sinx+siny=1/3 siny=1/3-sinxcos^2y=1-sin^2y=1-(1/3-sinx)^2sinx+cos^2y=sinx+1-(1/3-sinx)^2=-sin^2x+5/3sinx+8/9=-(sinx-5/6)^2+19/12sinx=5/6时,取最大值=19/12sinx=-2/3时,取最小值=-2/3