已知函数 y=sinx^2+2sinxcosx+3cosx^2,

y=sinx^2+2sinxcosx+3cosx^2
=(sinx^2+cosx^2)+2sinxcosx+2cosx^2
=1+2sinxcosx+2cosx^2
=2sinxcosx+(2cosx^2-1)+2
=sin2x+cos2x+2
=√2sin(2x+π/4)+2
(1)函数的最小正周期2π/2=π
(2)函数在区间[-5π/8+kπ,-π/8+kπ](k∈Z)上是增函数
(3)可由Y=sinX的图象向右平移π/8,再横向压缩1/2,再纵向拉长
√2倍,再向上平移2的变换得出