Understanding how atmospheric cosmic-rays are distributed on Earth is crucial for simulating cosmic-ray setups and detectors for rare-event detection. The accuracy and reliability of such simulations and experiments depend on obtaining this information. This study focuses on analyzing the impact of key parameters in the PARMA model on the angular distributions of terrestrial cosmic-ray nuclei. These parameters include geomagnetic cut-off rigidity, atmospheric depth and solar activity. Moreover, angular distributions of various particles, including protons, electrons, neutrons, and muons, were systematically calculated over relevant rigidities, solar modulations, and altitudes. For this purpose, the latest version of the Excel-based Program for calculating Atmospheric Cosmic-ray Spectrum EXPACS (v.4.13), which relies on updated experimental data, was used. The results of the calculations showed clear trends in the angular distributions of all cosmic-ray species as a function of the model parameters. These findings provide valuable insights into the dynamics of cosmic rays in our solar system. Moreover, they can contribute to developing more accurate models for predicting the distribution of cosmic rays on the Earth's surface.