This paper examines two approaches to determine power factor of the mechanical system. First approach is vector expression approach. This method is based on analogy of mechanical system and electrical system, especially focusing on phase characteristic of environment. Another approach is mathematical analysis approach. This method is based on power factor determination method focusing on active power and apparent power. Comparison suggests vector expression approach has advantage in simplicity, though it is only valid in pure cosine wave. Cosine wave with DC component and ramp velocity case is also analyzed to show how they differ from vector expression approach. Experiment and simulation results supports validity of analyses in this paper.