求y=cos^2x+2sinx-1/2的值域,X属于[π/6,5π/6]
问题描述:
求y=cos^2x+2sinx-1/2的值域,X属于[π/6,5π/6]
答
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...