for Y=cos(nX) the period is 2*pi/n

In your case it will be 2*pi/4 = pi/2

This means the cosine function will begin and end over the distance pi/2. Or if you like one wave of cosine will take the distance of pi/2 to complete.

As there is no implied horizontal translation then you can begin the cosine function at (0,1). For the domain [-pi/2, pi/2] you should have 4 cosine wavelengths, 2 either side of your y axis.