cos((pi)x/2) can be evaluated easily for integer x. Let x=4n, where n is an integer, so we get cos(2n(pi))=1. If x=4n-1 we get (pi)x/2=2n(pi)-(pi)/2, so cos((pi)x/2)=cos(2n(pi))cos(-(pi)/2)+sin(2n(pi))sin((pi)/2)=1*0+0*1=0. If x=4n-2, the expression = -1; if x=4n-3, the expression = 0.
So we can plot the expression's zeroes, maxima and minima, and then we can look at non-integer values of x.
When x=0, 1, 2, 3, ... we have 1, 0, -1, 0, 1, 0, -1, 0, ... as outputs. In between we have a typical sine wave pattern oscillating between the extrema and cutting the axis as it dips and dives all the way from minus infinity to plus infinity.
You can either draw a graph to evaluate the expression or build a table. Because x is a variable there is no one single evaluation so you need to use a calculator to put in various values for x or refer to basic tables. You don't need to build a table or graph for every value of x because the expression values repeat: x=0 to 4 is the only range of x you need, because x=-8 to -4, -4 to 0, 0 to 4, 4 to 8, 8 to 12, etc., give you the same values of the expression.