Question

已知：sinx+siny=1/3,求sinx-(cosy)^2的最值?】

Answer 1

简单分析一下，答案如图所示

Answer 2

因为sinx+siny=1/3
故：sinx=1/3-siny,
因为-1≤sinx=1/3-siny≤1
故：-2/3≤siny≤4/3
故：-2/3≤siny≤1
故：sinx-cos²y
=1/3-siny-(1-sin²y)
= sin²y-siny-2/3
=(siny-1/2) ²-11/12
因为-2/3≤siny≤1
故：-11/12≤(siny-1/2) ²-11/12≤4/9
且：当siny=1/2时,(siny-1/2) ²-11/12=-11/12,即：sinx-cos²y有最小值,最小值为-11/12
当siny=-2/3时,(siny-1/2) ²-11/12=4/9,即：sinx-cos²y有最大值,最小值为4/9