A presentation of four different schemes of semiclassical or Wentzel-Kramers-Brillouin-type approximations to planar waveguides is given. Attention is paid to a recent proposal for mapping a general symmetric waveguide into the hyperbolic secant or symmetric Epstein profile by exploring the dispersion relation and the fundamental mode field. As a test, these approximations are compared with the series solution of the cladded-parabolic profile.