已知sinx+siny=1/3 ,求z=sinx-cos^2y得取值范围

已知sinx+siny=1/3则 z=sinx-cos^2y=1/3-siny-cos2y=1/3-siny-1+2sin^2y=2[sin^2y-0。5siny-(1/3)]=2(siny-1/4)^2-1/8-2/3=2(siny-1/4)^2-19/24因为-1≤siny≤1,则 -1-1/4=-5/4≤siny-1/4≤3/49/8≤2(siny-1/4)^2≤25/81/4≤2(siny-1/4)^2-19/24≤7/3即,1/4≤z≤7/3