【三角函数值域】求y=cos^2x-2sinx,x∈[π/6,π/4]的值域

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【三角函数值域】求y=cos^2x-2sinx,x∈[π/6,π/4]的值域

【三角函数值域】求y=cos^2x-2sinx,x∈[π/6,π/4]的值域
【三角函数值域】求y=cos^2x-2sinx,x∈[π/6,π/4]的值域

【三角函数值域】求y=cos^2x-2sinx,x∈[π/6,π/4]的值域
y=cos^2x-2sinx=1-sin^2x-2sinx=-(sinx+1)^2+2
x∈[π/6,π/4],则1/2

y=1-sin^2x-2sinx
=-(sin^2x+2sinx+1)+2
=-(sinx+1)^2+2
x∈[π/6,π/4]
1/2<=sinx<=√2/2
3/2<=1+sinx<=1+√2/2
9/4<=(1+sinx)^2<=3/2+√2
1/2-√2<=2-(sinx+1)^2<=2-9/4=-1/4