Using both the exact enumeration method (microcanonical transfer matrix) for small systems (up to 9×9 lattices) and the Wang-Landau Monte Carlo algorithm for large systems (up to 30×30 lattices), we obtain the exact and approximate densities of states g(M,E), as a function of magnetization M and exchange energy E, for the triangular-lattice Ising model in the presence of an external uniform magnetic field. The method for evaluating the exact density of states g(M,E) of the triangular-lattice Ising model is introduced for the first time. Based on the density of states g(M,E), we investigate the properties of the various thermodynamic quantities as a function of temperature T and magnetic field h and find the phase diagram of the Ising antiferromagnet in the magnetic field. In addition, the zero-temperature thermodynamic properties are studied by reference to the density of states at the corner or along the edge line on the magnetization-energy (ME) diagram.