x+2sinx-1/2
=1-sin²x+2sinx-1/2
=-sin²x+2sinx+1/2
=-(sin²x-2sinx+1)+3/2
=-(sinx-1)²+3/2
∵x∈[π/6,5π/6],
∴当x=π/2时,有最大值:f(π/2)=3/2,
当x=π/6或x=5π/6,有最小值:f(π/6)=5/4.