(1)求y=2sin2x+2sinx-1的值域 (2)求y=3-2cos(2x+π/3),x∈[-π/3,π/6]的最值

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(1)求y=2sin2x+2sinx-1的值域 (2)求y=3-2cos(2x+π/3),x∈[-π/3,π/6]的最值

y=2sin²x+2sinx-1
= 2(sinx+1/2)^2-3/2
-1≤sinx≤1
-1/2≤sinx+1/2≤3/2
0≤(sinx+1/2)²≤9/4
-3/2≤(sinx+1/2)²≤3/4
值域【-3/2,3/4】
y=3-2cos(2x+π/3)
x∈[-π/3,π/6]
2x∈[-2π/3,π/3]
2x+π/3∈[-π/3,π]
2x+π/3=0时,有最小值3-2=1
2x+π/3=π时,有最大值3+2=5