Periods of Sin and Cosine Graph

The graph of sin x is the same as the graph of cos (x+3π/2). So, why are their periods different?
Check the graphs at HTTPS://WWW.desmos.com/calculator

@SarmisthaNag both have the same period of 2π.

@omvaykul0 So, how are we supposed to know whether graph is of sin x or of cos(x+3π/2) ? Or are we gonna say that it could be either of them?

@SarmisthaNag both graphs will be the same. If you want to check then draw graph of cos x and shift it along the x axis by 3π/2 interval to the left.