f(x)=loga[sin^2(x/2)-sin^4(x/2)],(a>0且a≠1),试确定函数的单调性

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/19 02:40:12
f(x)=loga[sin^2(x/2)-sin^4(x/2)],(a>0且a≠1),试确定函数的单调性
x)KӨдOO.̋3Ҩ71MX{: 옒s=:/O}pu}6uY-O{aMR>/;qEE"8PYV0?9"gD!a ak]IR@(_ 3I17T؀( F :ُ::^6LzWB(CY4&ΐZ$p4M 1U{

f(x)=loga[sin^2(x/2)-sin^4(x/2)],(a>0且a≠1),试确定函数的单调性
f(x)=loga[sin^2(x/2)-sin^4(x/2)],(a>0且a≠1),试确定函数的单调性

f(x)=loga[sin^2(x/2)-sin^4(x/2)],(a>0且a≠1),试确定函数的单调性
[sin^2(x/2)-sin^4(x/2)]
=sin^2(x/2)[1-sin^2(x/2)]
=[sin(x/2)cos(x/2)]^2
f(x)=loga[sin^2(x/2)-sin^4(x/2)]
=loga[sin(x/2)cos(x/2)]^2
=2loga[sin(x/2)cos(x/2)]
=2loga(0.5sinx)
02kπ2kπ+π/2a>1
2kπ+π/22kπ