函数f(x)=sin(x+fai)/3(fai∈[0,2π])是偶函数,则fai= A.π/2 B.2π/3 C.3π/2 D.5π3
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![函数f(x)=sin(x+fai)/3(fai∈[0,2π])是偶函数,则fai= A.π/2 B.2π/3 C.3π/2 D.5π3](/uploads/image/z/11294935-7-5.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28x%2Bfai%29%2F3%28fai%E2%88%88%5B0%2C2%CF%80%5D%EF%BC%89%E6%98%AF%E5%81%B6%E5%87%BD%E6%95%B0%2C%E5%88%99fai%3D+A.%CF%80%2F2+B.2%CF%80%2F3+C.3%CF%80%2F2+D.5%CF%803)
函数f(x)=sin(x+fai)/3(fai∈[0,2π])是偶函数,则fai= A.π/2 B.2π/3 C.3π/2 D.5π3
函数f(x)=sin(x+fai)/3(fai∈[0,2π])是偶函数,则fai= A.π/2 B.2π/3 C.3π/2 D.5π3
函数f(x)=sin(x+fai)/3(fai∈[0,2π])是偶函数,则fai= A.π/2 B.2π/3 C.3π/2 D.5π3
C,
(x+fai)/3=(x/3+pi/2)
可以化为cos形式
cos是偶函数
解选C
f(x)=sin(x+3π/2)/3
=[sinxcos3π/2+cosxsin3π/2]/3
=[sinx*0+cosx*(-1)]/3
=-cosx/3
即f(-x)=-cos(-x)/3=-cosx/3=f(x)
即y=f(x)是偶函数。