若函数f(x)=Asin(wx+φ)+1(w>0,丨φ丨<π)对任意实数t,都有f(t+π/3)=f(-t+π/3),记g(x)=Acos(wx+φ)-1,则g(π/3)= ( ) A.-1/2 B.1/2 C.-1 D.1

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若函数f(x)=Asin(wx+φ)+1(w>0,丨φ丨<π)对任意实数t,都有f(t+π/3)=f(-t+π/3),记g(x)=Acos(wx+φ)-1,则g(π/3)= ( ) A.-1/2 B.1/2 C.-1 D.1
若函数f(x)=Asin(wx+φ)+1(w>0,丨φ丨<π)对任意实数t,
都有f(t+π/3)=f(-t+π/3),记g(x)=Acos(wx+φ)-1,则g(π/3)= ( )
A.-1/2 B.1/2 C.-1 D.1

若函数f(x)=Asin(wx+φ)+1(w>0,丨φ丨<π)对任意实数t,都有f(t+π/3)=f(-t+π/3),记g(x)=Acos(wx+φ)-1,则g(π/3)= ( ) A.-1/2 B.1/2 C.-1 D.1
对任意实数t,都有f(t+π/3)=f(-t+π/3)
∴x=π/3是f(x)的对称轴
∴w*π/3+φ=π/2+kπ,k∈Z
∴g(π/3)
=Acos(w*π/3+φ)-1
=Acos(π/2+kπ)-1
=0-1
=-1
选C