函数f(x)=根号3sinxcosx-sin^2x-3/2在区间-派/2到0上的值域是
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f(x)=根号3/2 2sin x cos x+1/2 (1-2sin^2 x-1)-3/2
=根号3/2 sin 2x+1/2 cos 2x-1/2-3/2
=根号3/2 sin 2x+1/2 cos 2x-2
=sin 2x cos π/6+cos 2x sin π/腊稿6-2
=sin(2x+π/6)-2
因为-π/2<x<0,所以-5π/羡碧6<2x+π/6<π/6,
所以-1<sin(2x+π/6)<1/2
则 -3<sin(2x+π/6)-2<轮派孝-3/2
所以所求值域(-3,-3/2)
=根号3/2 sin 2x+1/2 cos 2x-1/2-3/2
=根号3/2 sin 2x+1/2 cos 2x-2
=sin 2x cos π/6+cos 2x sin π/腊稿6-2
=sin(2x+π/6)-2
因为-π/2<x<0,所以-5π/羡碧6<2x+π/6<π/6,
所以-1<sin(2x+π/6)<1/2
则 -3<sin(2x+π/6)-2<轮派孝-3/2
所以所求值域(-3,-3/2)
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