Question: Approximate a nonlinear DE for use in 3D graph

I need to plot [cos(v)*x(t), sin(v)*x(t), v] where x(t) is the solution to diff(x(t),t)=sqrt(1/(-x(t)^2+1)-1) I can use DEplot to show me an approximation of x(t), which is what I want, but I need to graph the afformentioned 3d plot. I am not having success with DEPlot3D, because I can't figure out how to plot it with the cosine and sine functions shown above. I would appreciate any help.
Please Wait...