y=2cos²x+sinx-1 x∈(-π/6,π/3) 求值域
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y=2cos²x+sinx-1 x∈(-π/6,π/3) 求值域
y=2cos²x+sinx-1 x∈(-π/6,π/3) 求值域
y=2cos²x+sinx-1 x∈(-π/6,π/3) 求值域
y=2cos²x+sinx-1
=2(1-sin²x)+sinx-1
=-2sin²x+sinx+1
=-2(sinx-1/4)²+9/8
x∈(-π/6,π/3)
sinx∈(-1/2,√3/2)
当 sinx=1/4时 有最大值为 9/8
当 sinx=-1/2时 有最小值为 0
所以值域为 [0,9/8]
y=2cos²x+sinx-1
y=2*(1-(sinx)^2)+sinx-1
=2-2(sinx)^2+sinx-1
=-2(sinx)^2+sinx+1
=-2(sinx-1/4)^2+9/8
-1/2