Question

函数y=sin(x+α)(0≤α≤π)是R上的偶函数，则α=__

我知道答案,我想要过程

Answer 1

偶函数满足条件f(x)=f(-x)
函数y=sin(x+α)(0≤α≤π)是R上的偶函数
所以sin(x+α)=sin(-x+α)
sinxcosα+cosxsinα=sinαcosx-cosαsinx
化简得sinxcosα=0
即cosα=0
α=kπ+π/2
0≤α≤π
只有k=0时满足题意
所以α=π/2

Answer 2

函数y=sin(x+α)(0≤α≤π)是R上的偶函数得f(0)=1或-1
所以,sin(0+α)=1或-1又因为,0≤α≤π
所以,α=π/2

Answer 3

π/2