这道高中数学题怎么做，写详细一点，谢谢各路大神。。 70
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(1) f(x)=1-sin^2x+sinx+1
=-(sinx-1/2)^2+9/4
∵x∈[-π/6,2π/3]
∴sinx∈[-1/2,1]
sinx-1/2∈[-1,1/2]
-(sinx-1/2)^2∈[-1,-1/4]
-(sinx-1/2)^2+9/4∈[5/4,2]
值域：[5/4,2]
(2) x0∈[-π/6,π/3]
2x0+π/6∈[-π/6,0]
2sin(2x0+π/6)∈[-1,0]
-1+2a^2-a<=0
2(a-1/4)^2<=1+1/8
(a-1/4)^2<=9/16
-3/4=<a-1/4<=3/4
-1/2=<a<=1
或者0+2a^2-a<=0
2(a-1/4)^2<=1/8
(a-1/4)^2<=1/16
-1/4=<a-1/4<=1/4
0=<a<=1/2
a的取值范围：[0,1/2]
=-(sinx-1/2)^2+9/4
∵x∈[-π/6,2π/3]
∴sinx∈[-1/2,1]
sinx-1/2∈[-1,1/2]
-(sinx-1/2)^2∈[-1,-1/4]
-(sinx-1/2)^2+9/4∈[5/4,2]
值域：[5/4,2]
(2) x0∈[-π/6,π/3]
2x0+π/6∈[-π/6,0]
2sin(2x0+π/6)∈[-1,0]
-1+2a^2-a<=0
2(a-1/4)^2<=1+1/8
(a-1/4)^2<=9/16
-3/4=<a-1/4<=3/4
-1/2=<a<=1
或者0+2a^2-a<=0
2(a-1/4)^2<=1/8
(a-1/4)^2<=1/16
-1/4=<a-1/4<=1/4
0=<a<=1/2
a的取值范围：[0,1/2]
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