y=3sinx+cos2x-4
=3sinx+(1-2sin^2 x)-4
=-2sin^2 x + 3sinx -3
=-2(sinx-3/4)^2 +(9/16-3)
=-2(sinx-3/4)^2 - 39/16.
-1≤sinx≤1,则可见y的最大值是 0 - 39/16 = - 39/16.
而关于sinx的函数y(sinx)=-2(sinx-3/4)^2 - 39/16 是顶点在上的二次函数,则在sinx取得端点值-1和1处之一能够取得最小值.
当sinx=-1时,y=-2-3-3=-8;
当sinx=1时,y=-2+3-3=-2;
-8
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