Several optical spectroscopy and imaging techniques have already proven their ability to identify different plastic types found in household waste. However, most common optical techniques feasible for plastic sorting, struggle to measure black plastic objects due to the high absorption at visible and near-infrared wavelengths. In this study, 12 black samples of nine different materials have been characterized with Fourier-transform infrared spectroscopy (FTIR), hyperspectral imaging, and terahertz time-domain spectroscopy (THz-TDS). While FTIR validated the plastic types of the samples, the hyperspectral camera using visible and near-infrared wavelengths was challenged to measure the samples. The THz-TDS technique was successfully able to measure the samples without direct sample contact under ambient conditions. From the recorded terahertz waveforms the refractive index and absorption coefficient are extracted for all samples in the range from 0.4 to 1.0 THz. Subsequently, the obtained values were projected onto a two-dimensional map to discriminate the materials using the classifiers k-Nearest Neighbours, Bayes, and Support Vector Machines. A classification accuracy equal to unity was obtained, which proves the ability of THz-TDS to discriminate common black plastics.