t, theta = var('t, theta', domain='real')
x(t) = cosh(t)
z(t) = t
formula = (x(t)*cos(theta), x(t)*sin(theta), z(t))
parameters = ((t, -3, 3), (theta, -pi, pi))
surface = ParametrizedSurface3D(formula, parameters)
show(surface.plot(aspect_ratio=1, color='yellow')) #, viewer='threejs')