@Rouben Rostamian  You are right, I should've made the smalls steps you suggest.

As I interpret it now:

r(t) = cos(ωt) i + sin(ωt) j represents a circle, so r(t) = (a cos(ωt))i + (b sin(ωt))j will respresent a ellips, and the (ct)k makes the graph 'go up along the z-axis' with factor (ct) at each 'step'. 

Thanks!

@acer Thank you so much!

@Kitonum Thank you very much!!