Try with;

plot(k(x), x = -2 .. 2, thickness = 3)

It's works for me on Maple 15.

Regards.

To understand the problem could be useful a graph;

implicitplot([.4 = a*cos(8*b)+3, .2 = -a*sin(8*b)*b], a = -5 .. 5, b = -3 .. 3, axes = normal, color = [red, green], numpoints = 50000)

There is a lot of solutions!

Using "fsolve" command you can pick some of them (dependent on the initial guess or starting value)

solve({x1+2*x2-x4 = -1, 2*x1+x2-x3+3*x4 = 2, 3*x1+2*x2-2*x3+x4 = 1}, {x1, x2, x3, x4})