求下列函数的值域:(1)y=4-3sin(x-π/3) (2)y=cos^2x-sinx

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求下列函数的值域:(1)y=4-3sin(x-π/3) (2)y=cos^2x-sinx
求下列函数的值域:(1)y=4-3sin(x-π/3) (2)y=cos^2x-sinx

求下列函数的值域:(1)y=4-3sin(x-π/3) (2)y=cos^2x-sinx
(1)y=4-3sin(x-π/3)
sinx的值域为[-1,1],所以,4-3sin(x-π/3) 值域为[1,7]
(2)y=cos^2x-sinx =1-2sin^2x-sinx=-2(sin^2x+1/2sinx+1/16)+9/8
=-2(sinx-1/4)^2+9/8
sinx的值域为[-1,1],(sinx-1/4)^2值域为[0,25/16]
cos^2x-sinx 值域为[-2,9/8]

1,(1,7)
2,(-1,1)