20.已知函数y=sinx的平方+sin2x+3cosx的平方

y=(sinx)^2+sin2x+3(cosx)^2
利用2倍角公式
=(1-cos2x)/2+sin2x+3(1+cos2x)/2
=cos2x+sin2x+2
=√2sin(2x+π/4)+2
1.取最小值时
sin(2x+π/4)=-1
2x+π/4=2kπ+3π/2
x=kπ+5π/8 k是整数
{x|x=kπ+5π/8,k是整数}
2. 2kπ+π/2≤2x+π/4≤2kπ+3π/2
kπ+π/8≤x≤kπ+5π/8
减区间是[kπ+π/8,kπ+5π/8]
3.由y=√2sin2x向左移π/8个单位变成y=√2(sin2x+π/4), 再向上平移2个单位得y=2+√2(sin2x+π/4)