已知函数f(x)=Acos(ωx+φ)的图象如图所示,f(π2)=-23,则f(0)=()A.-23B.-12C.23D.12-数学

题目简介

已知函数f(x)=Acos(ωx+φ)的图象如图所示,f(π2)=-23,则f(0)=()A.-23B.-12C.23D.12-数学

题目详情

已知函数f(x)=Acos(ωx+φ)的图象如图所示,f(
π
2
)=-
2
3
,则f(0)=(  )
A.-
2
3
B.-
1
2
C.
2
3
D.
1
2
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题型:单选题难度:偏易来源:辽宁

答案

由题意可知,此函数的周期T=2(class="stub"11
12
π-class="stub"7
12
π)=class="stub"2π
3

class="stub"2π
ω
=class="stub"2π
3
,∴ω=3,f(x)=Acos(3x+φ).
f(class="stub"π
2
)=Acos(class="stub"3π
2
+φ)=Asinφ=-class="stub"2
3

又由题图可知f(class="stub"7π
12
)=Acos(3×class="stub"7π
12
+φ)=Acos(φ-class="stub"1
4
π)
=
2
2
(Acosφ+Asinφ)=0,
∴f(0)=Acosφ=class="stub"2
3

故选C.

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