We investigate the sensitivities of searches for exotic spin-dependent interactions between the polarized nuclear spins of $^3$He and the particles of unpolarized or polarized solid-state masses using the frequency method and the resonance method. In the frequency method, the spin-dependent interactions act as an effective static magnetic field, causing the frequency shift to the spin precession of $^{3}$He. In the resonance method, proposed by Arvanitaki and Geraci [Phys. Rev. Lett. 113, 161801 (2014)] for the significant improvement of the experimental sensitivities on the spin-dependent interactions, the mass movement is modulated at the Larmor frequency of $^3$He. This results in the modulating spin-dependent interactions inducing an effective oscillatory magnetic field, which can tilt the $^3$He spins, similarly as an oscillatory magnetic field in nuclear magnetic resonance. We estimate the sensitivities of the searches using a room-temperature $^3$He target for its extremely long relaxation time. New limits on the coupling strengths of the spin-dependent interactions can be set in the interaction length range below $10^{-1}$ m.
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