I know this is really simple but I cant seem to figure it out:

Classify all critical points of f(x,y) = sin(x)cos(x)

I know that fx = cos(x)cos(y) and that fy = -sin(y)sin(x)

Then, the critical points are x = n*pi, y = pi/2 + k*pi OR x = pi/2 + k*pi, y = n* pi.

How do I go about classifying these? I see that for choosing n or k differently, I get alternating positive negative values in the hessian matrix.