The function f(x)=cosx has limited range between -1 and 1. Further its value is 0 at (2n+1)pi/2, where n is an integer and its value is 1 at x=2npi and is -1 at (2n+1)pi. The urve appears as follows
graph{cosx [-10, 10, -5, 5]}
But we have to draw the graph of f(x)=cos(x+pi/2). As cosine of any x is always between -1 and 1, value of cos(x+pi/2) will also be between -1 and 1.
The only difference that happens is that instead of x=0, as we have f(x)=cos(x+pi/2) it is at -pi/2 that f(x)=1. In fact, the entire graph of cosx will shift by pi/2 towards left.
This is called as phase shift.
and f(x) will be 0 at x=npi, will be 1 at x=(4n-1)pi/2 and will be -1 at x=(4n+1)pi/2.
The graph appears as shown below.
graph{cos(x+pi/2) [-10, 10, -5, 5]}
