已知偶函数f(x)在[-1,0]上为单调增函数,则()A.f(sinπ8)<f(cosπ8)B.f(sin1)>f(cos1)C.f(cos2)>f(sin2)D.f(cos7π12)<f(sin7π

题目简介

已知偶函数f(x)在[-1,0]上为单调增函数,则()A.f(sinπ8)<f(cosπ8)B.f(sin1)>f(cos1)C.f(cos2)>f(sin2)D.f(cos7π12)<f(sin7π

题目详情

已知偶函数f(x)在[-1,0]上为单调增函数,则(  )
A.f(sin
π
8
)<f(cos
π
8
)
B.f(sin1)>f(cos1)
C.f(cos2)>f(sin2)D.f(cos
12
)<f(sin
12
)
题型:单选题难度:中档来源:不详

答案

根据偶函数的性质,函数f(x)在[0,1]上为单调减函数.
对A,∵0<sinclass="stub"π
8
<cosclass="stub"π
8
,∴f(sinclass="stub"π
8
)>f(cosclass="stub"π
8
),A×;
对B,∵class="stub"π
4
<1<class="stub"π
2
,∴sin1>cos1>0,∴f(sin1)<f(cos1),B×;
对C,∵class="stub"π
2
<2<class="stub"3
4
π,∴sin2>-cos2>0,∴f(cos2)=f(-cos2)>f(sin2),∴③√;
对D,∵class="stub"π
2
class="stub"7π
12
class="stub"3
4
π,∴sinclass="stub"7π
12
>-cosclass="stub"7π
12
>0,∴f(cosclass="stub"7π
12
)=f(-cosclass="stub"7π
12
)>f(sinclass="stub"7π
12
),∴④×.
故选C

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