The trapped rainbow effect has been mostly found on tapered anisotropic metamaterials (MMs) made of low loss noble metals, such as gold, silver, etc. In this work, we demonstrate that an anisotropic MM waveguide made of high loss metal tungsten can also support the trapped rainbow effect similar to the noble metal based structure. We show theoretically that an array of tungsten/germanium anisotropic nano-cones placed on top of a reflective substrate can absorb light at the wavelength range from 0.3 micrometer to 9 micrometer with an average absorption efficiency approaching 98%. It is found that the excitation of multiple orders of slow-light resonant modes is responsible for the efficient absorption at wavelengths longer than 2 micrometer, and the anti-reflection effect of tapered lossy material gives rise to the near perfect absorption at shorter wavelengths. The absorption spectrum suffers a small dip at around 4.2 micrometer where the first order and second order slow-light modes get overlapped, but we can get rid of this dip if the absorption band edge at long wavelength range is reduced down to 5 micrometer. The parametrical study reflects that the absorption bandwidth is mainly determined by the filling ratio of tungsten as well as the bottom diameter of the nano-cones and the interaction between neighboring nano-cones is quite weak. Our proposal has some potential applications in the areas of solar energy harvesting and thermal emitters. ; Comment: 20 pages, 10 figures