定义在R上的函数f(x)满足f(x+2)=f(x),当x∈[3,5]时f(x)=2-|x-4|,则()A.f(sinπ6)<f(cosπ6)B.f(sin1)>f(cos1)C.f(sin2π3)<f

题目简介

定义在R上的函数f(x)满足f(x+2)=f(x),当x∈[3,5]时f(x)=2-|x-4|,则()A.f(sinπ6)<f(cosπ6)B.f(sin1)>f(cos1)C.f(sin2π3)<f

题目详情

定义在R 上的函数f(x)满足f(x+2)=f(x),当x∈[3,5]时f(x)=2-|x-4|,则(  )
A.f(sin
π
6
)<f(cos
π
6
)
B.f(sin1)>f(cos1)
C.f(sin
3
)<f(cos
3
)
D.f(sin2)>f(cos2)
题型:单选题难度:偏易来源:不详

答案

∵f(x+2)=f(x),
∴函数f(x)是周期为2的周期函数,又当x∈[3,5]时f(x)=2-|x-4|,
∴当-1≤x≤1时,x+4∈[3,5],
∴f(x)=f(x+4)=2-|x|,
f(sinclass="stub"π
6
)=f(class="stub"1
2
)=class="stub"3
2
>2-
3
2
=f(cos  class="stub"π
6
)
,排除A,
f(sin1)=2-sin1<2-cos1=f(cos1)排除B,
f(sinclass="stub"2π
3
)=2-
3
2
<2-class="stub"1
2
=f(cosclass="stub"π
3
)=f(cos  class="stub"2π
3
)
,C正确;
f(sin2)=2-sin2<2-(-cos2)=f(cos2)排除D.
故选C.

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