Different functions, one trigonometric and another exponential, are used to plot the same symmetric graphic; therefore they are equivalent functions. The curve has six-fold symmetry. The trigonometric function is plotted in the Cartesian plane (red curve), and the exponential function is plotted in the complex plane (green curve).
Reference: F. A. Farris, "Wheels on Wheels on Wheels—Surprising Symmetry," Mathematics Magazine 69(3), 1996 pp. 185–189.