函数y=1/2 sin2x+sin^2x x属于R的值域是—rt
问题描述：
函数y=1/2 sin2x+sin^2x x属于R的值域是—
rt
答
f(x)=sin2x/2+sin^2x
=sin2x/2+(1-cos2x)/2
=sin2x/2-cos2x/2+1/2
=(sin2x+cos2x)/2+1/2
=根号2sin(2x+pi/4)/2+1/2
利用相关原则，已知sinx属于[-1，1]
f(x)将sinx伸长根号2/2倍，再向上平移1/2
所以f(x)值域[（-根号2+1）/2，（根号2+1）/2]
答
y=1/2sin2x+(1-cos2x)/2
=1/2(sin2x-cos2x)+1/2
=√2/2*(√2/2*sin2x+√2/2zos2x)+1/2
=√2/2*(sin2xzosπ/4+cos2xsinπ/4)+1/2
=√2/2*sin(2x+π/4)+1/2
-1