In the current International System of Units (SI), it is conventionally assumed that rad=1, thereby treating angle as a dimensionless quantity. However, this convention presents a conceptual problem because of the relation sr=rad², so that the fundamental physical distinction between solid angles and plane angles is blurred. In this paper, I revisited the nature of physical equations based on the principle of dimensional homogeneity and the mathematical properties of the dimensional analysis function, demonstrated that angle is a physical quantity possessing its own fundamental dimension which means angle must be treated as one of the base quantities. Furthermore, I showed that, from the perspective of dimensional analysis, the domain of trigonometric functions and the codomain of inverse trigonometric functions—being inherently numerical-value equations—must consist of θ=θ/rad when θ means angle. Finally, some well-known equations are reconsidered comprehensively for dimensional homogeneity.