A y=sinx+cosx=√2sin(x+π/4),周期2π
B y=sinx -cosx=√2sin(x-π/4),周期2π
∴排出法就可以知道周期为π的是C,不过还是给你做一下好了.
C y= |sinx|+|cosx|
当x∈(2kπ,2kπ+π/2)时,sinx>0,cosx>0,∴y=√2sin(x+π/4)
当x∈(2kπ+π/2,2kπ+π)时,sinx>0,cosx<0,∴y=√2sin(x-π/4)
当x∈(2kπ+π,2kπ+3π/2)时,sinx<0,cosx<0,∴y=-√2sin(x+π/4)
当x∈(2kπ+3π/2,2kπ+2π)时,sinx<0,cosx>0,∴y=-√2sin(x-π/4)
∴由图像可知,周期为π